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More on pseudo forces and merges

But there's no pseudo force in that situation either, so I'm not certain what your point is really.- ( User) WolfKeeper ( Talk) 17:37, 29 April 2008 (UTC)

And there's really 3 different meanings of the phrase, reactive, pseudo, everyday.- ( User) WolfKeeper ( Talk) 17:37, 29 April 2008 (UTC)

Wolfkeeper, there is only one centrifugal force. The reactive thing is a knock on effect in a collision. All you need to do is describe what centrifugal force is in simple terms and leave the readers to make up their own minds as to whether it is real or not. My opinion is that it is real because the centrifuge effect can be observed from every frame of reference.

Rotating frames of reference only cloud the issue. David Tombe ( talk) 17:56, 29 April 2008 (UTC)

Coriolis effect comes out of the same equation as the centrifugal effect. Are you seriously saying that that doesn't exist either? Better tell those cyclones and anticyclones to stop spinning. "Stop! Stop I say, David says you don't exist! Stop!"- ( User) WolfKeeper ( Talk) 18:28, 29 April 2008 (UTC)

Wolfkeeper,That was a complete misrepresentation of everything I have been saying. I am the one that has been saying that the effect in the atmosphere is real. The others, such as Rracecarr are the ones that have been saying that it is purely fictitious. You have been sitting on the fence saying that it is not quite fictitious. David Tombe ( talk) 20:07, 29 April 2008 (UTC)

David, we are describing the centrifugal force as it is described in reliable sources. And in these reliable sources, the centrifugal force and the Coriolis force are pseudo-forces, artifacts of inertia when describing motion in rotating frames. We do not have to convince you that you are wrong, or that your understanding of physics is incorrect. Nor do you have to convince us that we are wrong. The other editors have shown great patience in trying to explain the physics, but at the end of the day it doesn't matter whether you believe it or not. Wikipedia is based on reliable sources and verifiability, and all sources support the rotating frame, pseudo-force view of the centrifugal force. So either provide a reliable source for the statement that inertia is a force and that the centrifugal force is real and not pseudo, or it doesn't go in. Simple as that. -- FyzixFighter ( talk) 19:37, 29 April 2008 (UTC)

FyzixFighter, There is nothing in any of my edits which you have deleted that either criticizes the orthodox position on rotating coordinate frames or make the claim that centrifugal force is real.

You have been deleting edits which describe in simple terms exactly what centrifugal force is. It is an outward radial acceleration which occurs when an object moves in a curved path. David Tombe ( talk) 20:15, 29 April 2008 (UTC)

Source, please? -- FyzixFighter ( talk) 20:17, 29 April 2008 (UTC)

No FyzixFighter, I won't give you a source for that fundamental fact. Children learned it in the garden when they swung a bucket of water over their heads. You have simply shown yourself up here as nothing but a trouble maker. You have stormed in on a wikistalking mission and then decided to go and make accusations against me when I hit back. You are just a trouble maker. You are not here to improve the article at all. David Tombe ( talk) 20:46, 29 April 2008 (UTC)

From "Analytical Mechanics", Hand & Finch, pg 267 (1998) - "The last three terms on the right hand side above [the centrifugal force, the Coriolis force, and the Euler force] aren't real forces; they are purely kinematic consequences of the rotation of the body coordinates." -- FyzixFighter ( talk) 21:46, 29 April 2008 (UTC)

Wolfkeeper, you should merge the articles. Reactive centrifugal force is a knock on effect which occurs when something that is experiencing centrifugal force knocks against something else. It is not even covered in this article because you have turned cause and effect upside down. and it doesn't really need to be covered at all unless you might wish to write a section on it.

There is only one centrifugal force but there is an argument about whether it is real or fictitious. David Tombe ( talk) 12:35, 29 April 2008 (UTC)

David is correct, there is no fictious centrifugal force and your attempt to invent one to satisfy your confused notions of physics is just a fiction itself. 72.64.49.249 ( talk) 13:20, 29 April 2008 (UTC)

Leave things as they are: it is clear and clean. Brews ohare ( talk) 14:55, 3 May 2008 (UTC)

When a bucket of water is swung in circular motion, it induces a hydrostatic pressure in the water. That is an effect which is observed from all reference frames. It is absolute. It is quite wrong to state that centrifugal force is an effect which is only observed in rotating frames of reference.

The closest that you could get to making that statement true would be to say that this effect is called 'centrifugal force' when it is observed from a rotating frame of reference but when it is observed from an inertial frame, the modern tendency is to refer to this effect as having been caused by inertia.

This effect, whether we call it centrifugal force or inertia, is not the same as the situation which we are dealing with when we observe a stationary object from a rotating frame. In the latter case, there is no real effect. These two circular motion situations are every bit as different from each other as two important circular motions in electromagnetism that are connected with the Faraday paradox. When we move a charged particle tangentially in the equatorial plane of a magnetic field, we get an induced electromotive force. But when we rotate the magnet on its magnetic axis with the particle stationary, we only get the artificial circle as observed from the frame of the rotating magnet. Nobody has ever said that these two effects are the same. Likewise in mechanics. There are two different effects and only one of these effects is centrifugal force.

Hence, there should be one single article on centrifugal force. Reactive centrifugal force does not need to be mentioned as it is merely a knock on effect in collisions and contact pressure situations. It can however be mentioned in a section, if somebody so wishes it to be. But I hope they manage to get the action and reaction the right way around.

Now moving on to the maths. If you look at the derivation of the rotating frame equations, you will see that ω which refers to the angular velocity of the rotating frame also refers to the angular velocity of the particle. It is a simple vector triangle. The particle velocity is split into two components. In the limit, this becomes a tangential component connected with ω, and a radial component which comes into play for Coriolis purposes.

That's quite simply wrong. If you believe that, then I want you to point to the equation where that is assumed in a reliable reference source. All the derivations I have seen make no such assumption.- ( User) WolfKeeper ( Talk) 02:49, 1 May 2008 (UTC)

Hence, these equations only apply to co-rotation, and to real Coriolis force when the radial velocity is physically referenced to the rotating frame such as in the hydrodynamics of the atmosphere, which of course is why the cyclones are real and not merely apparent.

So how should we proceed with a wording which does not conflict with the textbooks?

Centrifugal force is a term used within a rotating frame of reference, and it applies to the outward radial force which acts on objects which are stationary within the rotating frame. This effect can be extended to all curved path motion.

In the inertial frame of reference, this effect is said to be caused by inertia. David Tombe ( talk) 09:23, 30 April 2008 (UTC)

Steve, you mention about a spin off article for reactive centrifugal force. Do you mean another page? Can it not be handled as a section near the end of a united centrifugal force article?

The so-called reactive centrifugal force seems to have caused the editors to overlook a more fundamental division of effects within what modern textbooks call centrifugal force. This division splits along similar lines as in the Faraday paradox.

There is a real effect which occurs in a centrifuge. That is a radial outward pressure associated with actual curved path motion.

There is a fictitious effect which is associated with a stationary object being viewed from a rotating frame.

Personally, I would only use the term centrifugal force to cover for the real effect. But if the textbooks blend the two together under one set of umbrella maths, then we need to specify these two scenarios as per the Bucket argument. We cannot overlook the physical difference on the ostensible grounds of a unifying maths. That would be like overlooking the difference between the time dependent aspect of the Lorentz force and the motion dependent aspect on the grounds that one single equation covers them all.

We must specify the hydrostatic pressure in the rotating bucket as one scenario, and the stars rotating across the sky as another scenario.

We can have an introduction which sticks to textbook terminologies. But we cannot make the blanket assertion that centrifugal force is fictitious. It is sometimes fictitious and sometimes real.

Editors here have devolved all the real stuff to 'reactive centrifugal force' and deemed the rest to be fictitious. That is not a correct division. There is real centrifugal force before any reactions occur at centrifuge walls. David Tombe ( talk) 18:16, 30 April 2008 (UTC)

Wolfkeeper, If you had read the new introduction, you would have seen that it unequivocally maintained the position that the centrifugal force applies to all objects. I disagree with that, but that is the official position.

You reverted me on the false grounds that I had alleged otherwise.

I haven't got a citation that would explicitly state that the coordinate transformation equations only apply to co-rotation. I can see it just by looking at the vector triangle in the derivation. The particle velocity is split into two components. The tangential velocity of the rotating frame becomes one of those components. Hence the two things are physically linked.

That's WP:Original Research. Go away and get a proper citation, and we'll add it to the article.- ( User) WolfKeeper ( Talk) 18:36, 1 May 2008 (UTC)

The introduction which I have put in now was carefully thought out to cover all aspects of the controversy.

Read it and think about it before you revert it. David Tombe ( talk) 06:19, 1 May 2008 (UTC)

"To the extent to which the object or fluid element co-rotates with the frame, a radial acceleration or a hydrostatic pressure is induced."

A radial acceleration is always induced everywhere in the rotating frame proportional to distance from the axis. It may or may not be balanced or enhanced by other (pseudo)forces, but it's not a matter of the extent of corotation.- ( User) WolfKeeper ( Talk) 06:21, 1 May 2008 (UTC)

No Wolfkeeper. A radial acceleration only occurs in co-rotation situations as does hydrostatic pressure. I know exactly what you are thinking, and I deliberately worded it to avoid that controversy.

Let's just say for the sake of argument that those equations do actually apply to all situations. Whether the forces are balanced or not, there will be no radial acceleration when the object is stationary in the inertial frame.

The wording was chosen to maintain accuracy and avoid controversy. And now you are just digging in. David Tombe ( talk) 06:27, 1 May 2008 (UTC)

Let's examine the existing introduction. This paragraph here,

In some cases, it is convenient to use a rotating reference frame, rather than an inertial reference frame. When this is desirable, coordinate transformations from the inertial reference frame can be applied.

However, to do this correctly, in the rotating reference frame, a centrifugal force must be applied in conjunction with a Coriolis force for the correct equation of motion to be calculated. The centrifugal force depends only on the position and mass of the object it applies to (and does not depend on its velocity), whereas the Coriolis force depends on the velocity and mass of the object but is independent of its position.

is just clutter.

And it says nothing about any of the real effects that would occur in a centrifuge. Neither does it clarify about not to get confused with centripetal force.

Yet you have nevetheless chosen to revert. Your decision was not based on physics arguments. David Tombe ( talk) 06:32, 1 May 2008 (UTC)

"To the extent to which the object or fluid element co-rotates with the frame, a radial acceleration or a hydrostatic pressure is induced." By definition, the actual pressure must be independent of the reference frame. We don't live in an Alice in Wonderland world where from one reference frame something implodes from pressure, but in another the same thing is intact.- ( User) WolfKeeper ( Talk) 06:47, 1 May 2008 (UTC)

Wolfkeeper, when we rotate a bucket of water, centrifugal force creates a hydrostatic pressure in the water. That is a reality and it only happens in the co-rotation scenario.

At the moment, you are in a state of denial for which there seems to be no cure.

No cure you say! Damn these eyes!- ( User) WolfKeeper ( Talk) 07:41, 1 May 2008 (UTC)

You are living in a fictitious world in which you want to pretend that a rotating bucket of water is exactly the same thing as a stationary bucket of water as when viewed from a rotating frame of reference.

They are not the same thing. It is a centrifugal force version of the Faraday paradox.

Oh... but the Faraday paradox is completely different.- ( User) WolfKeeper ( Talk) 07:41, 1 May 2008 (UTC)

I tried to compromise with you and retain the initial line that centrifugal force applies to all the objects.

But you seem to be offended at any suggestion at all that centrifugal force can have any element of reality about it.

You are in denial and you are trying to impose your 'fictitiousist' view of the world on everybody else.

I deliberately worded the article to compromise between the mathematical definition and the layman's understanding. You have reverted it to a version which is clearly ill though out, ommitts important facts, and contains alot of unnecessary clutter.

With my introduction, we won't even need a separate article for reactive centrifugal force. The division is a total mess. David Tombe ( talk) 07:17, 1 May 2008 (UTC)

I really have no idea what you're trying to do here. The wikipedia is not the place for your OR on rotational physics.- ( User) WolfKeeper ( Talk) 07:41, 1 May 2008 (UTC)

Sorry, but based on your performance and stated opinions so far, my policy from here on in is that any non trivial edits in any of these rotation articles by you are going to be reverted at the earliest opportunity unless you include references from reliable sources, and the reliable sources self-evidently agree with your text. It's really nothing personal though.- ( User) WolfKeeper ( Talk) 07:41, 1 May 2008 (UTC)

Wolfkeeper, You are in a state of denial. Hydrostatic pressure exists in a rotating bucket of water. That is not original research and it does not require a citation. If you check the wikipedia rules, you will see that no citations are needed for facts that are obvious.

You adhere to some strange view of the world in which everything is relative and that absolute facts such as hydrostatic pressure in a rotating bucket of water do not exist. You do not live in the real world.

I doubt if you ever thought of the Bucket argument before. And now that you have been made aware of it, you have calmly stated that you are going to ignore it.

You are not in a position to be editing articles on real physics. You have made an absolute shambles of these pages and for some reason, everybody seems to be too scared to stand up to you. David Tombe ( talk) 09:09, 1 May 2008 (UTC)

• Excellent*!!!!! <Maniacal laugh>- ( User) WolfKeeper ( Talk) 11:34, 27 May 2008 (UTC)

I've just sent a note to David regarding Wikipedia's Neutral Point of View policy and attribution, verifiability and reliable sources principles. I look forward to him providing suitable cites to support his contributions from now on. -- The Anome ( talk) 11:15, 1 May 2008 (UTC)

Anome, I'm still awaiting anybody to point out what aspect of that introduction that I wrote was not neutral. I expect that I'll be waiting a long time. When you point out the non-neutral sentences, then I'll supply citations. David Tombe ( talk) 12:40, 1 May 2008 (UTC)

David, the addition you made to the introduction concerning centrifuges is, by and large, correct. However, when you made the edit, you removed statements about the rotating frame of reference that were also correct. You haven't improved the article; indeed, it is now less complete than before. (' Fictitious' force in the sense used in classical mechanics does not mean 'imaginary' or 'nonexistent,' as you seem to believe. It's an unfortunate choice of word; but then, it's what is used. 'Inertial,' 'pseudo,' or 'd'Alembert' would be better in my opinion. Please read further down in the article where the semantics is explained. Plvekamp ( talk) 16:52, 1 May 2008 (UTC)

Reading this only reinforces the perception that Wikipedia is not a valid source for physics information. The perception of Wikipedia is that it is a source of misinformation, and not a source of correct information. The evident fact is that the editors are unwilling to work out a correct version which incorporates the valid criticism of their attempted edits. Mr Wolfkeeper evidently knows nothing, and denies an experimental fact known for thousands of years to be true. Management has now confirmed that course of action, and validated the view that Wikipedia is more about enforcing certain opinions than benefiting from the criticism of independent scholars and experts. Most physics experts I know consider this web site a joke. Wikipedia is a known bad source of information, due to its policy of copying from others without regard to the quality of the information being blindly repeated. I personally have found so many mistakes here that I dont even attempt to correct them. It is not worth the trouble, considering the editor's attitudes. Sorry, but I do not beleive anything you state regarding physics, since your editiors have shown they dont understand what they are doing. Wikipedia dosen't work, and its failure to take into consideration valid criticism only reinforces the bad information already found here. 72.84.69.81 ( talk) 17:20, 1 May 2008 (UTC)

Judging by this diff, David's most recent centrifuge-related edit has not only been kept, but integrated into the article. -- The Anome ( talk) 17:46, 1 May 2008 (UTC)

Wouldn't it be more accurate to say that centrifuges separate based on density? Mangoe ( talk) 20:00, 1 May 2008 (UTC)

Good point. How about "denser element" instead of "heavier particle?" Thus you include both fluid elements and particles in suspension. If anyone disagrees, go ahead and revert my edit and we can discuss. Plvekamp ( talk) 20:26, 1 May 2008 (UTC)

Mistakes in the wikipedia are inevitable and are always going to be there. However, if you can show that there is a mistake, with references to it, I will gladly help you to fix any problems that there may be. In terms of comprehensibility and scope this article is not perfect, and probably due to article size and other constraints few articles can ever be perfect, but we need it to be as minimally imperfect as possible.- ( User) WolfKeeper ( Talk) 21:28, 1 May 2008 (UTC)

Would it be appropriate to include the Euler force in the introduction, since the Coriolis is also included ? Or would angular acceleration of the reference frame be overly complicating the issue ? Plvekamp ( talk) 21:53, 1 May 2008 (UTC)

Personally, I think it would overcomplicate the introduction, the most common case is for uniformly rotating frames. It's also not mentioned elsewhere in the article, but I noticed it was missing from the 'see also' section and inserted it.- ( User) WolfKeeper ( Talk) 22:59, 1 May 2008 (UTC)

Good compromise. Thanks Plvekamp ( talk) 23:18, 1 May 2008 (UTC)

This edit war will only be resolved when there is an open realization of what the war is about. What is the undercurrent that is driving it? And after making yesterday's edits and watching the response, I can now tell you all exactly what it is about.

I inserted a clause in the introduction which drew attention to the fact that in co-rotation situations, we obtain an actual outward acceleration or an actual hydrostatic pressure. Somebody correctly altered that to 'pressure gradient'. That is what constructive collaborative editing is all about. Somebody else changed 'heavier' to 'more dense'. Very good. That's the right idea. Keep improving the matter and making it progressively more and more accurate.

Now unusually, for the first time, my edits were not completely erased. These key bits of information, rather than being completely erased, were moved to a section further down the page where scan readers are less likley to go.

Compare this to the excessive invasion of the first line with copious references to the term 'fictitious'.

Clearly we have a party here who are very keen to emphasize the word 'fictititious', and to hide any examples that might undermine the suitability of the term 'fictitious'.

As regards the original research which I keep getting accused of, I'm still waiting to have that pointed out.

Now at the moment, the introduction is still most unsatisfactory. But I'm going to leave the first line alone and try and tidy up the incoherent clutter below it.

A member of the public reading about centrifugal force wants to see examples. They don't want to read about transformation equations that might be used by scientists behind the scenes.

And we have no examples in the introduction. All we have is a very amateurish statement to the extent that the matter is confusing. That's the kind of thing that somebody who doesn't understand the issue would write.

I'm going to make a different edit later today. When it gets erased, as it almost certainly will be, then we can discuss why. And I guarantee that it will all come down to the fact that the ruling party do not like attention being brought to the fact that centrifugal force can have real effects. It is being sold in the first line as a 'fictitious' effect and that's the party line which it seems must be upheld at any cost. David Tombe ( talk) 08:29, 2 May 2008 (UTC)

David, thank you for making small, specific edits, and discussing them individually. No-one is denying the reality of these phenomena, or that, within the rotating reference frame, they can be explained in terms of a centrifugal force. As far as I can see, your objection seems to be that for you, labeling centrifugal force "fictitious" is equivalent to calling the phenomena which appear to be caused by centrifugal force fictitious. Perhaps "fictitious force" is an unfortunate name, but it is the most common term used to describe entities such as centrifugal force and the Coriolis force. If you object to the term "fictitious force", would you be happier with any of the other terms for such a force, such as " inertial force", " d'Alembert force", or " pseudoforce"? I also agree with you that coordinate transformation is the key to this, and a mathematical treatment is the only way to properly resolve the apparent paradox. -- The Anome ( talk) 09:26, 2 May 2008 (UTC)

Anome, the terminology has never been the main issue, although it's true that I do not like the term 'fictitious force', and I would indeed prefer the term 'inertial force'.

The main issue has been that any attempt to illustrate any semblance of reality surrounding centrifugal force is swiftly removed from the introduction.

Interestingly, one critic yesterday stated that he agreed with my insertions but then ciricized me for having removed other stuff.

So today, I will reinsert a single sentence and not delete the other stuff. I guarantee it will be swiftly deleted.

Then we can discuss why. David Tombe ( talk) 10:07, 2 May 2008 (UTC)

Anome, we can now see what has happened. PeR has come along within minutes and deleted it. It is also of interest to note that PeR earlier inserted another reference to back up the idea that the term fictitious force is in widespread use. But nobody is denying that.

This illustrates clearly that PeR is pushing a point of view. He is determined to go over the top to emphasize the 'fictitious' aspect of centrifugal force but to hide all references to everyday phenomena that indicate that there may be an element of reality to centrifugal force.

Now you can see clearly what is going on. We have identified the offending clause. David Tombe ( talk) 10:33, 2 May 2008 (UTC)

I think the question here is one of explanatory power. You can explain the same phenomena in two different ways; either in a rotating frame, using Newton's laws with the addition of pseudoforces, or at the cost of some extra difficulty in getting your thinking straight about the various forces involved, in an inertial frame, using Newton's laws alone. While the first explanation is in better agreement with our naive physical intutitions about how the world works, and the calculations are easier to do (to first order), mathematicians and physicists prefer the latter, because it is a simpler explanation that requires fewer conceptual entities and an overall simpler mathematical framework, even if it involves slightly more difficulty in making the necessary calculations. The centrifugal force is "fictitious" in the sense that everything in the system can be explained without it, by choosing an inertial frame of reference; but as far as I can see no-one is denying that the effects that can be ascribed to it in the rotating frame are real, regardless of which system of ideas you use to explain them. -- The Anome ( talk) 10:53, 2 May 2008 (UTC)

Anome, the lines which PeR removed related to an effect which is absolute and which doesn't depend on which frame of reference we view it from. That outward acceleration or the associated hydrostatic pressure can be viewed from all reference frames. It is not a fictitious effect. That's why PeR removed it. He doesn't want attention brought to absolute effects in conjunction with centrifugal force. David Tombe ( talk) 11:07, 2 May 2008 (UTC)

David, please keep an open mind to the notion that when many editors disagree with your edits, those editors could be right. No one is out to persecute you. This page is the proper place to discuss the article, but your "I'm right and they're trying to silence me" attitude is making it difficult. Plvekamp ( talk) 11:13, 2 May 2008 (UTC)

Plvekamp, it was actually you who reverted me this time. Did you have a reason to do so? PeR has now informed me that his reason was that I hadn't provided sources. But we don't need sources for facts that are not in dispute.

Are you disputing the facts that you erased? David Tombe ( talk) 13:22, 2 May 2008 (UTC)

We are now getting closer to the truth. Of course centrifugal force and centripetal force act as an action-reaction pair in every circular motion situation.

A web link to Donald E. Simanek saying the opposite is not acceptable.

Anybody who claims that centripetal force and centrifugal force do not form an action-reaction pair in circular motion needs to provide a citation from a peer reviewed journal or a reliable textbook. David Tombe ( talk) 14:00, 2 May 2008 (UTC)

David, it doesn't work that way: editors are responsible for providing cites for the statements they add to the article, not for providing cites refuting other statements added by other people, on the basis that those statements are self-evidently THE TRUTH unless refuted. You are entirely entitled, per the verifiability policy, to ask other editors for cites supporting their own additions to the article, but if you expect them to do so you should also act in the same way, by providing cites for your own additions, rather than asking them to refute yours. -- The Anome ( talk) 15:22, 2 May 2008 (UTC)

From "Facts on File Dictionary of Physics", pg 34 (1999) entry on centrifugal force:

"If a car is moving around a bend, for instance it is forced in a curved path by friction between the wheels and the road...It is sometimes said that the centrifugal force is 'reaction' to the centripetal force - this is not true. (The 'reaction' to the centripetal force is an outward push on the road surface.)"

Moreover, the centripetal force and the centrifugal (pseudo)force cannot be a action-reaction pair since they are acting on the same object. Action-reaction pairs have to act on different forces - the centripetal force from the wall of the centrifuge on the fluid is equal and opposite to (acts as an action-reaction pair with) the force from the fluid on the wall of the centrifuge. -- FyzixFighter ( talk) 15:47, 2 May 2008 (UTC)

FyzixFighter, The statement that you erased read,

When the wall of the centrifuge applies an inward acting centripetal force such as to prevent further radial acceleration, we will have an action-reaction pair.

The wall acts inwards on the object and the object acts outwards on the wall. That is an action-reaction pair. If you insist otherwsie then you are lying and trying to pull the wool over the eyes of the readers.

Reading your passage above, it is clear that your example doesn't apply to the situation in question, and that you have ended up contradicting yourself. Basically, you haven't got a clue what you are talking about. Your reversion was vandalism. David Tombe ( talk) 16:01, 2 May 2008 (UTC)

For the force by the object on the wall, see Reactive centrifugal force. However, the sentence that was removed seemed to say that the centrifugal force was acting on the object, and that it existed before there was any contact between the object and the wall. However, regardless of whether it was The Truth, FyzixFighter was in his rights to remove the statement, since it was disputed (by me, and presumably by the other editors who deleted it also) and unsupported by citations. -- PeR ( talk) 16:20, 2 May 2008 (UTC)

David, you forgot the sentence before that one,

In cases of co-rotation, the centrifugal force induces an actual radial acceleration on the object. This effect is observed in the centrifuge device.

So, in your edit, the centrifugal (pseudo)force acts outward on the object, and the wall also acts inward on the object. So both these are acting on the same object, they therefore cannot be an action-reaction pair. Moreover, from the article on Newton's laws of motion (in the "Newton's third law: law of reciprocal actions" section):

It is important to note that the action/reaction pair act on different objects and do not cancel each other out.

You wanted a cite that said they don't form a action-reaction pair, and I gave you one. So now it's your turn to provide a source supporting your views.

(and after the edit conflict) How does the citation not apply to the situation in question, and how did I contradict myself? -- FyzixFighter ( talk) 16:23, 2 May 2008 (UTC)

I can see this is going nowhere. Would you like to rewrite the textbooks as well as wikipedia, David ?? What the other editors are putting in the introduction agrees with the texts. Your edits don't. Please stop sabotaging everyone's efforts. The only statement you have contributed that has been agreed upon is the one example you included on the centrifuge, which was put in the applications section where it belongs. Plvekamp ( talk) 16:28, 2 May 2008 (UTC)

FyzixFighter and PeR, The sentence read,

When the wall of the centrifuge applies an inward acting centripetal force such as to prevent further radial acceleration, we will have an action-reaction pair.

The wall pushes inwards on the object and the object pushes outwards on the wall. That is an action-reaction pair. And your citation had nothing to do with this scenario. David Tombe ( talk) 16:30, 2 May 2008 (UTC)

Actually, the citation is exactly about this situation. Replace wall with road, and object with car and they are identical. The object pushing outwards on the wall is the reactive centrifugal force (which is addressed by the ending parenthetical in the citation). I had interpreted your original edit to imply that the inward force from the wall on the object forms an action-reaction pair with the centrifugal (pseudo)force acting on the object - this is not true. However, I do agree with your restatement above - "The wall pushes inwards on the object and the object pushes outwards on the wall. That is an action-reaction pair." This is accurate, but was not what your original edit implied. -- FyzixFighter ( talk) 16:41, 2 May 2008 (UTC)

FyzixFighter, would you then be willing to reinstate the clause, reworded to your own satisfaction? David Tombe ( talk) 17:06, 2 May 2008 (UTC)

If it were reworded to be in agreement with reliable sources, then yes I could support it. However, the clause (as I currently understand it) deals with a centripetal force and a reactive centrifugal force, and not the centrifugal force that this article discusses (ie, a force in the rotating frame acting on the object), and so I'm not sure it belongs in the intro. I could see it being added to the third paragraph to address the confusion between the centrifugal pseudoforce on the object and the reactive centrifugal force the object exerts. Propose a rewording of the clause, and we can start working on wording and placement. -- FyzixFighter ( talk) 17:25, 2 May 2008 (UTC)

FyzixFighter, the very fact that this article has segregated the knock on effect to a different page means that the whole situation is quite hopeless now. So let's forget about action-reaction pairs for now. Wolfkeeper has split the topic and so we are not even permitted to adopt an overview of the events which are taking place. I would actually combine the articles if I knew how to, unless maybe it is an administrator power only. the reactive centrifugal force article is rubbish. It's in an even worse mess than this one and I think everybody is just ignoring it now.

So let's go to the first part of the sentence which you erased. That part drew attention to the fact that things actually accelerate outwards radially when they are undergoing co-rotation. Why did you ersae that clause? David Tombe ( talk) 17:51, 2 May 2008 (UTC)

Ok, my problem with that clause is that in the stationary frame, there is no outward, radial acceleration. Looking at the example of a person in the car turning a corner. From the stationary frame, the person is moving in a straight line, as the car turns and moves underneath them. From the rotating frame, this looks like the person is accelerating outward, but this is an artifact of the coordinate transformation into the rotating frame, or, as one source has put it, it is a purely kinematic consequence from transforming into the rotating frame. -- FyzixFighter ( talk) 18:11, 2 May 2008 (UTC)

FyzixFighter, I thought that the whole introduction was about things as viewed from the rotating frame. And all I did was give an example of a situation where the radial acceleration was real. And you erased it.

Would you consider reinstating that sentence? David Tombe ( talk) 18:35, 2 May 2008 (UTC)

Plvekamp, I inserted a clause in the introduction which is true and which draws attention to the real aspects of centrifugal force. You are clearly one of the 'Fictitious Party' that feels uncomfortable about this.

Rather than continuing to merely state that I am wrong and delete my entries, can you please explain exactly what it is about the centrifuge effect that makes you feel so uncomfortable? David Tombe ( talk) 16:37, 2 May 2008 (UTC)

It doesn't work like that. The statements in the intro are cited in textbooks. You want something different there, the onus is on you to prove it with citations, which you have so far refused to do. I am completely comfortable with the centrifugal effect being due to inertia in the inertial frame, and centrifugal pseudoforce in the rotating frame. Plvekamp ( talk) 16:44, 2 May 2008 (UTC)

Plvecamp, Does a co-rotating object accelerate outwards or not? David Tombe ( talk) 17:11, 2 May 2008 (UTC)

From which frame of reference? This is an important distinction. And is that object under a constraint, such as the side of the car or the end of the test tube?

If it is free (object in car, particle at top of test tube not encountering resistance):

- From inertial frame: No acceleration, no force, moves in straight line (and approaches end while doing so)
- From rotating frame: Acceleration outward in accordance with centrifugal pseudoforce covered in this article

When it encounters restraint (door of car, particle encountering resistance or at end of test tube)

- From inertial frame: Centripetal force exerted by restraint on object, object accelerates radially inward
- From rotating frame: No acceleration, object is stationary if frame rotates at same speed as constraint

Plvekamp ( talk) 17:28, 2 May 2008 (UTC)

Plvekamp, when I say a radially outward acceleration, I don't need to specify a frame of reference. If somebody is sitting in a car that is driving in a circle, will they experience a radially outward acceleration that will cause them to slide to the side door? The answer is either yes or no. We don't need to mention the word 'fictitious' or 'pseudo'. David Tombe ( talk) 17:42, 2 May 2008 (UTC)

David, when your talking about what "a person sit in a car driving in a circle" experiences, you are implicitly specifying a frame of reference. Namely, what a person experiences can only be described in a co-moving frame. Such a frame is typically non-inertial and will thus contain psuedoforces (or however one wishes to call them) from the perspective of this observer/person these forces are very much real. As you state the person feels himself pushed towards the outward door. An other observer will understand this diffently. An observer from an inertial frame will see the person in the car being forced to move in a circle by force exerted on him by the car.( TimothyRias ( talk) 14:32, 5 May 2008 (UTC))

This is so outrageous - "I don't need to specify a frame of reference" - that I'm at a loss for words. That has to be the most naive statement you've uttered yet. If you actually believe that, then nearly all of mathematical physics is beyond your understanding. Plvekamp ( talk) 18:02, 2 May 2008 (UTC)

Plvecamp, your reply above has given you away. You are not genuine. You won't answer the question because the answer would expose a real outward radial acceleration. You live in a fictitious world of denial and you are a wikipedia vandal that the administration can't see through. David Tombe ( talk) 19:27, 2 May 2008 (UTC)

David, you seem to be telling people that "they are living in denial" quite frequently. [1] [2] [3] [4] Such statements are unproductive, and will only lead to an escalating degree of impoliteness in the discussion. I'd appreciate it if you in the future try to only comment on the content, and not on the contributor. Thank you. -- PeR ( talk) 20:21, 2 May 2008 (UTC)

A link to Simanek's site is quite acceptable. He is a physics professor, after all. Mangoe ( talk) 16:55, 2 May 2008 (UTC)

Thanks Mangoe. I'll bear that in mind for future citations. The author only needs to be a physics professor.

My own view is that Donald E. Simanek is badly wrong, and it seems that he is the source of misinformation that has been guiding this 'Fictitious Party' that are dominating these pages. David Tombe ( talk) 17:10, 2 May 2008 (UTC)

If you aren't a physicist, then frankly I'm not really all that interested in your challenge to Simanek et al. Never mind my own understanding of the matter; he has credentials, and as far as I can tell, you don't. Mangoe ( talk) 17:50, 2 May 2008 (UTC)

Who is this guy??? Please explain which link is the link you are talking about. When you write something you need to be clear about what you mean. —Preceding unsigned comment added by 72.84.70.6 ( talk) 20:55, 3 May 2008 (UTC)

Steve, we'll continue this in a new section. You left off at,

David, I'll respond assuming you meant in the inertial frame, since that appears from context to be what you're saying. The acceleration of a rotating object is radially inward in any system of coordinates for the inertial frame. Here's polar, for example: The expression for outward radial acceleration is (r double dot - r (theta dot)^2). r isn't changing, so r-double-dot is zero. Theta is changing, with theta-dot = v/r. So you get (0-r(v/r)^2)=-v^2/r acceleration in the outward radial direction, which corresponds to +v^2/r acceleration in the inward radial direction. Exactly the same result as you can derive with cartesian coordinates, or with any stationary coordinate system, or with no coordinate system at all! (See the article uniform circular motion for a coordinate-independent derivation.) If you don't understand this, I promise that you'll find a clear explanation in an intro college-level physics textbook. Please do this simple step now, not later. -- Steve ( talk) 16:32, 2 May 2008 (UTC)

Steve, I'm quite familiar with orbital theory concerning hyperbolas, parabolas, and ellipses. I've had to solve many a difficult problem in this field.

Let me begin with a very simple example. Consider an object high above the Earth that has got zero tangential speed. The only force acting will be gravity, radially downwards. The object will accelerate downwards and the acceleration due to gravity will be equal to r double dot.

Now consider a circular orbit. There will be an additional outward centrifugal force given by mv^2/r. In this case, r double dot will be equal to zero. There will be no net radial force or acceleration.

True. For once. There's no NET acceleration- the gravitational acceleration balances the centrifugal acceleration, and in the rotating frame of reference there is no coriolis force if there is no motion in that frame.- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

Good. But you are now in disagreement with Steve and FyzixFighter below. David Tombe ( talk) 07:00, 3 May 2008 (UTC)

In elliptical orbits there is a constant oscillation between whether the centrifugal force is greater or the gravity force is greater.

Yes, due to variations in coriolis and in centrifugal and gravity in the rotating frame you get an elliptical orbital motion with a focus at the stationary point with the same orbital period.- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

No Wolfkeeper. There is no Coriolis force involved in central orbital theory. Kepler's law of areal velocity gets rid of the tangential components where you find the Coriolis force term. David Tombe ( talk) 07:00, 3 May 2008 (UTC)

I'm afraid that isn't the case; the angular momentum is constant (i.e. areal velocity is constant), but not the angular velocity. The reference frame rotates at constant angular velocity while the body doesn't (higher angular velocity close in, lower further out).- ( User) WolfKeeper ( Talk) 07:32, 3 May 2008 (UTC)

If we consider an ellipse in polar coordinates, centered on the focus, and solve it, we end up with exactly two radial accelerations. There will be an inverse square law acceleration inwards, and a v^2/r acceleration outwards. Centrifugal force is a very real thing.

Now lets get to the point. Your problem with all this is that it contradicts the pet theory that is being pushed on these pages by the 'Fictitious Party'.

That theory is that when an object is at rest in the inertial frame, it will be seen to trace out a circular motion when viewed from a rotating frame. Your argument is that there is a net inward fictitious centripetal force which is the sum of an outward centrifugal force and an inward Coriolis force which is twice as strong.

You will agree that this is the pet theory that the 'Fictitious Party' are trying to promote on these pages. Indeed there was once an entire section devoted to this idea on these pages. It was considered to be much more important than examples of the real effects which your colleagues are currently at this very moment in time trying to hide.

Your theory is wrong to the backbone on a number of counts.

(1) The transformation equations for rotating frames, only apply to co-rotation. This is clear when we look at the derivation. The angular velocity term ω which is ostensibly the angular velocity of the rotating frame, is in fact tied in with the tangential velocity of the particle in question. This is clear by virtue of the fact that it is one of two components of the particle velocity.

I'm sorry, but this is simply wrong, and shows that you have not followed the derivation at fictitious force- it nowhere assumes corotation. Such a theory would be pretty useless in the real world in any case. If you start from falsehood, you can only end up at another falsehood.- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

Wolfkeeper, the derivation at fictitious force only begins after that stage. It begins by already assuming that we know where the ω X term came from. You need to go back further to see that the ω term relates to the tangential velocity of the particle in question. David Tombe ( talk) 07:06, 3 May 2008 (UTC)

No, it comes from the velocity increment you get on any particle whatsoever when you go from one reference frame to another which is rotating at speed w relative to the first frame. And this is completely general, it applies to all velocities of particles in the initial and final frames whether they corotate or not.- ( User) WolfKeeper ( Talk) 07:44, 3 May 2008 (UTC)

(2)In the limit, the v term then becomes the radial velocity. Hence there is no Coriolis force in the radial direction. The Coriolis force and the centrifugal force can never act in the same direction because they are two mutually perpendicular aspects of the same thing. Hence the idea that the Coriolis force could be producing an inward radial force is absolute nonsense.

Um. Why is there a coriolis force anyway? It comes out of the derivation for centrifugal force/acceleration. But if something is corotating then it doesn't move in the rotating frame of reference, so no coriolis force. Strangely, all these physicists keep talking about coriolis, and how it influences the weather on Earth's rotating surface, but you say it doesn't exist at all. Why do you think that is? Could all these weather men have got it wrong all this time and been waiting for the genius of David Tombe to point it out? That NOBODY had ever worked it out as well as you? That's a lot of very smart guys, and they each would have been famous if they had found a hole in the theory, they would have been well-motivated. Or could it be that your corotation idea is a complete red herring for your thinking?- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

Wolfkeeper, something can be co-rotating and moving radially in a rotating frame of reference. When that occurs, we get Coriolis force, unless of course the radial motion is the deflection associated with the centrifugal force.

Irrelevant, coriolis applies to non corotating orbjects. None of the objects in the atmosphere corotate. Your understanding of these pseudoforces only apply to uninteresting cases where these equations would be unnecessary.- ( User) WolfKeeper ( Talk) 08:01, 3 May 2008 (UTC)

You are totally misrepresenting me on that next point. If you go to the Coriolis force page, you will see that I am actually the one arguing that the Coriolis force exists in the weather, and that it is real. David Tombe ( talk) 07:00, 3 May 2008 (UTC)

Yes, but the coriolis force acts at 90 degrees to the *velocity*, not the radial velocity. That's why you get these nice largely circular patterns. Nothing in a swirling cyclone or anticyclone corotates with the Earth.- ( User) WolfKeeper ( Talk) 08:01, 3 May 2008 (UTC)

(3)Even if we ignore points (1) and (2), the final result comes out to be a net inward radial acceleration. That is not circular motion. Circular motion requires a net zero radial acceleration.

Careful here. Stationary motion or motion in a straight line requires a net zero radial acceleration. Movement in a circle requires a (psuedo)force to rotate the velocity vector. You know- Newton's second law? You may have heard of it.- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

Wolfkeeper, circular motion means a net zero radial acceleration. You already agreed with me above that in a circular gravity orbit, the centrifugal force cancels out with gravity. David Tombe ( talk) 07:00, 3 May 2008 (UTC)

Incidentally, it's trivial to show this. If you differentiate the motion of a particle at x=cos(theta*t), y=sin(theta*t) twice with respect to time, you get the net acceleration. You will find it to be precisely radial, and inward. It is NOT zero. That is true in rotating reference frames as well as inertial ones.- ( User) WolfKeeper ( Talk) 19:58, 2 May 2008 (UTC)

Wolfkeeper, nobody was disputing that in cartesian coordinates we only see the centripetal acceleration. But in your theory about the artificial circle, you are using polar coordinates. So why bother mentioning Cartesian coordinates? And why do so in connection with simple harmonic motion? David Tombe ( talk) 07:00, 3 May 2008 (UTC)

So the pet theory of the 'Fictitious Party' is wrong.

When an object is stationary, nothing happens. There is no centrifugal force. There is no hydrostatic pressure gradient induced in a bucket of water.

Those things only happen when the object co-rotates.

And at the moment, your colleagues are desperately trying to hide any references to situations involving co-rotation that result in real physical effects.

There is a group of them who are winning on numbers but who clearly haven't got the first clue about physics but seem to presume that they have.

I would have thought that you would have been intelligent enough to see right through all this, unless perhaps you have got some vested interest in playing along.

But it is all one big fraud. David Tombe ( talk) 17:37, 2 May 2008 (UTC)

David, all the three cases of the falling object, circular orbit and elliptical orbit can also be solved in terms of coordinates and forces measured in an inertial frame, and will give exactly the same results as those above without any need to consider pseudoforces. In general, converting to an inertial frame from a rotating frame generates the same physical solutions, but without the need for pseudoforces.

Given these two possible interpretations, physicists choose the inertial frame interpretation, with its simpler physical laws, following the principle of Occam's Razor. Centrifugal force and Coriolis force are not wrong, so much as unnecessary. There is nothing to stop you from sticking with the rotating frame/pseudoforce interpretation, and your equations will continue to produce with exactly the same physical solutions, hydrostatic pressure and all, as the inertial frame/no pseudoforce interpretation, but you will be making life unnecessarily difficult for yourself in solving all but the simplest problems.

Have you considered the possibility that your disagreement with everyone else editing this page, and their agreement with one another in their differing interpretation (which includes your interpretation as a special case using d'Alembert forces), might be because they are -- independently from one another -- correct in their conventional interpretation of the underlying physics, as opposed to there being an organized conspiracy by desperate, unintelligent people to suppress THE TRUTH, which is apparent only to you? -- The Anome ( talk) 18:30, 2 May 2008 (UTC) [Updated 18:52, 2 May 2008 (UTC)]

Anome, I knew that already. I know that coordinate transformations don't effect physical reality. So what's your point in relation to the point that I was making to Steve? David Tombe ( talk) 19:15, 2 May 2008 (UTC)

Please see above where David told me "I don't need to specify a frame of reference" when I asked him which frame he was referring to. Make your own conclusions. Plvekamp ( talk) 18:43, 2 May 2008 (UTC)

Plvecamp, if we are already talking about a radially outward motion, then we don't need to specify a coordinate frame. You haven't answered my question. Will the person in the circularly moving car experience a radilly outward acceleration towards the side door or not? It's a 'yes' or 'no'. There is no need to cloud the answer with reference frames, or words like 'fictitious' or 'pseudo'. David Tombe ( talk) 19:12, 2 May 2008 (UTC)

David, for some wierd reason you can't remember how my username is spelled. The answer depends completely on the frame of reference. From an inertial frame, the card door is accelerating toward the person. From a rotating frame, the person is accelerating toward the car door. Same physical result, different accelerations due to differing frames of reference. What's so difficult to understand ??? Sorry I'm sounding grumpy, but this argument is starting to get to me. Time for a break; if you have any more questions ask somebody else. I'm going to leave this topic for awhile and cool off. "I don't need to specify a frame...." AARRRGGGHHHH!!!!!!!!!! Plvekamp ( talk) 19:36, 2 May 2008 (UTC)

Alright, I think I might see where you're coming from, and why we may be disagreeing. A person in the car will naturally take the car as his reference frame. When the car turns, he will experience the centrifugal force outwards - as described in the car's reference frame. BUT he is observing this from inside the car, which is turning ! This is a rotating reference frame ! YES, he experiencing a radially outward acceleration ! This is due to his inertia - His body is trying to go in a straight line per Newton's First Law. But from the viewpoint of someone observing from outside the car (this is an inertial reference frame), the car is turning and the person will continue in a straight line until he encounters a centripetal force (car door). Note that in this ideal example we are ignoring car seat friction. And with that I'm really REALLY going to depart this topic for awhile. Plvekamp ( talk) 20:15, 2 May 2008 (UTC)

David, just because r double dot is zero does not mean that there is no radial acceleration, but let's walk through this slowly, so we can identify were you disagree. For a perfectly circular orbit in a stationary frame, using polar coordinates:

1. ${\displaystyle r(t)=r,\theta (t)={\frac {vt}{r}}}$ where r, the radius, and v, the tangential speed, are both constants
2. ${\displaystyle {\vec {r}}=r{\hat {r}}}$ is the position vector
3. ${\displaystyle {\dot {\vec {r}}}={\dot {r}}{\hat {r}}+r{\dot {\hat {r}}}=0+r{\dot {\theta }}{\hat {\theta }}=v{\hat {\theta }}}$ gives us the velocity vector
4. ${\displaystyle {\ddot {\vec {r}}}={\dot {v}}{\hat {\theta }}+v{\dot {\hat {\theta }}}=0+(-v{\dot {\theta }}{\hat {r}})=-{\frac {v^{2}}{r}}{\hat {r}}}$ gives us the acceleration vector

So even though r is a constant, the acceleration does have a radial component. Now where do you disagree. -- FyzixFighter ( talk) 18:44, 2 May 2008 (UTC)

FyzixFighter, in your number (3), why did you drop the radial velocity component r dot r hat?

OK. I see. You assumed that because we have a circular motion that we can drop r dot. But we can't drop anything until we have derived the full acceleration formula.

What you did was derive the acceleration purely from the velocity vector. This is quite legitimate but it doesn't specify a cordinate frame and so the result is a vω at right angles to the direction of motion. This is the parent quantity to both the Coriolis force and the centrifugal force.

Had you gone to the full acceleration expression, this term would have been expanded into mutually perpendicular components. The radial component is the centrifugal force and the tangential component is the Coriolis force.

In this situation, r double dot must be zero in a circular orbit because the centrifugal force outwards cancels with the gravitational force inwards. David Tombe ( talk) 18:52, 2 May 2008 (UTC)

By the way, I can also recommend prolonged contemplation of this animation. -- The Anome ( talk) 18:55, 2 May 2008 (UTC)

David:I dropped the r dot r hat part in (3) because r dot is zero (r being constant). -- FyzixFighter ( talk) 19:06, 2 May 2008 (UTC)

Yes, I saw that. We must have cross wired. See my full reply above. David Tombe ( talk) 19:07, 2 May 2008 (UTC)

This derivation is to show you that even in a stationary frame, using polar coordinates and not cartesian coordinates, then acceleration is radially inward and not zero. I did specify a coordinate frame at the very beginning, a stationary, non-rotating frame with polar coordinates. How can r dot be anything but zero. If the r, the distance, is constant than r dot is 0 and r double dot is 0. Basic calculus. Do you have a problem with (1) given that this is a stationary, non-rotating frame? But just for kicks, the whole thing, putting in zeros only at the end:

1. ${\displaystyle r(t)=r,\theta (t)={\frac {vt}{r}}}$ where r, the radius, and v, the tangential speed, are both constants
2. ${\displaystyle {\vec {r}}=r{\hat {r}}}$ is the position vector
3. ${\displaystyle {\dot {\vec {r}}}={\dot {r}}{\hat {r}}+r{\dot {\hat {r}}}={\dot {r}}{\hat {r}}+r{\dot {\theta }}{\hat {\theta }}={\dot {r}}{\hat {r}}+v{\hat {\theta }}}$ gives us the velocity vector
4. ${\displaystyle {\ddot {\vec {r}}}={\ddot {r}}{\hat {r}}+{\dot {r}}{\dot {\hat {r}}}+{\dot {v}}{\hat {\theta }}+v{\dot {\hat {\theta }}}={\ddot {r}}{\hat {r}}+{\dot {r}}{\dot {\theta }}{\hat {\theta }}+{\dot {v}}{\hat {\theta }}+(-v{\dot {\theta }}{\hat {r}})}$ gives us the acceleration vector

Now, from (1) r is constant which kills the first (r double dot=0)and second term(r dot=0), and the tangential speed, v, is constant which kills the third term. This again leaves us with just the fourth term, a radially inward acceleration for the stationary frame in polar coordinates. -- FyzixFighter ( talk) 19:46, 2 May 2008 (UTC)

FyzixFighter, before your equation (4) can have any meaning, we have to account for all the terms. Let's forget about the 'theta hat' terms because we are not interested in angular acceleration.

Now supposing the circular motion was a gravity orbit. Where do you see the inverse square law gravity term fitting into equation (4)? Does it go to the general acceleration term on the left hand side, or does it go to the r double dot term on the right hand side? David Tombe ( talk) 20:06, 2 May 2008 (UTC)

Account for the terms, as in give them names? Sorry, I don't see why we need to do this. This is a simple derivation with no hidden assumptions. All the assumptions I'm making are in (1) and in the statement that this is a stationary frame. Your argument, if I understood it correctly, is that in polar coordinates the radial acceleration for circular motion is zero. This derivation shows that you are wrong. The theta hat terms don't matter, not because we're not interested in angular acceleration, but because r dot is zero and v dot is zero. For circular motion in a stationary frame with polar coordinates, the acceleration in the tangential (theta hat) direction is zero and the acceleration in the radial (r hat) direction is non-zero.

The gravity, inverse square law question seems a bit non-sequitur. It's not there in (4) because (4) is just the general acceleration for polar coordinates in a non-rotating frame. If we were to combine (4) with Newton's 2nd law of motion (which requires a stationary frame) and Newton's law of gravity, then we would get the equations of motion, but the only terms appearing in the sum of forces would be gravity - no centrifugal force, no coriolis force. -- FyzixFighter ( talk) 20:36, 2 May 2008 (UTC)

In other words, David, acceleration is the second derivative of position. If you know the position as a function of time, then you know the acceleration by differentiating twice. If the position as a function of time happens to be "uniform circular motion", then this is a proof that the acceleration is v^2/r inward, as is well-known, and taught in every intro college physics course. Now the question arises, if an actual particle had this motion, what would be the forces on it? Well, force equals mass times acceleration, so you would get this motion if and only if there were a net, total inward force of mv^2/r. This force can come from gravity, for example, or from a string. Note that the force is not and cannot be "balanced out" by any other force -- if it were, then the net force would be zero, so the total acceleration would be zero, so the direction of the velocity wouldn't be changing, and it wouldn't be circular motion! Do you dispute Newton's second law? Or do you dispute the calculation of the acceleration of a uniformly-rotating point? :-P -- Steve ( talk) 22:32, 2 May 2008 (UTC)

Steve and FyzixFighter, it would be a help if the two of you discussed this together and appointed a spokesman to ask me the questions.

Equation (4) tells us nothing until we know exactly what scenario we are applying it to and what the forces involved are. I asked FyzixFighter were he wanted to put the gravity force if it were a circular gravity orbit, and I didn't get a clear response.

Lets then deal with an easier situation. Let's deal with a weight being swung around on the end of a string. We use the symbol T to represent the inward tension. Can you please present me with equation (4) as per this scenario, showing me where you have inserted the tension T. David Tombe ( talk) 06:45, 3 May 2008 (UTC)

Hang On! I think I now see the source of alot of the confusion. You have been assuming that the v^2/r term is centripetal force. In fact, this error is mirrored in your pages on Kepler's laws. I've copied a chunk here,

"So the position vector

${\displaystyle \mathbf {r} =r{\hat {\mathbf {r} }}}$

is differentiated twice to give the velocity vector and the acceleration vector

${\displaystyle {\dot {\mathbf {r} }}={\dot {r}}{\hat {\mathbf {r} }}+r{\dot {\hat {\mathbf {r} }}}={\dot {r}}{\hat {\mathbf {r} }}+r{\dot {\theta }}{\hat {\boldsymbol {\theta }}},}$

${\displaystyle {\ddot {\mathbf {r} }}=({\ddot {r}}{\hat {\mathbf {r} }}+{\dot {r}}{\dot {\hat {\mathbf {r} }}})+({\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}+r{\ddot {\theta }}{\hat {\boldsymbol {\theta }}}+r{\dot {\theta }}{\dot {\hat {\boldsymbol {\theta }}}})=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}.}$

Note that for constant distance, ${\displaystyle \ r}$, the planet is subject to the centripetal acceleration, ${\displaystyle r{\dot {\theta }}^{2}}$, and for constant angular speed, ${\displaystyle {\dot {\theta }}}$, the planet is subject to the coriolis acceleration, ${\displaystyle 2{\dot {r}}{\dot {\theta }}}$.

Inserting the acceleration vector into Newton's laws, and dividing by m, gives the vector equation of motion

${\displaystyle ({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}=-GMr^{-2}{\hat {\mathbf {r} }}}$ "

This maths is all correct but he has wrongly referred to the centrifugal force term as the centripetal force. How could it be the centripetal force when it was derived from a parent term 'v times ω' of which the other component is the Coriolis force?

This seems to be a common error. The v^2/r term is unequivocally the centrifugal force term and in the full orbital equation (radial component), the centrifugal force outwards cancels with the gravitational force inwards in circular orbits.

The term can't possibly mean centripetal force because it is a general equation for acceleration which doesn't assume any particular kind of motion. It would certainly not incorporate centripetal force as a matter of course. The fact that the mutually perpendicular component of it is Coriolis force means that it undoubtedly refers to centrifugal force. David Tombe ( talk) 10:21, 3 May 2008 (UTC)

Nope. He has correctly referred to centripetal force as centripetal force. One way you can tell is that it's pointing inward, whereas centrifugal force can only point outward.

Also, note that the auther correctly says it's "coriolis acceleration", not coriolis force. The acceleration is r-dot*theta-dot, while the force that causes this acceleration is unspecified. -- Steve ( talk) 01:03, 4 May 2008 (UTC)

Steve, I'm going to ignore the issue of whether we talk about force or acceleration. We are talking about inertial forces here so it is quite irrelevant.

Now can we get to the key point. You are quite wrong in thinking that the v^2/r term is centripetal force. How could it be? How would a general expression for acceleration suddenly produce a centripetal term in conjunction with a Coriolis term? The parent inertial term vXω expands in two mutaully perpendicular components in polar coordinates. One is the Coriolis term and the other is the centrifugal term. In fact it is quite ridiculous to think that it could possibly be referring to the centripetal force.

Let's consider how that equation is used in orbital theory. The term that you think is a centripetal term is brought over to the left hand side to join the gravity expression. Hence gravity will have a negative sign and the term that you think is the centripetal term will have a positive sign. on the right hand side, we have r double dot.

So we have a second order differential equation in r.

If r double dot is zero, then the gravitational force inwards is exactly cancelled by the centrifugal force outwards.

If you are correct, it would imply that centripetal force is something that occurs naturally. That is not so. The gravitational force IS the centripetal force in this situation, and the v^2/r term is the centrifugal force. David Tombe ( talk) 03:22, 4 May 2008 (UTC)

Trying to find the disagreement

David, I think I've come to understand a key yet subtle point of disagreement. This is an honest attempt to understand how you understand the physics; I think we might be disagreeing on how we define radial acceleration. So let me set the stage. This is a stationary frame described by polar coordinates. We have an object move in some arbitrary fasion in this frame, and whose position is defined by the coordinates ${\displaystyle r(t)}$ and ${\displaystyle \theta (t)}$. In this case, what is the proper expression for the radial acceleration, defining the radial acceleration as ${\displaystyle a_{r}={\ddot {\vec {r}}}\cdot {\hat {r}}}$:

1. ${\displaystyle a_{r}={\ddot {r}}}$
2. ${\displaystyle a_{r}={\ddot {r}}-r{\dot {\theta }}^{2}}$

Or do you disagree that the radial acceleration should even be defined as ${\displaystyle a_{r}={\ddot {\vec {r}}}\cdot {\hat {r}}}$? -- FyzixFighter ( talk) 04:41, 4 May 2008 (UTC)

FyzixFighter,

1. ${\displaystyle a_{r}={\ddot {r}}-r{\dot {\theta }}^{2}}$

is the correct expression for radial acceleration. The signs can however be confusing and so it is important to match it all up correctly with the physics. Remember, the signs in the above expression are only a result of vector calculus notation.

Hence when we set up a differential equation for a gravity orbit, we have,

-GM/r^2 + v^2/r = r double dot

In other words, in a circular orbit, r double dot is zero, therefore the inward gravity cancels with the outward centrifugal force.

More generally in elliptical orbits, the two alternate between which is the greater at any point in time.

In the artificial circle which is the subject of this controversy, r double dot will also have to be zero. but since the net force is not zero, then we have a problem.

I can assure you that when we differentiate the polar equation for a conic section (hyperbola, ellipse, parabola) in order to obtain the acceleration, that the final result will come out to be, not only an inverse square law inwards, but also a v^2/r acceleration outwards. David Tombe ( talk) 06:13, 4 May 2008 (UTC)

Ah, and here's where we disagree. You can't just pull whatever terms you like to the other side and suddenly call it a force. If we instead pull over the r double dot term to the left hand side of the equation, can we call that a force, too? At a simplistic level, in physics a force is whatever appears on the left hand side of F_net=m*a. In the case of the gravity you bring up, the instant you pull the m*v^2/r term over to the left hand side, the right hand side is no longer the acceleration. And once the acceleration label no longer applies to the right hand side, the label of force no longer applies to the left hand side; it's just a differential equation then. It seems to me that this is a key point of disagreement; you can't rearrange the differential equation, moving terms from one side to the other and then reapply the original physics labels. Physics doesn't work that way. -- FyzixFighter ( talk) 06:51, 4 May 2008 (UTC)

FyzixFighter, I'm sorry but you're very badly mistaken here. The equation that I wrote out is the central force orbital equation. That is the equation that is used to solve central force orbital problems. I solved many a complex problem using that equation.

The equation which you have used is a general acceleration equation derived from a position vector using vector calculus theorems and notation. Whereby I have always been impressed by the amount of information that this equation reveals, we can not allow a quibble about terminologies to alter the reality of the final central force orbital equation.

Your equation effectively exposes the fact that centrifugal force is inherent in straight line motion as viewed from polar coordinates. In fact, I ought to draw the attention of Brews to that point.

But there is no further argument regarding the form of the orbital equation. One side contains a second order time derivative of the radial distance and the other side contains an inward gravity force and an outward centrifugal force. You can call that second order time derivative whatever name you like. But in circular orbits, it will be zero.

And if you try messing around with the signs in the orbital equation, you will no longer have the orbital equation. If you want a conic solution, then that is the equation. David Tombe ( talk) 08:56, 4 May 2008 (UTC)

Plvekamp has finally responded,

From a rotating frame, the person is accelerating toward the car door.

Now the whole introduction is about centrifugal force which it claims is a force only ever viewed from a rotating frame.

I added a line saying that in situations of co-rotation, an object accelerates radially outwards.

Plvekamp erased this sentence on the specious grounds that this true fact didn't agree with the references.

What references was he talking about? Was he referring to all the references that were wheeled in to enforce the fact that the term 'fictitious' is widely used?

So can we conclude that Plvekamp sacrificed reality in order to comply with the references?

If a centrifuge proves to us that centrifugal force is a real and absolute effect, but the references tell us that this shouldn't be so because the force is question is only a fictitious force, then rather than question the references, we should be better to erase the sentences that draw attention to these inconvenient truths.

Plvekamp, it's about time that you opened your eyes a bit to what's going on in the world around you. David Tombe ( talk) 20:17, 2 May 2008 (UTC)

I will no longer respond to your goading, David. I have tried to civilly respond, and you have continually misunderstood my answers. Nowhere have I said that centrifuges don't work or that car passengers don't experience centrifugal force in a turning car. These phenomena are entirely explicable by inertia. I'm leaving it to others to explain the physics to you. Plvekamp ( talk) 20:46, 2 May 2008 (UTC)

If you weren't denying those phenomena, then why did you erase mentions of them in the introduction? David Tombe ( talk) 06:27, 3 May 2008 (UTC)

I will no longer respond to your goading, David. Plvekamp ( talk) 12:12, 3 May 2008 (UTC)

David, is there any conceivable argument that might convince you that you are wrong, or are you simply committed, as is suggested by your most recent response above, to promulgating the WP:TRUTH as you see it?

The reason everyone else in this discussion appears to disagree with you, whilst all agreeing with one another, is that they are describing the apparent phenomenon of "centrifugal force" in rotating non-inertial frames in terms of inertial effects within standard Newtonian physics. This has been the standard physical interpretation of this phenomenon for several centuries, and is not likely to change. On reviewing this very lengthy discussion, I can see that this has been explained to you over and over in many different ways, carefully and politely, by numerous different people, with only you taking the dissenting position.

You are unlikely to succeed in ever getting your views represented in the article if you continue in this way. Here's why.

Wikipedia is a tertiary source; it summarizes the information in secondary sources, such as peer-reviewed scientific papers, physics textbooks, and other texts written by qualified physicists. It is not a mechanism for determining the WP:TRUTH; we accept that people disagree about just about everything, and we try to reflect this in our articles. For this reason, we have a set of ground rules for editing here which explicitly try to avoid determining truth here on Wikipedia, relying instead, wherever there is controversy, on restricting ourselves to opinions which can be attributed to external, verifiable, reliable sources.

If you want to change the article, and have your changes kept, you must, like every other editor here, abide by Wikipedia's basic ground rules, namely

• Adhering to a Neutral point of view whilst avoiding giving fringe views undue weight.
• Attributability
• Verifiability
• Reliable sources
• No original research

Furthermore, we have another requirement: that editors conduct themselves according to our civility policy. Statements that imply that other editors are acting in bad faith, lack intelligence, or are conspiring against you, go against that policy. Repeated breaches of the civility policy may result in accounts being blocked from editing.

Unfortunately, a personal conviction, no matter how strong or sincere, that your views are the WP:TRUTH does not override these policies and guidelines. -- The Anome ( talk) 21:53, 2 May 2008 (UTC)

Anome, the argument is not over yet, so it is far too early to be deciding who is right and who is wrong. There are still a number of key issues to be highlighted.

And as regards this statement by you "they are describing the apparent phenomenon of "centrifugal force" in rotating non-inertial frames", the evidence is quite to the contrary. Yesterday, I was the one who put such entries into the introduction, and they were swiftly erased.

On the issue of politeness, you very much seem to be overlooking the responses which I received from some of your editors when I first began editing this page. David Tombe ( talk) 06:34, 3 May 2008 (UTC)

David, please re-read what I wrote above. It's not about who is "right" or who is "wrong": where there is controversy, and agreement cannot be reached through argumentation, Wikipedia's policies require content disputes are ultimately decided by applying the principles I listed above. If you want to provide "evidence to the contrary", you must provide citations to attributable, reliable, verifiable sources that directly support your statements; WP:original research and synthetic arguments are not suitable alternatives to this.

Unless you can work within Wikipedia's rules, the "argument" is irrelevant, and has been for some time; no amount of repetition of your position in ways that do not follow Wikipedia's content polices will make Wikipedia's policies adapt to your desires. If you do not want to abide by Wikipedia's policies, you might want to consider choosing another forum for your contributions. -- The Anome ( talk) 12:27, 3 May 2008 (UTC) [Updated 12:46, 3 May 2008 (UTC)]

Anome, you know perfectly well that the edits that I made yesterday were not about ideas that are contrary of current theory. I drew attention to the actual acceleration that occurs outwards when an object co-rotates with a rotating frame. An example would be a passenger in a car getting swung to the side door as a car goes round a corner.

You know fine well that that was not a controversial sentence. You are misrepresenting the situation by continuing to imply that I was trying to insert controversial clauses into the article.

Plvekamp, PeR, and FyzixFighter removed that sentence because they are uncomfortable with the truths inherent in it. Their actions were essentially vandalism which you could have prevented but you chose not to do so. David Tombe ( talk) 12:39, 3 May 2008 (UTC)

David, please provide a cite to a reliable, verifiable, attributable source that supports your sentence: if you can do so, we can move forward. Otherwise, you are doomed to repeat this cycle over and over. If what you say is common knowledge, it should be easy to find such a reference. Even if it is merely a significant fringe position, it should still be possible to find a cite. If you can't find a cite, you might want to consider the possibility that your statement represents a fringe position without significant support. -- The Anome ( talk) 12:46, 3 May 2008 (UTC)

Anome, I'm not going to bother. That wasn't the issue. I have no intention of going to search for a citation for such a trivial and undisputed fact. It wasn't erased because there was no citation. That was just the cover story. It was erased for other reasons, and the point was proved.

By the way, I am watching your efforts to re-word the introduction. Note what Woodstone says over on the Coriolis force talk page.

There seems to be a school of thought that is saying that the term fictitious actually means that it refers to a mathematical term which comes into effect only in the accelerated frame (in this case, the rotating frame) as an alternative way of describing real effects.

I don't think that that is the universal interpretation of the term fictitious. I think you will find that some of the editors here will try and slowly but surely graft it back to the extent that it literally means that the effects can only be viewed in the rotating frame.

If what you are saying is true, RRacecarr and PeR wouldn't have cocnsistently reverted my removal of the word 'apparent' on the Coriolis page.

I would perhaps tend to agree with your amendments if I am interpreting you correctly. You are saying that these effects are real but best dealt with mathematically by what we term 'fictitious forces'. If that is so, I think that you will also agree with me that the term 'inertial force' is infinitely superior. David Tombe ( talk) 15:28, 3 May 2008 (UTC)

For what it's worth, David, I completely agree with your last two sentences. One sentence agrees with the explanations in current textbooks, in relation to rotating reference frames. The other sentence is a purely personal preference in terminology, which we also share. Having said that, I still insist that statements you provide in the article be backed up by citations per Wikipedia policy. I will do the same. Plvekamp ( talk) 16:43, 3 May 2008 (UTC)

PlveKamp, I think that the big problem that we are up against is that the modern textbooks are pushing these mathematical transformation equations in a way which disguises a very important difference between two completely different situations. These two different situations are described in the famous Bucket argument.

My natural inclination would be to view centrifugal force as a convective force. In other words it is a force which comes into existence at right angles to the direction of motion of a particle moving in a curved path. And that the effects, which are now described to be real, in the introduction are only effects which have come into existence BECAUSE the object is engaged in a curved path motion.

At the moment, the introduction is now admitting to real effects. It was never actually an issue in the edit war about whether or not these real effects could be explained in different ways in different frames.

Initially, I was arguing against a party which were adamant that these effects were entirely fictitious and could only be viewed in the rotating frame.

Finally by pushing the issue of the centrifuge which clearly disproves such a fictitious outlook, the reality of these effects was finally acknowledged. However, in a sense it is being whitewashed by pointing out that centrifugal force is a fictitious force by virtue of the fact that it is merely an appropriate way of describing effects in a rotating frame which could be described by other means in the inertial frame.

This is an improvement. But it still lacks the most important clause of all.

That clause is that centrifugal force is about real radial effects which come about BECAUSE of curved path motion.

Unfortunately the interpretation of the maths that these guys are pushing is indeed the official line. I did it myself many years ago in applied maths and I can confirm that.

The maths itself is correct. But they are interpretating it such as that ω^2r means that the centrifugal force acts on any body in a rotating frame.

I am adamant that the ω term is telling us that it only applies to objects that themselves have that ω. And the fact that a centrifuge only works for co-rotation would tend to back that idea up.

It would seem however that what they are preaching is indeed what is being preached in the universities.

So there's not really very much that anybody can do to help the situation. The first line in the introduction messes it all up from the outset.

I would have liked a line that drew attention to the absolute reality of co-rotation situations. That is essentially what the recent stage of the edit war was about.

But at the end of the day, there is no doubt that fictitiousism is in the ascendency at the moment.

I have just heard that sometime in the early 1950's the textbooks on orbital theory switched the centrifugal force term in the equations into centripetal force.

So really the problem is too far gone now for anybody to be able to do anything about it. David Tombe ( talk) 17:53, 3 May 2008 (UTC)

Brews, in Cartesian coordinates, the centripetal force shows out alone as you say. I am totally familiar with the derivation. We take two velocity vectors on the arc of the circle and make a vector triangle. This leads to an inward pointing acceleration of value v^2/r.

But you are overlooking something very important. This centripetal acceleration is with reference to the straight line path that would have occured had the centripetal acceleration not been there.

This straight line path is in fact inertia. Now do that exact same vector triangle again using the straight line path referenced to the exact same point. This time you will get an outward acceleration of v^2/r. In other words, the centrifugal force is implicit in the inertia.

In polar coordinates, we only consider the radial direction, and in that case inertia becomes centrifugal force. David Tombe ( talk) 06:25, 3 May 2008 (UTC)

Hi David: Well, knowing your interest in history, I think you're pulling my leg, and setting up to embroil me in the same controversies that prevailed in the 16th and 17th centuries. I'm sure it is amusing to see put into practice the old saw: "Those who cannot remember the past, are condemned to repeat it". Brews ohare ( talk) 14:23, 3 May 2008 (UTC)

Brew's, if you can derive centripetal force, just repeat that derivation, but this time instead of considering the velocity vector as having changed its direction in relation to the Cartesian frame, consider it to have changed its direction outwards in relation to the radial vector. You will get exactly the same expression outwards and it applies to straight line motion in the Cartesian frame. Inertia IS centrifugal force.

There is another way of looking at it. Consider the general central force orbital equation. Gravity and centrifugal force combined yield a conic section. In the extreme case of when the gravity is negligible, we get a highly eccentric hyperbola. This is effectively a straight line.

In other words, centrifugal force acting alone leads to a straight line.

Centrifugal force in conjunction with centripetal force leads to a circular motion.

Conclusion. Centrifugal force is always there in the outward radial direction in circular motion, but in the Cartesian frame it is masked as 'inertia'. David Tombe ( talk) 15:12, 3 May 2008 (UTC)

Hi David: The vector-based analysis of centripetal force uses the basic definition of change of displacement r( t + dt ) − r( t ) = ds, which is independent of any coordinate system. There is no issue to consider about "relative to the radial vector" or "in relation to the Cartesian frame". The vector ds exists in space as determined by the path r ( t ) and nothing else. It appears to me that all your verbal arguments simply collapse in the face of this extremely fundamental kinematic argument, which transcends all such considerations. Brews ohare ( talk) 15:59, 3 May 2008 (UTC)

No Brews, let's consider the case when there is no centripetal acceleration and the particle moves in a straight line.

Now do that same vector triangle again referenced from the centre of that same circle that you would have used if there had been centripetal force.

This time you will discover a net outward direction changing acceleration.

In other words, the centrifugal force is there all along but disguised in the straight line motion which is inertia. It doesn't show up in the Cartesian analysis. But it is there.

Now go into polar coordinates and if we have circular motion, the centripetal force inwards will be exactly balanced by a centrifugal force outwards.

Consider an elliptical orbit. Consider the stage when the object is closing in on the centre. According to you this closing in is a consequence purely of the one and only inward acting centripetal force. And based on the expression for gravity (inverse square law), you might think that the fact that the gravity is getting stronger as it gets closer, would mean that it should spiral in even more so.

But it doesn't. At some stage of the orbit, it starts to go up again. What is that radially outward force that suddenly overcomes gravity? David Tombe ( talk) 17:28, 3 May 2008 (UTC)

David: I am sorry, but you are dead wrong on this one. If the path is a straight line, the kinematical argument predicts zero acceleration. The kinematical argument outlined in the earlier comment and used in centripetal force simply does not use "triangles" or "Cartesian coordinates". Brews ohare ( talk) 18:26, 3 May 2008 (UTC)

Brews, if we treat the straight line path from a Cartesian perspective, then the acceleration is zero if it has constant speed.

But if we treat it as measured radially from a fixed point, then it reads a centrifugal acceleration outwards of v^2/r.

Imagine an object going in a straight line with constant speed in the Cartesian frame. Imagine a lamp post which is not on its path.

At some stage the object will be getting progressively closer to that lamp post. Then a point of nearest distance will be reached and the object will then begin to get further away. If we consider the distance between the object and the lamp post, the second time derivative of that distance will be v^2/r away from the lamp post, where v is the component of the actual speed that is perpendicular to the radial vector. In other words, the maximum centrifugal force will occur at the point of nearest approach.

This is a central force orbit. The lamp post exerts negligible gravity and so the solution is a highly eccentric hyperbola which is efectively a straight line.

That is inertia and it is centrifugal force too. David Tombe ( talk) 18:46, 3 May 2008 (UTC)

I'd suggest that you're doing some math in your head and making errors. If you actually put it on paper, you'll find that a straight-line motion as seen from the lamp post requires zero acceleration, even if the object does a near miss. To support this view, I can measure distance from the lamp post to the object as r ( t ). Then, for straight-line motion, at another time Δt later, r ( t + Δt ) = r ( t ) + v Δt. Hence, dr / dt = v. And if v is constant, a = dv / dt = 0 . Nothing here depends on where r is measured from. No use is made of any coordinate system. Brews ohare ( talk) 19:14, 3 May 2008 (UTC)

Brews, in the scenario that I have given you, the direction of the position vector will be constantly changing and so it will be accelerating when viewed in that coordinate system. David Tombe ( talk) 06:16, 4 May 2008 (UTC)

David: Math can greatly cut down on verbiage and contradictory assumptions. In this case, for example, r ( t ) = r ( t₀ ) + v•( t − t₀ ) shows clearly that r changes direction because the time-dependent vector v•( t − t₀ ) is added to it, changing its direction as time increases. However, the velocity associated with r ( t ) is v, and v is constant in magnitude and direction , so a = dv / dt = 0.

Again, no coordinate system is used in this discussion, and analysis in any coordinate system will agree with these results. Brews ohare ( talk) 15:19, 4 May 2008 (UTC)

Wolfkeeper, if you have failed to see the link between Kepler's law of areal velocity and the "2 times r dot theta dot" term in the tangential component, which is Coriolis acceleration, then it would appear that you really do have some fundamental misunderstandings of this topic. There is no angular acceleration involved in central force orbital theory.

While you are attempting to back up Steve and FyzixFighter, you are actually saying things that contradict them.

I suggest that the three of you get together to appoint a spokesman so that you can speak with a united voice and we can then bring this argument to a definite conclusion. David Tombe ( talk) 09:54, 3 May 2008 (UTC)

Plvekamp, this is what I mean by the whitewash. This line here sums it all up,

The results obtained by considering these pseudo-forces to be "real" within the rotating frame are identical to those given by calculations made in the inertial frame without them.

That line totally fails to address the fact that the most important aspects of centrifugal force, such as getting thrown to the side door of a swerving car, actually arise BECAUSE of the rotation.

The whitewash line evades that issue totally and acts as if we have these effects that just happen to be going on and we have different ways of describing them in different frames of reference. It misses the entire point of what centrifugal force is about in the name of trying to reconcile two conflicting viewpoints over whether centrifugal force is real or fictitious. David Tombe ( talk) 18:04, 3 May 2008 (UTC)

Hi David: Maybe the problem here is semantical. The person thrown against the door sees "real" effects, maybe even has to visit the hospital. But these results are described differently in the inertial frame: the car turned but the passenger didn't. On an icy road, when the tires don't work, it's a "real" accident, but its because the driver did nothing "real" by turning the steering - the car went straight, the road turned. The use of "real" here in ordinary language is ambiguous. Brews ohare ( talk) 18:53, 3 May 2008 (UTC)

Brews, the problem here is that any real effects only occur when the object co-rotates with the rotating frame and this fact is being suppressed. The passenger in the car is made to co-rotate by the back of his seat. A mutually perpendicular deflection is then induced which throws him to the side door. (vXω)

There are patterns of real cutting of lines of force here which are mirrored in electromagnetic induction. These are being ignored. The dominating 'Fictitious Party' here are trying to insinuate that the effect would be the same for a stationary object that is not co-rotating. No it wouldn't be the same. No forces will act on the stationary object. It is the Faraday paradox.

A spinning bucket of water induces a hydrosatic pressure. But no real effect is ever induced on a stationary object merely by viewing it from a rotating frame of reference.

At the moment, I can see that your big problem is that you haven't yet realized that polar coordinates are the only viable way to analyze these issues. Cartesian coordinates are useless for the purposes because they don't match the underlying reality. No matter how hard you try to analyze it all in Cartesian coordinates, you will still end up talking about the radial direction.

The polar system is the system that yields the clues about the underlying reality behind it all.

You try and see if you can successfully put any mention of actual radial acceleration into the introduction.

At the moment the bottom line of the introduction is effectively saying "If you came here to read about centrifugal force, you have come to the wrong page". David Tombe ( talk) 04:24, 4 May 2008 (UTC)

This would not have been a problem if the article had not defined the centrifugal farce as fictious. So you need to say real, to distinguish it from fictious. Fictious means not real or imaginary. Pseudo means false. The confusion is on the part of the people who use these terms to discuss physics. I say again that the editors, and this means Mr Anemone, you dont understand physics, and this article on the centrifugal farce should be deleted from wikipedia since you will never get the physics right in this discussion. 72.84.70.6 ( talk) 20:28, 3 May 2008 (UTC)

As numerous independent contributors to this thread have pointed out, we use this term in the article simply because "fictitious force" is the standard usage and terminology for things like centrifugal force. This is because from the viewpoint of an inertial frame, generally chosen by physicists for the simplicity of its equations of motion, it does not exist. I personally prefer the less confusing term "pseudo-force", following Feynman, but ultimately it means the same thing. The universe does indeed "[act] as if we have these effects that just happen to be going on and we have different ways of describing them in different frames of reference", something which can not only be confirmed theoretically by transforming equations, but has also been demonstrated in practice in thousands of engineering applications involving rotational motion that have been constructed using these theories.

You are perfectly at liberty to use rotating coordinates and perform calculations using it, and call it a real force; your equations of motion will still describe the same universe as the simpler equations set in the inertial frame. You can even measure it with instruments within the rotating frame, and it will appear to behave exactly as you predict: this is a consequence of the equivalence principle. Nevertheless, your viewpoint, if not your terminology, will remain perfectly compatible with the simpler inertial frame treatment which treats this "force" as the mere result of the effect of coordinate transformations on the laws of classical mechanics as formulated in an inertial frame; and as a result, everyone else will also remain at liberty to continue to regard centrifugal force as nonexistent within the context of that system.

If you want this practice changed, you will first need to change the standard treatment of classical mechanics and the working practices of professional physicists and physics educators, and once you have done that, we can change the article to fit your tastes. Please read the essay at WP:TRUTH, if you have not done so already. -- The Anome ( talk) 22:24, 3 May 2008 (UTC)

Anome, You've missed the point entirely. Centrifugal force is an effect which comes about BECAUSE of rotational motion. Spin an object and a centrifugal pressue will be induced.

It has got nothing to do with how we describe it in different frames of reference.

At the moment, the article begins by stating that centrifugal force is fictitious and that it is only apparent in rotating frames.

The article then continues by contradicting this and stating that there are real effects but that they would be there anyway whether there is rotation or not. Wrong.

The article then mentions that the centrifugal force that involves actual outward motion, which would be what people have in mind when they look up an article on centrifugal force, is not the centrifugal force that is dealt with in this article.

And it finally ends by stating that the whole matter is very confusing.

Anybody reading this introduction would simply say 'what?'. And they would be less wise about centrifugal force than before they read it.

I'm going to put in a qualifying clause regarding the necessity of the real effects to be induced by rotation. If this clause is deleted, which I am sure it will be, then I can only conclude that the person who deletes it has got absolutely no comprehension of the topic whatsoever.

In fact if I had been the one that had put in what you put in, it would have been deleted already because these people are not even happy with the idea of real effects at all.

But when it was deleted, somebody who would have deleted it if I had been the author, actually restored it.

It is clear from observing the activities on this page, that there is a certain group who revert according to who made the edit, rather than what the edit involved. David Tombe ( talk) 03:47, 4 May 2008 (UTC)

David, the problem appears to be with the term "fictitious force". I don't think it's a great term, but that's what people have called it. I prefer the term inertial force. I find the article is perfectly clear and straightforward, but there is no way around wrapping your mind around the concept of an "apparent force" here. You seem to be confusing a rotating body (which is very real, and has of course real, not "ficticious" effects), and rotating coordinate systems which may be chosen at will. Edit-warring on Wikipedia is not a recommended way of getting to grips with elementary physics. Most people achieve that in the traditional way of picking up a book or visiting a school. dab (𒁳) 17:44, 4 May 2008 (UTC)

No Dbachmann, the problem is that you don't seem to realize that nothing actually happens at all unless there is very real rotation. That nmeans co-rotation in the rotating frame. You will notice that any attempts on my part to emphasize that fact, are systematically deleted. If you think otherwise, then please tell me all about the physical effects which are felt by a stationary object that is observed from a rotating frame of reference. David Tombe ( talk) 09:09, 5 May 2008 (UTC)

Careful here, yet again. If a body is moving inertially- in a straight line, when viewed from a rotating frame of reference there is very evidently both a centrifugal force as well as a Coriolis force. There is no need at all for any real rotation to be present, all that is necessary is to do the relevant coordinate transformation, and it appears.- ( User) WolfKeeper ( Talk) 13:13, 5 May 2008 (UTC)

No Wolfkeeper, the Coriolis force does not occur in the natural state of affairs, but the centrifugal force does. This is a direct consequence of Kepler's law of areal velocity which eliminates the Coriolis force and the Euler force from planetary orbital motion. Everyday straight line motion is a special case of planetary orbital motion. David Tombe ( talk) 15:43, 5 May 2008 (UTC)

Consider somebody standing in a rotating space station (e.g. O'Neill cylinder). Because it is spinning the convenient frame of reference is the rotating reference frame that rotates with the station. You're standing there, and you let go of a ball. Due to centrifugal effect, the ball falls to the ground. OK? Now, look at this from the external, stationary frame of reference, you've got this guy spinning around with the station, but his feet are going at a faster linear velocity than his hand (because the hand is nearer the rotation axis). So when he lets go of the ball, it is going to move (in a straight line, with constant speed, due to inertia, in the non rotating frame.) But if the feet are going faster, then they will be ahead of the ball when it lands- they are going faster at each and every point, and their angular velocity is higher at each and every point. So the ball lands behind. In the rotating frame of reference it looks like a magic force has pushed the ball backwards. (If that isn't obvious, take a simple example, and calculate how long the ball takes to hit the ground in the non rotating frame, and how far the feet have moved- I can do the calculation if it's too hard for you.) My questions is, what's the name of that magic force that pushes the ball backwards when you drop it in the space station, David? It's not centrifugal force, because that acts strictly outwards. And it's not Kepler's areal law, because there's no significant gravity.- ( User) WolfKeeper ( Talk) 16:21, 5 May 2008 (UTC)

I'm still waiting for an answer David.- ( User) WolfKeeper ( Talk) 04:39, 7 May 2008 (UTC)

The problem with inertial force is that it sounds like a real force. I prefer fictitious myself. Or pseudoforce perhaps, but I'm not sure about that. -- Doug Weller ( talk) 18:02, 4 May 2008 (UTC)

well, it is a "real force" in a way. The point is, forces are something "real" (i.e., they don't just appear for no reason). That's unless you choose a non-inertial coordinate system. But in real life you'll only ever do that if something is moving along non-inertial lines, which means that there are forces present. Be aware that I am not discussing the physics here, which I understand, but the presentation to somebody who doesn't yet understand it. David is confused because we tell him a force is "fictitious" which has a real effect. That's because he keeps imagining items (cars, water buckets) that do experience some force, and the choice of coordinate system does only follow suit. Nobody will ever choose a rotating coordinate system if there isn't some rotating body involved. This is imho the origin of the confusion. The confusion is all David's, of course, and he has no business disrupting the article, but I am addressing the question as if he had asked politely on WP:RD/S where misunderstandings such as this one would properly belong. dab (𒁳) 18:24, 4 May 2008 (UTC)

Dbachmann, the confusion is not all mine. The confusion is all yours for failing to be able to see that actual rotation induces real radial effects, whereas no effects at all are induced on a stationary object whether it is observed from a rotating frame of reference or not. David Tombe ( talk) 09:18, 5 May 2008 (UTC)

A little different way of looking at people's positions is to divide them into the "theorists" for whom inertial frames are "it", and "experimentalists" who aren't interested in formalism, but in what they actually experience. If you love pure thought you can tell the man slammed against the subway door that in a different world (an inertial frame) he got smashed by a fictitious force, but he is likely to tell you where to put your inertial frame: he is living in this frame. Brews ohare ( talk) 18:38, 4 May 2008 (UTC)

my point is: the man being slammed against the door isn't experiencing a "fictitious" force, he is experiencing a force that has a real physical cause. The "fiction" part is just that it appears the force is acting on him while it is in fact acting on the subway train. dab (𒁳) 19:35, 4 May 2008 (UTC)

Does it only appear that his bones are broken? 119.42.68.141 ( talk) 10:09, 9 May 2008 (UTC)

From the McGraw Hill Dictionary of Mathematics and Physics centrifugal force: (1) An outward pseudo-force, in a reference frame that is rotating with respect to an inertial reference frame, (2) The reaction force to a centripetal force. —Preceding unsigned comment added by Denveron ( talk • contribs) 04:48, 4 May 2008 (UTC)

One of the requirements of scientific thinking is that the terms used in science have a definite and clear meaning and that there is an economy of terms used. This is not the case in modern physics which has multiplied a profusion of confusing and ambigous terms to discuss centrifugal force. There was no problem with this definition for several hundred years. Yet now, one can not read a physics book without being subjected to a multitude of ambigous confusing and absurd definitions that basically are meaningless metaphysical entities which contribute nothing to the understanding of the physics involved. The fact that wikipedia can not make sense out of this centrifugal farce demonstrates the useless aspect of these absurd terms. Wikipedia editors dont know what these terms mean and they cant explain them here, so you should call this article the centrifugal farce. The article should be entirely deleted since you will never get it right. 72.84.66.108 ( talk) 15:04, 4 May 2008 (UTC)

People have been wrong about many things for enormous lengths of time; further, life was arguably much simpler in the past. That is not an argument for keeping outdated and incorrect ideas, particularly not in the name of "scientific thinking". ETA I think that the second definition above is perfectly clear and straightforward, and could be used as the basis for simplifying and clarifying the introduction. Most readers are not going to want to read anything about reference frames—rotating, intertial or otherwise. SHEFFIELDSTEEL ^TALK 17:35, 4 May 2008 (UTC).

Sheffield Steel, I have been advocating that very point. There is no need to mention rotating frames of reference at all. It merely provides a mechanism within which to perform conjuring tricks with the maths. It obscures the underlying reality of the fact that centrifugal force only occurs when actual curved path motion happens.

In relation to your reply to 72.84.66.108, can you please tell us all exactly what outdated and incorrect ideas you have in mind. From what I can see, he is saying the same as me, which is that we need to have co-rotation in order for centrifugal force to occur. Is that an outdated and incorrect idea? David Tombe ( talk) 09:15, 5 May 2008 (UTC)

Yeah, actually.- ( User) WolfKeeper ( Talk) 14:26, 5 May 2008 (UTC)

What I got from the above pages of chatter was that the Introduction was too geeky - not everybody is a mathematical aficionado. So to please David and provide a bit broader attack on the subject than "coordinate transformations" I rewrote the first few paragraphs. I know it's presumptuous of me, but somebody said it's easier to revise something than to look at a blank page. So go for it. Brews ohare ( talk) 06:19, 4 May 2008 (UTC)

Brews, You mention about these 'real physical effects'. Then you erased my reference to co-rotation. Can you please tell me which real physical effects, that aren't co-rotating, are best described from a rotating frame of reference? What 'real physical effects' have you got in mind?

Are you seriously trying to tell me that a stationary bucket sitting on the ground is best described from the perspective of a rotating frame of reference?

I think that you will soon realize why I inserted that clause into your revised introduction. This is the key point in the whole dispute. What I am currently arguing with Steve and FyzixFighter about now is only a secondary issue.

On that other point about centrifugal force being inherent in straight line motion past a lamp post, imagine the traffic police standing at the lamp post and pointing their speed radar gun at the oncoming object.

Now remember, the object, let's say a car, is driving at a constant speed in a straight line Cartesianly. It is coming from a distance and it passes the lamp post at a nearest distance of 50 yards.

Will the radar gun register the same speed the whole time? David Tombe ( talk) 08:44, 4 May 2008 (UTC)

David: the intro is not a place to throw in a "co-rotating" reference, which cannot help being confusing as an inserted parenthetic aside in a sentence of general nature. If this topic is central, it needs specific discussion with examples in a separate sub-section later on. Insertion of only a few words mid-sentence may avoid careful scrutiny, but it will not explain the subject.

I'll reply to the centrifugal force discussion in the earlier segment. Brews ohare ( talk) 15:06, 4 May 2008 (UTC)

In response to your repeated attempts to insert a "co-rotating objects" reference; what exactly does that add to the meaning of the sentence? Do you regard it as a clarification? I think it is a confusing limitation upon the general argument of the sentence. Brews ohare ( talk) 15:38, 4 May 2008 (UTC)

You must be joking. The entire article is a morass of confusion, and you are complaining about a small attempt at clarification. The article is nonsense as it stands and the attempts to sort out the confusion by imposing more rigorously defined nonsense is a joke. 72.84.66.108 ( talk) 16:52, 4 May 2008 (UTC)

This subsection should be deleted. What is not a rant is either repetitious or unsupported. Brews ohare ( talk) 16:04, 4 May 2008 (UTC)

Deleted. I've created a new section to address the matter of whether centrifugal force is "real". -- The Anome ( talk) 16:57, 4 May 2008 (UTC)

I think we may need to cover centrifugal effect, and then extend it to cover centrifugal force. There's no other article on centrifugal effect per se.- ( User) WolfKeeper ( Talk) 00:00, 5 May 2008 (UTC)

As in this treatment? That seems like a really good plan. -- The Anome ( talk) 00:29, 5 May 2008 (UTC)

'Rotating frames of reference' only clouds the entire issue. The key point which is being consistently swept under the carpet is the fact that the transformation equations only apply to co-rotating objects. If there is no co-rotation, then nothing happens.

It is clear that this entire mess is a result of total denial of this fact. I have looked through the edits of the last day and I can see that Virginia anonymous has been trying to push this same point, but that just as when I do it, it gets deleted immediately.

It seems to me that it is much more important to all of you to emphasize trivial facts, such as 'These real effects can also be described equally well in an inertial frame', than to mention the most important fact of all which is that these real effects are actually induced by the rotation itself.

Recently we saw the parent force for both the centrifugal force and the Coriolis force. It takes the form vXω.

The manner in which the editors here have been trying to present this very real inductive effect would be analgous to trying to explain electromagnetic induction as follows,

As viewed from the frame of reference of a rotating bar magnet, an electric current is seen to be induced in a nearby electric circuit. This effect can be equally well described from the inertial frame.

I'm sure that you would all agree with me that it would be the height of nonsense to explain electromagnetic induction like that because it misses out on the most crucial aspect of all which is that the induced electric current occurs BECAUSE the bar magnet is rotating.

Um. LOL. You do know that electromagnetism forms a 4-vector, and due to Lorentz coordinate transformation magnetism and electic fields can convert into one another in moving frames of reference, and that this is considered to be a form of rotation (in a hyperbolic geometry)? In other words, its pretty similar...- ( User) WolfKeeper ( Talk) 13:19, 5 May 2008 (UTC)

You are all doing exactly the same in this article. You are all denying the underlying induction aspect that is caused by absolute rotation.

So if you guys are going to insist on deleting all references to the importance of co-rotation, then you will all remain confused for a very long time. David Tombe ( talk) 08:58, 5 May 2008 (UTC)

LOL. No, it happens with inertial paths, stationary objects, curved paths, things that are spinning around the frames' axis, things that are spinning about a different axis, things that are spinning at a different rate about the same or different axis, or variable axis... It occurs to everything that isn't on the frames rotation axis...- ( User) WolfKeeper ( Talk) 13:17, 5 May 2008 (UTC)

No Wolfkeeper, it doesn't. A stationary object in the inertial frame experiences no physical effects by virtue of being observed from a rotating frame. David Tombe ( talk) 15:19, 5 May 2008 (UTC)

I notice that there is now a section entitled 'Is centrifugal Force Real?'.

Well at the beginning of the edit war, I mentioned that Newton, Maxwell, and Bernoulli had believed it to be real. I even provided references. But that true fact was instantly deleted. The 'Fictitious party' are not even comfortable with any mention of the fact that centrifugal force was once believed to be real by the great masters of physics.

You can read this interchange with PeR at the beginning of the edit war and make up your own minds,

David, The centrifugal force was never considered to be real by Newton, Maxwell, or Bernoulli. If you want to put a statement like that you need to cite a source. Specifically you need to cite a source that says "the centrifugal force was considered to be real", or something very similar to that. If you read a text by, say Maxwell, and interpret that as him saying that the centrifugal force is real, that is still original research, since it is your interpretation of what he says. --PeR (talk) 17:16, 20 April 2008 (UTC)

Reply: Admissibility of Evidence

PeR, I think that you are going to have to repeat yourself. We need to get something straight here regarding the issue of admissibility of evidence. You declared that centrifugal force was never considered to be real. You further went on to state that if I were to produce any quotes from Newton or Bernoulli which indicated that they believed that centrifugal force was real, that this would not be deemed to be admissible evidence on the grounds that it would be my own original research. Here is a quote from Bernoulli out of the ET Whittaker book on the history of aethers.

"The elasticity which the Aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools."

And here is a quote from Maxwell's paper 'On Physical Lines of Force',

"The explanation which most readily occurs to the mind is that the excess of pressure in the equatorial direction arises from the centrifugal force of vortices or eddies in the medium having their axes in directions parallel to the lines of force"

And you are trying to tell me that this is not evidence to suggest that Bernoulli and Maxwell believed that centrifugal force was real?

YES! I am trying to tell you that this is not evidence to suggest that Bernoulli and Maxwell believed that centrifugal force was real. However, if you don't want to accept this you don't have to. Just don't write anything in the article. If you do want to write something like that then you must (and here I am repeating myself, as requested) cite a source that says "the centrifugal force was considered to be real" or something very similar to that. If you read a text by, say Maxwell, and interpret that as him saying that the centrifugal force is real, that is still original research, since it is your interpretation of what he says. --PeR (talk) 19:42, 21 April 2008 (UTC)

reply: PeR, There is a controversy about whether or not centrifugal force is real. The official position today is that it is not real. The current introduction is abominable because it tries to fudge the issue by pretending that there are two centrifugal forces. One for the realists, and one for the fictitiousists. This is an extreme case of ecclecticism. The current introduction cannot remain because it is a total disgrace.David Tombe (talk) 08:02, 21 April 2008 (UTC)

He replies. You misinterpret what it says. However, the fact that you don't understand it is evidence that it is not clearly enough written, so I agree that it should be rewritten. --PeR (talk) 19:42, 21 April 2008 (UTC)

David Tombe ( talk) 09:33, 5 May 2008 (UTC)

So Maxwell and Bernoulli mention centrifugal force in their papers. That's a bit of a non-sequitor. Physicists today also mention centrifugal force in their papers. Can you find a quote from M or B in which they talk about the character of centrifugal force, instead of a side mention ? These two quotes don't address the issue. Plvekamp ( talk) 13:21, 5 May 2008 (UTC)

Yes I could dig up alot more on the subject. Maxwell uses centrifugal force to explain magnetic repulsion. Read his whole 1861 paper. But we don't need to go into that here.

Those quotes which you deleted simply drew attention to the fact that Maxwell and Bernoulli believed centrifugal force to be real. The section was entitled 'Is centrifugal force real?' and so I was letting the readers know what Maxwell and Bernoulli thought. What exactly is your problem with this kind of information? David Tombe ( talk) 15:48, 5 May 2008 (UTC)

Simply because they use the concept, doesn't mean they interpreted it the same way you do. Modern physicists also use the concept, yet disagree with your interpretation. You need to show a quote that shows that their interpretation agrees with yours. Those two mentions don't give any more information than that they were familiar with the concept, and used it in their theories. Plvekamp ( talk) 16:35, 5 May 2008 (UTC)

David: This discussion is all a bit silly. The article already says that "fictitious" has the meaning "unnecessary in an inertial frame of reference". Would you argue against that as a definition? As a fact, so far as centrifugal force is concerned?

The article also says that centrifugal force is a very real effect in a non-inertial frame. What exactly are you trying to accomplish here? Brews ohare ( talk) 14:14, 5 May 2008 (UTC)

Brews, when actual co-rotation occurs, the centrifugal force is (1) real, (2) radial, and (3) it can be observed from all reference frames. It is an absolute effect.

When there is no co-rotation, then there is nothing. There is no centrifugal force. There are no physical effects in any reference frame. David Tombe ( talk) 15:17, 5 May 2008 (UTC)

David, Just to clarify what I meant, above. (If you didn't read WP:OR and WP:V the last times you were asked to, then please do it now.) If you were to state "Maxwell mentions a 'centrifugal force'", then the above citation would be sufficient. But if you want to say that he believed that it is real, then you'd need a statement by Maxwell along the lines of "I believe that the centrifugal force, which others say is fictitious, is actually real", or a statement by some authority on science history asserting what Maxwell thought. From what you quote, the reader has no way of knowing whether Maxwell is referring to the term used in this article, or if he is using it in its literal sense to mean any "force that is directed away from the center". Hope this helps. -- PeR ( talk) 20:45, 5 May 2008 (UTC)

PS. Maxwell was considered a genius of his time. If he was wrong on a matter of elementary physics that would be a widely published fact, so you wouldn't have a hard time finding a reference. For comparison see how easy it is to find reliable sources asserting that Einstein said that [God] does not play dice. -- PeR

Timothy, this is a reply to,

David, when your talking about what "a person sit in a car driving in a circle" experiences, you are implicitly specifying a frame of reference. Namely, what a person experiences can only be described in a co-moving frame. Such a frame is typically non-inertial and will thus contain psuedoforces (or however one wishes to call them) from the perspective of this observer/person these forces are very much real. As you state the person feels himself pushed towards the outward door. An other observer will understand this diffently. An observer from an inertial frame will see the person in the car being forced to move in a circle by force exerted on him by the car.(TimothyRias (talk) 14:32, 5 May 2008 (UTC))

You have got completely confused between (1) the force that causes the co-rotation ie. the pressure on the man's back from the seat of the car, which is in the tangential direction, and (2) the centrifugal force which is induced by this co-rotation and acts outwards in the radial direction causing him to slide to the side door.

The induced centrifugal force is (1) real, (2) radial, (3) and can be observed by everybody irrespective of what frame of reference they are in. In fact, there are no frames of reference. The centrifugal force is an absolute effect, associated with absolute rotation. David Tombe ( talk) 15:27, 5 May 2008 (UTC)

What happens when there is no seat back? Same thing happens, he slides to the door. Thus your co-rotation argument here is a red herring. Plvekamp ( talk) 16:59, 5 May 2008 (UTC)

If you want to argue from ancient references, please take a look at Newton's Principia Book 1 and Euler's Mechanica Chapter 5, in which curvilinear motion is discussed. Neither author finds it necessary to use centrifugal force; but centripetal force is ubiquitous. Why is that? (Clue: the analysis in both cases uses inertial frames of reference.) Additionally, why do modern physicists also mention centrifugal force in their articles, but yet, none of them here on Wikipedia agree with your interpretation? There must obviously be a cabal, since you have the WP:TRUTH. Plvekamp ( talk) 15:49, 5 May 2008 (UTC)

Plvekamp, what ancient references are you talking about in realtion to my reply to Timothy Rias? David Tombe ( talk) 15:57, 5 May 2008 (UTC)

Surely you're pulling my leg. The only references you've used, Maxwell and Bernoulli. Plvekamp ( talk) 16:04, 5 May 2008 (UTC)

David, instead of just stating that people are completely confused, you might try and use actual arguments. Our at least try to understand other people's arguments. And actually the centrifugal force induced on the man in the car is only perceived in the co-moving frame. And observer in an inertial frame will only perceive one force acting on the man in the car and that is the force exerted on the man by the car. (well if you would also count gravity that would be two, but that is really beside the point) ( TimothyRias ( talk) 20:56, 5 May 2008 (UTC))

Timothy and Plvekamp, If the back seat of the car is not causing the man to move with the car, then something else will be. If nothing is causing the man to move with the car, then he will not be co-rotating and he will not experience any acceleration in the radial direction in the car's frame of reference. The Maxwell and Bernoulli references had got absolutely nothing to do with that point. David Tombe ( talk) 07:32, 6 May 2008 (UTC)

David, you are missing my point. Sure the seat in the car is exerting a force on the person in the car causing him to follow its movements. My point was that if viewed from an inertial frame this is the only force acting on the man even when going around a corner. When the car is driving around in a circle at constant speed the force exerted on the man by the car is completely radially inward. (I'm neglecting gravity here for the moment for convenience of speech) ( TimothyRias ( talk) 07:48, 6 May 2008 (UTC))

Timothy, if a man was standing in the street watching the swerving car, he would see the back seat of the car pushing the passenger tangentially and he would see a radial centrifugal force induced that causes the passenger to slide outwards towards the side door. David Tombe ( talk) 08:05, 6 May 2008 (UTC)

No David he would not! If what you say would be true, then the person on the street would see the person in the car make a curve in the opposite direction of the car. We all know this to be false, the person will move in a straight line as seen from the street. ( TimothyRias ( talk) 08:18, 6 May 2008 (UTC))

No Timothy, the person in the street sees the passenger move in a straight line in the Cartesian frame, but he also sees the passenger moving out radially towards the side door in the rotating frame. He can see both frames at once. David Tombe ( talk) 08:44, 6 May 2008 (UTC)

David, you have convinced me. You have have absolutely no clue about physics whatsoever. You can only describe physics from one frame of reference at a time. Concepts like forces, energy, etc. are very much frame dependent and need conversion when translated frame on frame to an other. Sure the man on the street can describe the physics in the car using a co-rotating frame, in which case there is pseudo force present in the form of the centrifugal force. But, when he describes the physics from the his natural frame (ie the one that is comoving with his motion, ie an inertial frame) then no such force is present. ( TimothyRias ( talk) 09:17, 6 May 2008 (UTC))

Timothy, I was only describing it all in one frame at a time. The centrifugal force occurs radially when the passenger is subjected to a tangential motion. You can consider that effect real or fictictious. It's up to you. But one thing is sure. It only occurs when the passenger has a tangential velocity. It does not occur on objects that are not co-rotating with the car. David Tombe ( talk) 13:32, 6 May 2008 (UTC)

Um, but the passenger is also pushed forwards by the seat in that scenario- this is because as the passenger slides outwards he meets the seat- and the seat is moving faster than he was. This causes the passenger to sink backwards in the seat cushions, because he is being accelerated as he slides. Or, easier to see, if he was sitting near the front of the seat and the seat is slippery, he would tend to slide backwards with respect to the car, for the same reason- the back of the seat is moving faster than him because it's on a wider curve, and traversing it in the same time as the rest of the car.- ( User) WolfKeeper ( Talk) 04:47, 7 May 2008 (UTC)

Really? What happens if a ball is flying over the car in the same direction and speed? That would follow exactly the same trajectory as the man in the car but just a couple of meters higher. (again neglecting gravity and any friction for the moment) ( TimothyRias ( talk) 14:10, 6 May 2008 (UTC))

Yes, Timothy. And the ball would also have centrifugal force in relation to the centre point of the car's circular motion. The actual factor that induces centrifugal force is 'tangential velocity relative to a point in space', and the centrifugal force is a radial force measured relative to that point.

Co-rotation in a rotating frame of reference is only one particular scenario that brings about centrifugal force. It is not the most general scenario. When I said above It does not occur on objects that are not co-rotating with the car., I was specifically referring to stationary objects. David Tombe ( talk) 04:25, 7 May 2008 (UTC)

This is copied from above:

--- Brews, when actual co-rotation occurs, the centrifugal force is (1) real, (2) radial, and (3) it can be observed from all reference frames. It is an absolute effect.

When there is no co-rotation, then there is nothing. There is no centrifugal force. There are no physical effects in any reference frame. David Tombe ( talk) 15:17, 5 May 2008 (UTC)

David: Blanket assertions like this cannot carry your argument. To be persuasive, you'll have to get mathematical. For example, take a look at the derivation and point out what you think is at stake here in mathematical terms. Brews ohare ( talk) 17:03, 5 May 2008 (UTC)

More to the point, to comply with Wikipedia's verifiability policy, it must be accompanied by a reference that states that this is the case: bold assertion is not enough. -- The Anome ( talk) 17:56, 5 May 2008 (UTC)

Exactly what do you mean by 'co-rotation' then? Are you saying that both the rotational frame and the object have to be rotating at exactly the same angular rate and if they were moving 0.0000000001 radians per second differently, then there's no centrifugal force? So the surface of the Earth is not subject to centrifugal force due to the tiny difference in angular rate due to continental drift?- ( User) WolfKeeper ( Talk) 18:52, 5 May 2008 (UTC)

Wolfkeeper, You have changed the context. In my original discussion with Brews, I was saying that in straight line motion in the inertial frame, centrifugal force is built into that motion in the form of inertia. If we measure the second order time derivative of radial distance from a fixed point, we will get v^2/r where v is the component of the velocity that is perpendicular to the radial line.

You tried to cloud the issue by introducing Coriolis force. Coriolis force is not involved in that scenario. Kepler's laws have eliminated Coriolis force from planetary orbital theory.

You then went on to introduce a rotating frame of reference scenario which would indeed involve fictitious tangential effects. David Tombe ( talk) 07:49, 6 May 2008 (UTC)

Brews, If something is not co-rotating, there will be no centrifugal force. What citations would I need to back up such a trivial point?

Imagine a long straight metal arm attached to a fulcrum and rotating in a horizontal plane one inch above the ground. Put a ball in its path. That ball will move out radially. That is centrifugal force.

Now repeat this expereiment with the long metal arm raised up ten feet. It will not touch the ball. The ball will not co-rotate and so it will just sit there still. There will be no centrifugal force on the acting on the ball.

Now the maths that you talk about suggests that there is actually a centrifugal force acting on the stationary ball but that it is over ridden by a Coriolis force twice as strong that acts radailly inwards.

Coriolis force never acts radially inwards. Coriolis force and centrifugal force both derive as mutually perpendicular components of a parent convective force vXω.

Those fictitious force equations are certainly correct when applied to the oceans and the atmosphere. But that's because the oceans and the atmosphere co-rotate with the Earth.

Those equations are only designed to deal with objects that are physically connected with the ω vector. You take a close look at the derivation of those equations and see if what I am saying is not true. David Tombe ( talk) 07:49, 6 May 2008 (UTC)

Lets derive those equations shall we. Lets consider a particle ${\displaystyle {\vec {x}}}$ moving in a rotating frame rotation with angular speed ${\displaystyle {\vec {\omega }}}$. At any time the kinetic energy of this particle will be given by ${\displaystyle T=1/2m({\dot {\vec {x}}}+{\vec {\omega }}\times {\vec {x}})^{2}}$. The corresponding action is ${\displaystyle S({\vec {x}})=\int T-V({\vec {x}})dt=\int \left(1/2m({\dot {\vec {x}}}+{\vec {\omega }}\times {\vec {x}})^{2}-V({\vec {x}})\right)dt}$ By the action principle the variation of this should vanish

${\displaystyle {\begin{aligned}0&=\delta S=S({\vec {x}}+\delta {\vec {x}})-S({\vec {x}})\\&=\int \left(1/2m({\dot {\vec {x}}}+{\dot {\delta {\vec {x}}}}+{\vec {\omega }}\times ({\vec {x}}+\delta {\vec {x}}))^{2}-V({\vec {x}}+\delta {\vec {x}})\right)dt-\int \left(1/2m({\dot {\vec {x}}}+{\vec {\omega }}\times {\vec {x}})^{2}-V({\vec {x}})\right)\\&=\int \left(m({\dot {\vec {x}}}\cdot {\dot {\delta }}{\vec {x}}+({\vec {\omega }}\times {\vec {x}})\cdot ({\vec {\omega }}\times \delta {\vec {x}})+{\dot {\vec {x}}}\cdot ({\vec {\omega }}\times \delta {\vec {x}})+{\dot {\delta }}{\vec {x}}\cdot ({\vec {\omega }}\times {\vec {x}}))+{\vec {F}}({\vec {x}})\cdot \delta {\vec {x}}\right)dt+O(\delta {\vec {x}}^{2})\\&=\int \left(m(-{\ddot {\vec {x}}}-{\vec {\omega }}\times ({\vec {\omega }}\times {\vec {x}})-2{\vec {\omega }}\times {\dot {\vec {x}}})+{\vec {F}}({\vec {x}})\right)\cdot \delta {\vec {x}}dt+O(\delta {\vec {x}}^{2})\end{aligned}}}$

This implies the equation of motion:

${\displaystyle {\vec {F}}=m\left({\ddot {\vec {x}}}+{\vec {\omega }}\times ({\vec {\omega }}\times {\vec {x}})+2{\vec {\omega }}\times {\dot {\vec {x}}}\right)}$

which is equivalent to the transformation formula present in the article. From this derivation it is manifest that ${\displaystyle {\dot {\vec {x}}}}$ can take any vector value, and is independent of ${\displaystyle {\vec {\omega }}}$. In particular, ${\displaystyle {\vec {v}}={\dot {\vec {x}}}-{\vec {\omega }}\times {\vec {x}}}$ is not radial as you have been claiming. ( TimothyRias ( talk) 09:07, 6 May 2008 (UTC))

Timothy, ${\displaystyle v={\dot {\vec {x}}}}$ was radial right from your very first equation of kinetic energy. You split that equation into a radial and a tangential component in Pythagoras format. David Tombe ( talk) 09:16, 6 May 2008 (UTC)

I did no such thing. I subtracted a vector and then took the norm. The vector I subtracted ${\displaystyle {\vec {\omega }}\times {\vec {x}}}$ has no relation with ${\displaystyle {\dot {\vec {x}}}}$ whatsoever, it is just a position based factor having to do with the fact that we are describing the physics in a rotating frame. Really, start listening to the people with actual degrees in physics that understand what they are talking about. ( TimothyRias ( talk) 09:26, 6 May 2008 (UTC))

Mr Rias, This seems to be original research. These equations need verification. Please cite your peer reviewed journal article reference and the textbooks that explain the source of your argument so that it can be checked to see if it is correct. You should know that citations are required by Wikipedia policy. Where are they? This argument can not be accepted as true until the citations are provided and the math is checked. 72.64.40.44 ( talk) 13:15, 6 May 2008 (UTC)

Argument is true by simple mathematical logic. There is nothing orgininal about this calculation. The basic principle, the action principle, is well established. Similar (equivalent) computations can be found in most textbooks on classical mechanics. Probably as an exercise in one of the sections on Lagrange formalism. ( TimothyRias ( talk) 14:05, 6 May 2008 (UTC))

It's true that one can't use math to prove an original point, when that point cannot be cited from a reliable source, when writing an article. This is a talk page, and math is a perfectly valid tool for giving an explanation to another user; and in any case, the conclusion of the calculation can be cited. -- SCZenz ( talk) 14:11, 6 May 2008 (UTC)

And what's sauce for the goose is sauce for the gander. David Tombe ( talk) 05:12, 7 May 2008 (UTC)

There is no sauce, and no gander. A conclusion of any kind from a talk page cannot be cited on any of wikipedia's articles.- ( User) WolfKeeper ( Talk) 06:08, 7 May 2008 (UTC)

Timothy, Yes, I see what you have done now. It is indeed an arbitrary velocity. But I can't see how you have linked that arbitrary velocity to the velocity term in the transformation equations. I simply don't follow your arguments above. There is absolutely no need to introduce that kind of mathematics to the problem. You are beginning at a very strange point. You begin with the general expression for kinetic energy for a particle in a rotating frame of reference. Correct. But then you introduce a potential energy term that is not needed. After a few manipulations which I simply don't follow, you conclude that it all implies the relevant transformation equations. You would need to show what all the maths terms mean at each stage of the derivation. Those same equations can be derived much more transparently in such a way that we can clearly see that the velocity term has to be the radial velocity. Why did you choose to introduce all that unnecessarily complicated maths above? There was absolutely no need for it. The point has been proved with a much more simple maths. So it can hardly be disproved just by introducing more complicated maths. David Tombe ( talk) 13:25, 6 May 2008 (UTC)

The "complicated" maths you are referring to is simply varitional calculus, and it is not hard it is basic undergrad physics. it is just Lagrange formalism. It is the tool of choice when deriving equations of motion. Newtons laws serve the same purpose. (If you do the same thing for a particle in an inertial frame you just get Newtons second law. (which thus can be derived from the action principle!) The potential term is there to provide for other convention (conservative) forces (such EM or gravity) which added there own specific terms to the Lagrangian. You could also leave it out, but then you would the EoM for a free particle, i.e. the one without F, which would also be fine.

To me this one of the simplest ways to derive the EoM in a rotating frame. You haven't provided any "proof" of your statements. Here I have provide a simple proof that transparently disproves your claim. If this already goes above your head, you might want to reconsinder meddling in something that you clearly do not understand completely. ( TimothyRias ( talk) 14:05, 6 May 2008 (UTC))

Timothy, I've had a bit of time to think about your so-called proof. Your expression for kinetic energy is wrong because the velocity term is wrong.

The actual kinetic energy of the particle would pertain to its velocity as measured from the inertial frame. That velocity can be split into two components. One of those components is the velocity of the particle relative to the rotating frame. The other component is the velocity of the point that it is at in the rotating frame, measured relative to the inertial frame.

So we are back to the original argument. If we are going to use the expression ωXr for the latter, then it can only refer to the tangential velocity in the limit. It follows therefore that the other component must be the radial velocity.

Your expression for kinetic energy is wrong by virtue of the negative sign, and if you corrected it to a positive sign you immediately impose the restriction that the velocity term must be radial.

Regarding Hamiltonian mechanics, I did it in applied maths many years ago and it is totally unnecessary for the analysis of single particle motion where no potential energy is involved. Your error is present before your Hamiltonian maths even begins. There is absolutely no justification whatsoever for introducing Hamiltonian mechanics into a simple discussion about whether centrifugal force is induced on particles that are stationary in the inertial frame. David Tombe ( talk) 04:15, 7 May 2008 (UTC)

Since ${\displaystyle {\dot {\vec {x}}}}$ is the velocity in the rotating frame, ${\displaystyle {\dot {\vec {x}}}-{\vec {\omega }}\times {\vec {x}}}$ is the velocity in the inertial frame. You're right it should be ${\displaystyle 1/2m({\dot {\vec {x}}}+{\vec {\omega }}\times {\vec {x}})^{2}}$, I changed the derivation above to reflect this. In any case, whatever the relative sign, ${\displaystyle {\dot {\vec {x}}}}$ is independent of ${\displaystyle {\vec {x}}}$ so there is absolutely nothing forcing any one of the above expressions to be tangential. Sure, ${\displaystyle {\vec {\omega }}\times {\vec {x}}}$ is always tangential, that doesn't mean it is the tangential component of ${\displaystyle {\dot {\vec {x}}}}$.

And regarding Lagrangian formalism, it is the tool of choice in physics when in doubt what EoMs to use. It is very suitable to derive the EoM in a rotating frame. It is at least a lot less messy than trying to derive them directly from the coordinate transfromation. (which is also possible and gives exactly the same result. ( TimothyRias ( talk) 06:36, 7 May 2008 (UTC))

Timothy, Hamiltonian and Lagrangian have got nothing to do with it. Your error lies in your interpretation of the expression for kinetic energy. In fact you don't even need to involve kinetic energy. We only need to look at the particle velocity. The moment I see the ωXr expression, I can tell instantly that you have routed the velocity through a point on the rotating frame. ωXr is the tangential component of the particle velocity in the limit. And because it is in the limit, the other component must be radial. You cannot escape that fundamental reality which lies right at the heart of those transformation equations. What you did above was to cloud that reality up with a whole package of Hamiltonian, and integrals, and potential energies. David Tombe ( talk) 09:43, 7 May 2008 (UTC)

What, limit? We are not taking any limit. There is no need to take a limit. ωXr is the tangential component of the particle only in the very specific case that the we choose the rotation of the frame of reference to be co-rotating with the particle. This is a very special case.

BTW, if you want a physical example of Coriolis forces acting radially you might want to look at the stability analysis of Lagrangian points. For example, without the contribution of the coriolis force, L1 en L2 would be radially unstable. The Coriolis contribution to the radial force stabilizes these points, allowing space ships to hover (or orbit) these points, a fact that is used effectively for many space missions. ( TimothyRias ( talk) 10:59, 7 May 2008 (UTC))

Timothy, the expression is absolutely dependent on it applying to the limit. If we consider the velocity vector split into two larger components, then none of those components are ωXr.

I repeat; what limit? ( TimothyRias ( talk) 12:54, 7 May 2008 (UTC))

On Coriolis force, it is not involved in Lagrange points or stability because there is no curl in the gravitational field. And in your books, it cannot be involved in stability because it is only a fictitious force.

FWIW coriolis force has absolutely no curl. If it had curl it would be a non conservative force. But it always acts at 90 degrees to the velocity vector and hence can't change the energy, and hence it's conservative (actually has no effect on the energy at all).- ( User) WolfKeeper ( Talk) 07:40, 8 May 2008 (UTC)

I never stated that. The effect of fictitious forces in non-inertial frames is very real. If it were not apples would not be falling from trees, since gravity is a fictitious force too! Anyway, it very simple if you remove the Coriolis force from the analysis of Lagrangian points no stable orbits are possible. This a simple fact anybody can do by doing the calculation/numerical simulation.( TimothyRias ( talk) 12:54, 7 May 2008 (UTC))

This is another example of your tactic which is to move the discussion into unnecessarily complicated zones such as Lagrangian, Hamiltonian, and the three body problem which has never been satisfactorily resolved. It is actually a deceptive tactic used by alot of people who have been proved wrong in the simple arena. Move the debate into the dark dirty jungles and cloud the whole issue. David Tombe ( talk) 11:46, 7 May 2008 (UTC)

First, you haven't proved anything, you have just made a bunch of blanket statements and provided no arguments. I've provided you with an argument, that apparently goes over your head, so you resort to accusing me of using dirty tricks.( TimothyRias ( talk) 14:02, 7 May 2008 (UTC))

This argument can not be resolved because Mr Rias continues to claim his suspect proof, which has no verification, validation or corroboration, be accepted. It should rightly be rejected, because it proves nothing. The larger problem is that wikipedia continues to endorse an interpretation of physics that contradicts the classical textbooks written up to circa 1950. During the 1950s Sears and Zemansky introduced a different interpretation in their physics textbooks, and there is no proof that what they said is true. Apparently generations of students accepted what Sears and Zemanski said uncritically. It is now scientific dogma. I want to see the peer reviewed journal articles and committe reports that justify the revisionist interpretation that is the basis of what is claimed to be true by wikipedia editors. Where is the proof that what you say in the article is actually true? Where are the peer reviewed papers that prove this opinion, which you repeat here as truthful physics? I see citations to sources which are merely hearsay. I dont beleive hearsay. Where are the original peer reviewed journal papers that prove this is true?? Obviously one can only begin to decide the issue once they have been produced, since they obviously need to be analysed for errors before one can accept what they say is valid physics. So I again demand that you produce the poof that what you say in the article is valid physics and stop this nonsense. 72.84.65.25 ( talk) 13:50, 7 May 2008 (UTC)

It is a simple six line proof. I'm not saying you believe my word, you can just check the argument for yourself since it is all there. Anyway, up till now I have had very little to do with the actual content of the article except some rearranging and damage control. I've been focussing on trying to resolve the conflict on this talk page by introducing actual arguments. ( TimothyRias ( talk) 14:02, 7 May 2008 (UTC))

As pointed out above, nothing demonstrated on the talk page is relevant to the main article. So you have wasted your time. I want to see the peer reviewed proof that justifies the statements made in the main article. These need to be peer reviewed journal articles or reccomendations from a physics education committee and cited in the main page. As far I can determine, there is no peer reviewed, critically examined proof of what is said in the main article. Citations which refer to sources that repeat or draw conclusions from other unproved sources are not acceptable. I want to see the actual real proof, not hearsay that it exists in theory. 72.84.65.25 ( talk) 14:48, 7 May 2008 (UTC)

Timothy, your six line proof fails on the first line before you even reach all the fancy Hamiltonians, integral signs, and potential energy terms.

Your proof fails at the point where you assume that if one component of the particle velocity is ωXr, that the other component has got arbitrary direction. The much more basic and less pretentious vector calculus that is used to derive the term ωXr insists that this term only applies when it is the tangential component of the particle velocity in the limit that this component tends to zero. It is the very same calculus that is involved in differentiating the position vector to obtain the general acceleration equation in radial/polar coordinates. We differentiate r and we end up with ωXr in the tangential direction and r dot in the radial direction. Your big problem is that when you were first shown the derivation of the rotating frame of reference equations, you never questioned that detail. You just accepted what you were told. Now that you have seen that there are restrictions of applicability which you had never thought about before, you are just digging in because you entered this argument without first checking your facts. Hence you are trying to cloud the whole issue by introducing high powered maths topics like Hamiltonians, and Lagrangians, and best of all, the ever controversial three body problem. None of these complications are necessary in order to analyse a simple vector triangle of velocity for a simple one particle motion with no potential energy terms. David Tombe ( talk) 15:58, 7 May 2008 (UTC)

OK, lets examine shall we:

• We fix a rotating frame with angular velocity ω.
• In this frame we describe the trajectory of a particle, starting a t=0.
• At this point we are free to choose any starting conditions. In particular we can choose the starting position x(0) and velocity v(0) of the particle.
• To obtain the speed in the inertial frame we need to add the velocity of the rotating frame at the starting position ωXx(0). That is v_inertial(0) = v(0) + ωXx(0).
• At this points you are concluding that this implies that ωXx(0) is the tangential component of v_inertial(0).
• Since we were free to choose ω, x(0) and v(0), we can clearly choose values such that this is the not case.

( TimothyRias ( talk) 21:06, 7 May 2008 (UTC))

Timothy, no you cannot. You are free to choose whatever value of velocity you like. But if one of its components is described by the expression ωXr, then it must necessarily be the tangential component, and therefore the other component must be the radial component. David Tombe ( talk) 06:34, 8 May 2008 (UTC)

Why? What is stopping us from having a velocity of, say,v_inertial(0) = 2 ωXx(0) such that v(0) = ωXx(0)? We are not making an orthogonal decomposition of the velocity. If we wanted we could decompose the velocity in a million non-zero components. Obviously, these would not all be linearly independent, but that is not a problem. ( TimothyRias ( talk) 07:19, 8 May 2008 (UTC))

Timothy, you can split the particle velocity into as many components as you like. But if one of those components is ωXr then the other component must be radial. This follows directly from the transport theorem. ωXr is the tangential component of the particle velocity in the limit. Hence the other component must be radial. You are ignoring a restriction that is built into the derivation. David Tombe ( talk) 10:09, 8 May 2008 (UTC)

This is only true if you assume ω to be the angular velocity of the particle. We were free to choose ω independently of the velocity of the particle, so we can clearly choose ω not to be the angular velocity of the particle in which case ωXr cannot be the tangential part of the velocity. Your assertion basicly comes down to stating that there can only exist particles which are co-rotating with the frame. That is obviously false. ( TimothyRias ( talk) 12:23, 8 May 2008 (UTC))

No Timothy, it means that the equations only apply to particles that are co-rotating with the frame, because in those equations ω will represent both the angular velocity of the frame and the particle. If you choose ω not to be the angular velocity of the particle, then you cannot derive the transformation equations. There will be no physical linkage. v must be routed through the tangential term ωXr which is common to both the frame and the particle. 119.42.65.152 ( talk) 13:30, 8 May 2008 (UTC)

Now, you are just talking in circles. There is absolutely no reason for any linkage between ω and the angular velocity of the particle. Moreover, if you assume no such connection, as I did, you find EoMs, that perfectly describe the kinematics of a (not necessarily co-rotating) particle in a rotating frame as can be perfectly checked. (and is used in all sorts of every day applications such as the calculation of space trajectories of satellites. —Preceding unsigned comment added by TimothyRias ( talk • contribs) 07:36, 9 May 2008 (UTC)

Timothy, let's see you deriving the transformation equations using a particle with an angualr velocity that is different from the angular velocity of the rotating frame? 119.42.68.141 ( talk) 10:14, 9 May 2008 (UTC)

The above derivation does just that but we can do an even simpler derivation if you want. Let ${\displaystyle {\vec {x}}_{\mathrm {in} }(t)}$ describe the position of a particle in an inertial frame. Choose ${\displaystyle {\vec {\omega }}\neq {\dot {\vec {x}}}_{\mathrm {in} }\times {\vec {x}}_{\mathrm {in} }}$ (i.e. it is not the angular velocity of the particle). Transformation to the frame rotating with angular velocity ${\displaystyle {\vec {\omega }}}$ is given by multiplying ${\displaystyle {\vec {x}}_{\mathrm {in} }(t)}$ with

${\displaystyle R_{{\vec {\omega }}t}={\begin{pmatrix}\cos(\omega t)&\sin(\omega t)&0\\-\sin(\omega t)&\cos(\omega t)&0\\0&0&1\end{pmatrix}}}$, where ${\displaystyle \omega =|{\vec {\omega }}|}$.

Thus the position of the particle in the rotating frame is: ${\displaystyle {\vec {x}}_{\mathrm {rot} }(t)=R_{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t)}$. Hence

${\displaystyle {\begin{aligned}{\ddot {\vec {a}}}(t)_{\mathrm {rot} }&=({\frac {d}{dt}})^{2}{\vec {x}}_{\mathrm {rot} }(t)\\&={\frac {d}{dt}}^{2}R_{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t)\\&={\frac {d}{dt}}(R_{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)+{\dot {R}}_{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t))\\&={\frac {d}{dt}}(R_{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)-{\vec {\omega }}\times \mathbb {R} _{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t))\\&=R_{{\vec {\omega }}t}{\ddot {\vec {x}}}_{\mathrm {in} }(t)+{\dot {R}}_{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)-{\vec {\omega }}\times \mathbb {R} _{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)-{\vec {\omega }}\times {\dot {R}}_{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t)\\&=R_{{\vec {\omega }}t}{\ddot {\vec {x}}}_{\mathrm {in} }(t)-2{\vec {\omega }}\times R_{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)+{\vec {\omega }}\times ({\vec {\omega }}\times R_{{\vec {\omega }}t}{\vec {x}}_{\mathrm {in} }(t))\\&={\vec {F}}_{\mathrm {rot} }(t)/m-2{\vec {\omega }}\times {\dot {\vec {x}}}_{\mathrm {rot} }(t)-{\vec {\omega }}\times ({\vec {\omega }}\times {\vec {x}}_{\mathrm {rot} }(t))\end{aligned}},}$

where we used that ${\displaystyle {\dot {R}}_{{\vec {\omega }}t}{\vec {y}}=-{\vec {\omega }}\times R_{{\vec {\omega }}t}{\vec {y}}}$ for any vector ${\displaystyle {\vec {y}}}$ and in the last line that ${\displaystyle R_{{\vec {\omega }}t}{\dot {\vec {x}}}_{\mathrm {in} }(t)={\dot {\vec {x}}}_{\mathrm {rot} }(t)+{\vec {\omega }}\times {\vec {x}}_{\mathrm {rot} }(t)}$ and Newton's second law in the inertial frame. The first statement is easy to check if done explicitly. The second statement basically is just line four of the argument. Here the derivation of the transformation formula if ${\displaystyle {\vec {\omega }}}$ is not the angular velocity of ${\displaystyle {\vec {x}}_{\mathrm {in} }(t)}$. ( TimothyRias ( talk) 14:06, 13 May 2008 (UTC))

No Timothy, this is just another elaborate deception. The same vector triangle applies. You can't claim that the particle in question has a different angular velocity from the rotating frame simply by stating this to be the case before the derivation begins.

Sure you can. ${\displaystyle {\vec {\omega }}}$ has no a priori relation the particle we are describing. It is just a parameter defining the the coordinate transformation that we are going to make. Clear this cannot in anyway be restricted by the particle trajectory in the inertial frame. Nor can the particle trajectory in the inertial frame be affected in anyway by the choice of coordinate transformation that we are going to make. To be brief the parameter ${\displaystyle {\vec {\omega }}}$ and the trajectory ${\displaystyle {\vec {x}}_{\mathrm {in} }(t)}$ are completely independent. In particular we can choose ${\displaystyle {\vec {\omega }}}$ not to be equal to ${\displaystyle {\frac {{\vec {x}}_{\mathrm {in} }(t)\times {\dot {\vec {x}}}_{\mathrm {in} }(t)}{|{\vec {x}}_{\mathrm {in} }(t)|^{2}}}}$, the angular velocity of the particle. The derivation above after this just proves that your assertion that "rXω must be the tangential component of v" is plainly false. Since you have provided no argument for that statement whatsoever, maybe it is just time for you to admit that you are wrong? Or else you might want to try to give an actual prove of your ridiculous claim. ( TimothyRias ( talk) 08:33, 14 May 2008 (UTC))

The derivation ensures that the angular velocity of the particle and the frame must be the same because as soon as we end up with one component of velocity given by rXω, then it must be tangential. And as such, the other component then has to be radial. 118.175.84.92 ( talk) 16:26, 13 May 2008 (UTC)

Elaborate deception? So anybody that thinks differently to you on this topic is lying?- ( User) WolfKeeper ( Talk) 21:55, 13 May 2008 (UTC)

FyzixFighter, the orbital equation is found widely throughout applied maths textbooks. It takes the form,

-GM/r^2 + v^2/r = r double dot

It solves to give an ellipse, parabola, or hyperbola.

The inward -GM/r^2 term is the centripetal force. The outward v^2/r term is the centrifugal force. They both work together in the radial direction in tandem with each other.

I have been accused by two administrators of introducing unverified material by virtue of mentioning this information. That shows me that the editors that are dominating this page know very little about the subject matter. David Tombe ( talk) 08:01, 6 May 2008 (UTC)

Yes, that is one way to write the orbital equation. However, it can also be written,

-GM/r^2 = r double dot - v^2/r

The only difference between this way and the way you wrote it is that I grouped all the (radial) acceleration terms on the right hand side. If applied math textbooks do write it the first way, then the question is what physical significance do they give the terms? By the way, what's a good applied math textbook that treats this problem as I would truly be interested to see how applied maths treat it? Back to the equation -

1) Since r double dot is not the radial acceleration, then

2) the left hand side is not the net force.

3) When the right hand side is made to be the radial acceleration (r double dot - r*(theta dot)^2) (and multiplied by the mass) then

4) we can call everything on the left hand side a force. When this is done for the orbital equation, the net force is found to be simply -GMm/r^2.

So where in this reasoning do we disagree, or rather, where does a reliable source disagree with this reasoning. -- FyzixFighter ( talk) 15:22, 6 May 2008 (UTC)

FyzixFighter, Let's leave names and terminologies out of it altogether. We have a second order time differential for the radial distance from the focus. Call it acceleration if you like, or don't call it acceleration if you don't like. That second order differential term is equated to two other terms. One is an inward acting GM/r^2 term. Call it gravity if you like. Don't call it gravity if you don't like. We also have an outward acting v^2/r term. Call it whatever name you like. But one thing is sure. Both of these terms are very real. They are both radial, and they both act in opposition to each other. That's what planetary orbital theory is all about. It could be correctly said that one of these terms is the centripetal force and the other is the centrifugal force. That second order differential equation is difficult to solve, but it has been tackled over the last couple of hundred years by the top applied mathematicians and there are a number of ways of solving it. I have seen at least two methods. The one that I actually had to learn for my exams involved substitution and we ended up with a new variable U. The derivation went for at least a couple of pages. Maybe even three or four pages. The final result is the geometrical expression for a conic section. There will be two arbitrary constants in that expression. One is the semi latus rectum and the other is the eccentricity. When we know the initial speed, position, and direction, we can work out what these two constants are and that tells us the exact shape of the conic section. If the eccentricity is less than 1 we will have an ellipse. A circle is a special case of the ellipse. If we have an eccentricity that is equal to 1, we get a parabola. In other words, the object has escaped from closed orbit. If we get an eccentricity greater than 1, we will have a hyperbola. If you want to study this topic in more detail, I advise you to first of all brush up on the geometry of conic sections in polar coordinates. After that, you should find the orbital equation in any good undergraduate classical mechanics textbook. Goldstein probably has it. Here is another point of interest. There is a theorem which dircetly links Kepler's law of areal velocity to the tangential terms of the general acceleration vector which you quoted. That gets rid of both the Euler force and the Coriolis force. Gravity orbits are a zero curl affair. To have Coriolis force, we need a curl. But let's get back to the original point. Thanks to SCZenz's comments to the anonymous, I now know that my mathematical reasoning does not need any citations. For a circular motion to occur, the second time differential of the radial distance must equal zero. Hence the sum of v^2/r and the inward centripetal force must equal zero. In the artificial circle, which is purely an artifact and doesn't involve any centrifugal pressure at all, your team have been arguing that the outward centrifugal force v^2/r is counterbalanced by an inward acting Coriolis force. This is nonsense on a number of counts. The Coriolis force never acts radially. The Coriolis force and the centrifugal force are always mutually perpendicular. Do you remember the acceleration expression which results if we act directly on v? It is vXω. That is the parent force of both Coriolis and centrifugal before it gets expanded into two mutually perpendicular components. Also,even if your team are correct and we can make the Coriolis force act radially inwards, then the result will be twice that of the centrifugal force. So the second order time differential of the radial distance will not be zero. Hence we can't have a circular motion. Those transformation equations are only designed to deal with actual rotation. To invoke the Coriolis force we need a physical curl such as we get in hydrodynamics when an element of a rotating fluid moves radially inwards (or outwards) within itself. David Tombe ( talk) 04:55, 7 May 2008 (UTC)

I suggest you submit your physics reasoning to a physics journal, so that after it is published we can use it to explain to the readers of the wikipedia how David Tombe overturned basic physics.- ( User) WolfKeeper ( Talk) 05:01, 7 May 2008 (UTC)

Some remarks:

• The orbital equation in question is not a vector equation, it is just the EoM for the radial coordinate in polar coordinates. Any mumbling about terms being (not) radial is thus just gibberish since the terms have no direction.
• The v in the equation is somewhat misleading. It is not the speed of the orbiting object, it is r times phi dot; the tangential speed of the object. The equation is better understood in terms of l = r v the angular momentum per unit mass.
• The v term can be thought of an fictitious force induce by co-rotating coordinates. It encompasses components contributitions from the centrifugal, Euler and Coriolis forces.

( TimothyRias ( talk) 09:09, 7 May 2008 (UTC))

Timothy, all that was just a quible. It bore no relationship to the point I was making to FyzixFighter. I'm fully aware of the fact that I used 'short cut' symbolism. I was merely trying to drive home the point that two opposing effects work in opposition to yield the second order time derivative of the radial distance. David Tombe ( talk) 09:35, 7 May 2008 (UTC)

The current introduction ends with the sentence, Colloquially, the term "centrifugal force" is sometimes also used to refer to any force pushing away from a center; this article discusses only the centrifugal force related to rotating reference frames. So where is the page on colloquial centrifugal force? That's the page the readers want. This sentence is effectively the same as saying, If you are looking for centrifugal force, you have come to the wrong page. David Tombe ( talk) 06:12, 7 May 2008 (UTC)

That would be an incredibly short article, since the above sentence says pretty much everything there is to say about that use of the term. Namely, that it refers to an outward pointing force. ( TimothyRias ( talk) 08:31, 7 May 2008 (UTC))

I could certainly trim a single article on centrifugal force down to a few key points. David Tombe ( talk) 09:36, 7 May 2008 (UTC)

I think the current article could probably do with a section devoted to the colloquial use of the term. There are probably somethings that need to be explained with that respect. ( TimothyRias ( talk) 11:04, 7 May 2008 (UTC))

Probably everything to do with centrifugal force. David Tombe ( talk) 11:32, 7 May 2008 (UTC)

It seems to me like the discussion of the colloquial "centrifugal force" in an inertial frame might belong on the page Centripetal force, which is already dealing with the situation of rotation in an inertial frame? Perhaps we could add a note to that sentence accordingly? (And make sure that the centripetal force article has a good enough discussion.) Also, regardless, that sentence should probably read: "any "force" pushing away from a center", with scare quotes around force, since it's not a force in the technical sense. Oops, let me rephrase for David: ...since reliable sources say that it's not a force in the technical sense. :-) -- Steve ( talk) 16:57, 7 May 2008 (UTC)

I want to see the peer reviewed proof that justifies the statements made in the main article. These need to be peer reviewed journal articles or reccomendations from a physics education committee and cited in the main page. As far I can determine, there is no peer reviewed, critically examined proof of what is said in the main article. Citations which refer to sources that repeat or draw conclusions from other unproved sources are not acceptable. I want to see the actual real proof, not hearsay that it exists in theory. 72.64.51.14 ( talk) 16:03, 7 May 2008 (UTC)

Wikipedia has specific guidelines on what constitutes a reliable source. Most of the statements in the article are in essentially every intro university-level physics textbook, and every dedicated classical mechanics textbook, which are gold-standard reliable sources according to those guidelines. Are those good enough sources for you? If so, please point out any specific statements that you doubt, and it will be a straightforward task for me or you or anyone else to provide specific textbook references for them. If not, then your standards of proof are different than Wikipedia's, and this is not the right forum for you to be posting that request. This page only exists for the purpose of making this Wikipedia article a better article according to Wikipedia's own standards. :-P -- Steve ( talk) 16:34, 7 May 2008 (UTC)

Translation, you don't really know if what you state in the article is verified by a peer reviewed journal article or not, just as I suspected. Since it is clear that you don't have the proof as required by standard scientific procedure, it is a justifiable conclusion that this article is making nonscientific false statements. Again, please produce the proof from a peer reviewed journal article or physics education report that justifies the statements made in main article. 72.64.51.14 ( talk) 18:54, 7 May 2008 (UTC)

This is the wikipedia. If you have any reliable sources that show that can show that centrifugal force and coriolis force are defined or derived incorrectly, then by all means give it here. If you can't understand the standard proofs, then that's not our problem in any way, shape or form.- ( User) WolfKeeper ( Talk) 19:03, 7 May 2008 (UTC)

Textbooks are a perfectly fine source. Peer review journals except references to textbooks, so why shouldn't wikipedia? If anything, textbooks usually provide much more extensive proofs of statements, whereas journal articles usually state "after some simple algebra..." ( TimothyRias ( talk) 20:41, 7 May 2008 (UTC))

Thank you. As I understand it, you are officially stating that Wikipedia does not have a peer reviewed journal paper or physics education committe report to validate what you state in the main article. Therefore, I demand that you accept Mr Tombe's edits as valid edits, since you have failed to prove him to be wrong. He has produced textbook citations which back up his position, while you have produced nothing to validate your opinions. Evidently Wikipedia policy has failed in this case to produce the required proof to support the claims made in the main article. I insist that you correct the mistakes in this article, and allow Mr Tombe to make edits to this article. You have totally failed to prove him to be wrong and your actions and behavior are certainly objectionable in this matter, as you have behaved unfairly and rudely to him. You also need to correct these and apologise to him officially. 72.64.51.14 ( talk) 21:40, 7 May 2008 (UTC)

As far as I see, Mr Tombe has not produced any textbook citations to back up any part of his position. Other editors have. Take for example "Analytical Mechanics", Hand & Finch pg 267 (1998); Oxford's "A Dictionary of Physics" (1996); "McGraw-Hill Dictionary of Physics" (1984) to name a few that support the current consensus version of the article. -- FyzixFighter ( talk) 23:00, 7 May 2008 (UTC)

FyzixFighter, I refered you to Goldstein's Classical Mechanics. There, as well as in many other applied maths textbooks, you will see the orbital equation which I described to you above. That equations makes it clear that the second time derivative of radial distance is only zero when we have two opposing forces cancelling each other out, one of which takes the form v^2/r outwards.

Anome never demands citations from other peoples' edits. He only demands citations for my edits. And when I give citations, he ignores them and continues to demand citations.

When I give maths reasoning, I get the red card held up against me. When Timothy Rias gives maths reasoning, SCZenz comes in to say that it's all fine. David Tombe ( talk) 06:29, 8 May 2008 (UTC)

Thank you gentlemen. You have again failed to meet the minimum requirement of proof in science. That is a peer reviewed journal article that has been reviewed, discussed, debated, and validated. You have no physics education committe report that produces reccomendations, resulting from physics education studies, and justified by a peer reviewed journal paper that scientifically validates that what you write in the main article is correct. You are basically citing only opinion, and that opinion is not validated by any scientific procedure that I can determine. Therefore your main article claims are false and invalid and Mr Tombe has very right to dispute them and insist that they be changed. Your refusal to permit this is an injustice to him. Wikipipedia needs to correct this officially. I far as I can see Wikipedia policy has been officially used to abuse and insult Mr Tombe and that injustice needs to be corrected. Your failure to produce the required proof is a disgrace. 72.84.68.195 ( talk) 13:38, 8 May 2008 (UTC)

I can't get my hands on Goldstein's at the moment. But in the mean time while I'm getting my hands on a copy, here's something from "Intermediate Classical Mechanics" Joseph Norwood Jr, pg 196 (1979 published by Prentice Hall):

"Suppose, as an example, that a body rotates about the sun. The only real force is the force (gravitational in the case of the earth and the sun) toward the center. An observer on the rotating body notes that the body does not fall toward the center. In order to reconcile this observation with the requirement that the net radial force vanish-that is, that the circular orbit be maintained-the observer postulates an additional force, the centrifugal force. This is an artificial construct that arises solely from our wish to extend Newton's second law to a noninertial system. The same comments apply to the Coriolis force; this force is necessary to describe motion relative to the rotating body."

I'm pretty sure that this satisfies WP:RS. -- FyzixFighter ( talk) 15:27, 8 May 2008 (UTC)

Citation for Taylor? That quote looks good to me. A lot of this book is on line at Taylor. I think it is worth referencing - do you have a page number? Brews ohare ( talk) 16:30, 8 May 2008 (UTC)

FyzixFighter, I don't think that Goldstein will overtly recognize centrifugal force either. It will adopt the same attitude as your book and work on the premises that gravity is the only force involved. But when the chips are down and the orbital equation appears, there will be two terms acting in opposition to each other in the radial direction. There will be a gravity term acting radially inwards and a term of the basic mathematical form v^2/r acting radially outwards. Whatever that v^2/r is, it is certainly not an artificial construct and it certainly doesn't arise because of any human desires as your book seems to suggest. It works in tandem (opposition) with gravity to produce conic section orbits.

A high quality textbook will generally remain silent on the issue of what this term actually is. It will be quietly borrowed from that general acceleration equation that we have been looking at. And as you must surely be aware, that general acceleration equation merely exposes inertia in the Cartesian frame to be the centrifugal force and the Coriolis force in a polar frame.

Yes, you are correct in that no modern textbook is likely to overtly declare the centrifugal term to be real. In fact, your book's declaration that it is artificial should surely alarm you. To claim such with regards to that scenario is the height of delusion.

Now I'd like to draw your attention to this line in your reference,

In order to reconcile this observation with the requirement that the net radial force vanish-that is, that the circular orbit be maintained

Now consider the artificial circular motion which is associated with viewing a stationary object from a rotating frame. How does it reconcile with this requirement? According to the 'Fictitious party' there is a radially outward centrifugal force and a radially inward Coriolis force that is twice as large. Yet if we are to have a circular orbit the centripetal force and the centrifugal force must be balanced.

The reality is that the equations for the coordinate frame transformation are only designed to cater for co-rotating objects. This condition is totally satisfied in meteorology.

Can you show me an explicit citation stating that these equations apply to objects that are stationary in the inertial frame. I wouldn't be entirely surprised if you could. But nevertheless, I would like to see it explicitly stated in a book. I have a feeling that the restriction to co-rotation has been overlooked by many people who have been introduced to these equations, and the error has been passed on from textbook writer to textbook writer.

Or perhaps the error isn't even in the textbooks and the mistake lies entirely with the readers. That's why I'd like you to find an explicit reference which overtly states that these equations apply to objects that are at rest in the inertial frame. David Tombe 119.42.65.152 ( talk) 16:11, 8 May 2008 (UTC)

Nobody ever mentions frames of reference when they describe the effects that take place due to centrifugal force inside a swerving car. They talk about these events as they stand in their kitchen, which is an inertial frame, and they state that as the car swerved around the corner, they got flung to the side door.

It is a matter of opinion which I don't subcribe to, to state that these events are more conveniently described from a rotating frame of reference. No such frame is needed in the description. When have you ever heard anybody going to the bother of explaining that as they viewed things from within the car, they were accelerated twoards the side door. The man standing watching it from the street saw exactly the same thing.

lol. But the man watching from the street saw no flung. All they saw was linear momentum. And describing what happened in the car is describing it from the frame of reference of the car- which is an accelerating frame.- ( User) WolfKeeper ( Talk) 17:10, 7 May 2008 (UTC)

Such an argument however does not necessarily extent to the Coriolis force in relation to meteorology. 119.42.69.123 ( talk) 16:16, 7 May 2008 (UTC)

lol- ( User) WolfKeeper ( Talk) 17:10, 7 May 2008 (UTC)

Wolfkeeper, the man in the street is quite capable of observing a radial acceleration towards the side door. We don't need to consider a rotating frame of reference to observe this. David Tombe ( talk) 06:23, 8 May 2008 (UTC)

But the man isn't corotating. Why does he move towards the side door?- ( User) WolfKeeper ( Talk) 07:10, 8 May 2008 (UTC)

Wolfkeeper, the man in the street sees the man inside the car getting flung to the side door. David Tombe ( talk) 09:55, 8 May 2008 (UTC)

I repeat, the man in the car isn't corotating with the car, since he's on a skiddy seat, why does he get flung to the side door inside the car? According to you, centrifugal force only happens in corotation. If he's not rotating (the man on the street says he's going in a straight line!), then there's no centrifugal force is there?- ( User) WolfKeeper ( Talk) 10:09, 8 May 2008 (UTC)

Wolfkeeper, the man in the car is co-rotating. The back of his seat pushes him tangentially. This induces a vXω force radially. If he wasn't co-rotating with the car, he wouldn't be in the car, and he wouldn't be experiencing any outward tangential force.

And yes, this radially outward acceleration translates into straight line motion in the Cartesian frame. Centrifugal force in the polar frame is the same thing as inertia in the Cartesian frame.

Look at the conversion equation. Then remove the tangential components because of Kepler's law of areal velocity. Centrifugal force stands out as an inbuilt feature of straight line motion. David Tombe 119.42.65.152 ( talk) 16:32, 8 May 2008 (UTC)

Hi everyone. I understand that there are already textbook references that support the current version of the article straight down the line. However, it would be helpful if users would add in-line citations to sections that are being "warred" over. Talk page discussion is not settling this "argument"; I think administrative action will, but the case for administrative action is far stronger if directly-cited statements are being removed. I am willing to use my knowledge of physics to evaluate whether a source actually supports a statement, but not to treat a statement as cited just because I personally know it's correct and that it could be. So if instead of just reverting, you would consider in-line citations for the statements you re-add, it would save us all time in the end! -- SCZenz ( talk) 07:30, 8 May 2008 (UTC)

What about the Goldstein classical mechanics textbook reference that states the orbital equation and shows that the second order time derivative of radial distance arises from an inward acting gravity term and an outward acting centrifugal term? Why is that not allowed as evidence that centrifugal force is real?

What about the Bernoulli and Maxwell references that show that they believed centrifugal force to be real?

And why should we need any references at all to state that centrifugal force is connected with rotation? David Tombe ( talk) 10:13, 8 May 2008 (UTC)

I notice that Timothy Rias has responded to this message by filling up the introduction with references for matters which are not in dispute. That is a bad sign. It shows that he has lost sight of the higher picture. David Tombe ( talk) 10:32, 8 May 2008 (UTC)

In reply to the above statement. I can provide just as many textbook references that contradict what is stated in the main article. Therefore I must conclude, that since I have just as many references that contradict what you say, then what you say is not justified by your selection of certain references that agree with what you beleive. That is not science. So you need to prove what you say is true, and you have not done it. 72.84.68.195 ( talk) 14:25, 8 May 2008 (UTC)

If you can provide such textbook references, please do so. -- SCZenz ( talk) 22:29, 8 May 2008 (UTC)

Wolfkeeper, I am fully aware of the fact that the Coriolis force doesn't involve any change in kinetic energy. But the Coriolis force does not occur in a zero curl field. There is no vorticity in the gravitational field that could invoke the Coriolis force. Kepler's law of areal velocity eliminates the Coriolis force from gravitational problems.

Curl is a measure of the sum of forces around a circle in a field of force. If a force sums to zero- then it creates no change in energy, and conversely if it sums to non zero, then it is non conservative. Coriolis creates no change in energy and hence has no curl.- ( User) WolfKeeper ( Talk) 20:13, 8 May 2008 (UTC)

There is however Coriolis force in hydrodynamics because there can be vorticity. The ω is to all intents and purposes the vorticity. David Tombe ( talk) 10:24, 8 May 2008 (UTC)

Oh sure, vortexes have curl. Stick a windmill in a vortex, and you can generate energy, no problemo. But the coriolis force due to that vortex motion does not.- ( User) WolfKeeper ( Talk) 20:13, 8 May 2008 (UTC)

Whether or not the curl of vXω is equal to zero is irrelevant. Kepler's laws eliminate the Coriolis force from all planetary orbital theory. 119.42.68.141 ( talk) 10:11, 9 May 2008 (UTC)

I have just blocked David for 31 hours for reinsertion of the same unreferenced assertions as before (see this diff), in spite of extensive warnings regarding the need to adhere to Wikipedia's polices. David, you are welcome to edit again when the block expires, but please try to edit according the WP:V and WP:NOR policies; that is to say, please provide verifiable cites to third-party reliable sources that back up your assertions. -- The Anome ( talk) 11:00, 8 May 2008 (UTC)

Sir, Again you have created an injustice with respect to Mr Tombe. As stated above, what you state in the main article is false, and Mr Tombe has every right to dispute it. Your policy is a disgrace as I stated above. You need to correct your behavior in this matter. Mr Tombe has clearly stated his sources on this talk page and you have none to prove him wrong. You need to produce the proof and you have not produced it. 72.84.68.195 ( talk) 13:54, 8 May 2008 (UTC)

The burden of proof lies with the person making the claim, and the consensus point of view, by contrast, meets this requirement by already providing multiple supporting cites to reliable sources. Since I cannot find the sources you are referring to above on his talk page, other than the Maxwell and Bernoulli quotes already excluded by the WP:SYN policy, I would appreciate it if you could tell me what they are. Something like a physics textbook or peer-reviewed paper saying "centrifugal force is a real, not fictitious, force" would meet the requirements just fine. The mere use of the concept of centrifugal force will not, since, as the mainstream opinion expressed in the consensus version of the article states, using the concept of a fictitious centrifugal d'Alembert force is a perfectly legitimate verbal and computational shorthand for describing many simple rotating physical systems, without any implication that it should be confused with an actual physical force (which, for example, would conserve momentum, unlike the fictitious centrifugal force). -- The Anome ( talk) 18:08, 8 May 2008 (UTC)

Thank you for your answer. I take your answer to mean that you are making excuses for the fact that you do not have the demanded proof and that you feel entirely justified in treating Mr Tombe unfairly as a deliberate policy of Wikipedia. You have answered my demand by making a counter demand, and that is not a valid procedure in a debate. I ignore your demand, since I make no assertions other than that you produce the required proof and apologise to Mr Tombe, since he is certainly justified in disputing what is stated in Wikipedia, when you have not produced a satisfactory proof that what you say is valid physics.

The issue now at hand is a simple matter of your proving your case not me proving my case. I am simply demanding that you prove your case in order to justify that what you say in the subject article on centrifugal force is true. This is what Mr Tombe disputes and your editors response demonstrates that they did not do the investigation required to back up what they state has actually been proved. This could have been easily accomplished if you had editors who were competent to do it, and not prone to nasty, offensive and rude, disputation. It is now certainly clear that there is no proof of what your editors claim is true, and that you should not be supporting them, but instead demand that they produce the proof, or stop disputing what Mr Tombe says in a nasty manner. You respond to my simple request for proof in the same manner as you did with Mr Tombe, rudely. The issue is the question of the justification of certain revisionist statements of physics, and the request is simply that you produce peer reviewed journal papers, and physics education committee reports that prove what you say is actually true and not a mistake in the opinion of certain writers from which your editors have uncritically copied statements in physics. I look forward to your providing these required proofs and an official apology from you to Mr Tombe. 72.64.50.119 ( talk) 22:21, 8 May 2008 (UTC)

Citations given in the current version of the article

The article cites five independent sources for the consensus content:

1. Wolfram Scienceworld website.
2. Britannica online encyclopedia.
3. Stephen T. Thornton & Jerry B. Marion (2004). Classical Dynamics of Particles and Systems, 5th Edition, Belmont CA: Brook/Cole, Chapter 10. ISBN  0534408966.
4. John Robert Taylor (2004). Classical Mechanics. Sausalito CA: University Science Books, pp. 343-344. ISBN  189138922X.
5. Vladimir Igorevich Arnolʹd (1989). Mathematical Methods of Classical Mechanics. Berlin: Springer, §27 pp. 129 ff.. ISBN  0387968903.

URLs and page references are provided in the article itself.

• Wolfram Scienceworld is a well-regarded resource edited by Eric W. Weisstein, who is a PhD-educated planetary astronomer and physicist. It is published by Wolfram Research, famous for their Mathematica software, and for their founder Stephen Wolfram.

• The Encyclopædia Britannica is the world's highest-regarded English-language general encyclopedia.

• John Robert Taylor is Professor of Physics at the University of Colorado in Boulder. You can see the book's back cover for his other credentials. His book is available online, so you can read the cited sections directly.

• Vladimir Igorevich Arnolʹd is a famous and highly esteemed mathematician. He works at the Steklov Mathematical Institute in Moscow and at the University of Paris IX. As of 2006 he was reported to have the highest citation index among Russian scientists, and an h-index of 40. His list of mathematical awards and other honours is too lengthy to list here. He solved Hilbert's 13th problem at the age of 19. See this biography for more details.

I'm sure the credentials of Stephen T. Thornton & Jerry B. Marion can be tracked down with similar ease, but I don't have the time to do so right now.

In each case, each work has a publisher that is independent of its author. The combination of all of these sources more than suffices to comply with the Wikipedia:Verifiability policy, as well as WP:NOR and WP:NPOV, which is all that is required here.

-- The Anome ( talk) 22:58, 8 May 2008 (UTC) [updated with more details 23:45, 8 May 2008 (UTC)]

Your answer is not responsive to the demand. I repeat produce the proof as required, and apologise to Mr Tombe for the nasty behavior of your editors. 72.64.50.119 ( talk) 23:04, 8 May 2008 (UTC)

Please read Wikipedia's WP:NPOV, WP:V and WP:OR policies, which are the relevant principles to be applied here. If you would like to start a new encyclopedia which conforms to your ideas of how an encyclopedia should be run, you are welcome to do so. -- The Anome ( talk) 23:08, 8 May 2008 (UTC)

From this I conclude that nastiness is a policy of your encyclopedia and that misinformation is also a deliberate policy, since one needs a reference to correct misinformation, and that is not possible if you are misrepresenting cited references. So it is fundamentally a hopeless task to correct you when you are wrong, since by definition, your rules make it impossible to correct your errors. 72.64.56.156 ( talk) 16:13, 17 May 2008 (UTC)

Perhaps the discussion at Taylor, p. 358, which seems to cover many of the points raised, and can be viewed at Google books, would help to settle the disputes. Brews ohare ( talk) 19:56, 8 May 2008 (UTC)

That seems to be a good general reference for many articles, including this one, fictitious force, and Coriolis force. Of course, many textbooks would, but the fact that it is available online makes it very accessible to readers. Whether this will settle any disputes remains to be seen. But one way or the other this place is going to calm down eventually. Until then, I will for my part avoid discussing physics, and only discuss whether particular edits are supported by reliable sources or not. In the end, that is what really matters here on Wikipedia. -- PeR ( talk) 20:38, 8 May 2008 (UTC)

There are clearly at least three interpretations of the term "Centrifugal force"

1. A pseudo force
2. A reaction force as described in reactive centrifugal force
3. Any (real) force that is directed away from the center of rotation

I think most people here will agree that the most common interpretation of the term "Centrifugal force" is the pseudo force. The question is, how important are the other two interpretations? I'm beginning to think that maybe giving the second one its own article is undue weight when in fact it is just a small minority that uses it in that precise sense. Note that the second interpretation is a subset of the third, so in most cases you can't tell from a quote that it only implies the second meaning and not the third. There are some cases where it would clearly be strange to use the term as in the second interpretation. For example, consider a binary star. For star A, the gravity from star B provides a centripetal force. Consequently, the gravitational pull on star B from star A would be the "reactive centrifugal force" even though it is not acting away from the center of rotation.

My conclusion is that both interpretations 2 and 3 are significant enough to warrant inclusion in this article, perhaps in an "etymology" section, but neither is important enough to have its own article. -- PeR ( talk) 21:00, 8 May 2008 (UTC)

I'd agree. The main advantage of separate articles just now is to avoid the imbroglio. Brews ohare ( talk) 22:11, 8 May 2008 (UTC)

Under the rules of an encyclopedia an encyclopedia is supposed to have a topic, and describe it well; and it's not supposed to be a 'different meanings of a phrase'. The only major connection I can really see between them is the same name; and that's specifically excluded under wp:NOT- ( User) WolfKeeper ( Talk) 23:38, 8 May 2008 (UTC)

Lots of wikipedia articles have etymology sections, and some of those include archaic meanings of the term. (See, for example, stereotype.) So the question is really whether reactive centrifugal force is an important concept today (in which case it should have its own article) or just an archaic term (in which case a mention in an etymology section will suffice). -- PeR ( talk) 07:02, 9 May 2008 (UTC)

I've just been scouting around for some more citable references.

Here's a peer-reviewed paper that describes centrifugal force as fictitious, for those that insist that only peer-reviewed sources are valid: Merab Gogberashvili, Coriolis Force and Sagnac Effect, Found.Phys.Lett. 15 (2002) 487-493. Quote: "In the rotating frame two fictitious gravity-like forces appear, namely the centrifugal and Coriolis forces. This is an illustration of the equivalence principle, which asserts that gravity and the accelerated motion are locally indistinguishable."

And for those who like citation by independent third-party reviews of the field, and/or appeals to authority: Richard Feynman, quoted in The Natural Philosophy of Leibniz by Kathleen Okruhlik, James Robert Brown (Springer, 1985, ISBN  9027721459, page 138) as saying (referring to rotation and centrifugal force) "These forces are due merely to the fact that the observer does not have Newton's coordinate system, which is the simplest coordinate system." -- The Anome ( talk) 00:40, 9 May 2008 (UTC)

Anome has totally misrepresented what the edit war is about. He has presented this war as being over the issue of whether or not centrifugal force is real.

The war is not about whether or not centrifugal force is real, although that did become a side issue when Anome opened up a special section entitled 'Is the centrifugal force real?'.

The war is not about whether the term fictitious force is applied to centrifugal force in the textbooks. We all know that it is.

The war is about the fact that all attempts to mention the cause of centrifugal force get instantly erased from the article. That cause is rotation. And we don't need any citations to back up that assertion because it is a well known and undisputed fact. 58.147.58.54 ( talk) 06:19, 9 May 2008 (UTC)

David, you are not allowed to evade a block by not logging in. When you do that, an admin may reset your block, and the IP that you are editing from may also be blocked. -- PeR ( talk) 07:08, 9 May 2008 (UTC)

58.147.58.54 is not David Tombe, I don't think. 119.42.65.152 is and has been blocked. The way, the truth, and the light ( talk) 07:43, 9 May 2008 (UTC)

According to whois, both of those IP-addresses are from the same area. My guess is that one is dialup and the other is from an internet café. But of course there is a nonzero probability that there are two different people who live in the same area, share the same views on this subject, and have very similar editing style. -- PeR ( talk) 07:58, 9 May 2008 (UTC)

(I think that discussing with David Tombe and its (virtual?) defenders is a complete loss of time. Not only he obviously does not have a clue about this topic, but is completely unwilling to try understanding what people tell him. Anyway...) There is no cause for the centrifugal force! It just appears (together with other virtual forces) when you compute the acceleration of a body as seen from a non-inertial frame of reference, and want to interpret this acceleration according to Newton's law (i.e., as being due to forces acting on the body). Then obviously, you get, additionnaly to the real forces possibly acting on the body, additional terms (corresponding to virtual forces) which are merely due to the fact that the observer is in a non-inertial frame of reference (for example rotating). And of course it does also apply to objects that are at rest w.r.t. some inertial frame of reference (and would be seen as moving from the non-inertial one as if subjected to some forces (that do not really exist, that's why they are called virtual forces)). That's a completely obvious mathematical fact, and certainly not the source of any debate among people with any real understanding of physics...-- 129.194.8.73 ( talk) 08:17, 9 May 2008 (UTC)

129.194.8.73, Does a centrifuge work if it is not rotating? 119.42.68.141 ( talk) 10:05, 9 May 2008 (UTC)

Just to clarify: the matter currently at issue is not whether centrifugal force is real or fictitious, caused or uncaused, or any other issue related to content. The only issue now on the table is whether statements can be attributed to and supported by verifiable reliable sources, according to the WP:NPOV, WP:V and WP:OR core policies. The "orthodox" side of this dispute have now produced extensive cites to reliable sources that support their position that their view is the standard physical interpretation of the apparent phenomenon of centrifugal force. Their opponents, who have now been given ample opportunity to do so, have not so far provided evidence even that their point of view represents a significant minority point of view, preferring to simply replace the consensus point of view with their own on the basis that it is indisputably true. This is not in accordance with Wikipedia's policies for editing on disputed topics, and its continuation is now becoming disruptive to maintaining those policies. A request to provide sources is not unreasonable; continuing this editing behavior without doing so, in direct opposition to Wikipedia's policies, is. -- The Anome ( talk) 11:05, 9 May 2008 (UTC)

Anome, absolute nonsense. I'll ask you one single question,

Does a centrifuge work if it is not rotating?

The answer is 'no'.

Nowhere in the whole article does it say that the real effects of centrifugal force arise due to actual rotation. I tried to insert it yesterday and you blocked me and reverted the clause.

That was a very bad management decision and it was done on a false pretext. It had got absoloutely nothing to do with references, and besides that, I did give a reference to the wikipedia page on the Bucket argument which illustrated the point that co-rotation situations give actual effects whereas observing a stationary object from a rotating frame yields no effects.

You are pandering to a group such as the anonymous 129.194.8.73 above who are clearly not living in the real world. His mind is focused entirely on how a stationary object appears from a rotating frame of reference. And he deduces from that, that because the effect is artificial, that then it must be artificial for all cases including the centrifuge.

And you know that the effect is not artificial in a centrifuge. And you know that the centrifuge effect only occurs when the centrifuge is rotating.

So you blocked me on totally false grounds. It had got nothing to do with citations. The wikipedia rules clearly state that no citations are needed for obvious facts. And it is obvious that a centrifuge only works when it is rotating.

As for PeR's whinning about me evading the block, I never went unto the main article. How am I supposed to answer a hail of questions coming at me on the talk pages if I'm blocked from editing? PeR is actually the root cause of this entire problem because he is the arch-fictitiousist who is desperate to conceal the cause and effect aspect of centrifugal force. David Tombe 119.42.68.141 ( talk) 12:17, 9 May 2008 (UTC)

Unfortunately, Wikipedia articles do not count as a reliable source when providing references to support assertions made in other Wikipedia articles. Please supply cites that meet the WP:RS criterion needed to meet the WP:V policy.

Regarding blocks; you are supposed to wait until the block expires. As per policy, the IP above has now been blocked for 31 hours for self-admitted block evasion, resetting the earlier block; please come back when the block expires. Further block evasion will result in progressively longer blocks being applied. -- The Anome ( talk) 12:42, 9 May 2008 (UTC)

Actually, I don't think there's precedence for prolonging a block just for evasion. Only resetting, and blocking the IP.

David, please stop saying that people are "whining" or "not living in this world" or similar. I've told you before: Comment on content, not the contributor. Uncivil edits can get you blocked, or your block prolonged.

-- PeR ( talk) 15:12, 9 May 2008 (UTC)

You're quite right. Resetting, and blocking the IP, is the appropriate procedure. Which reminds me: I just blocked the IP and didn't reset the block. Since the IP edit above was 6 hours ago, I believe this means that David's now-reset block should have another 31 - 6 = 25 hours to go: I'll take an extra hour off to cover any imprecision. Blocking accordingly. -- The Anome ( talk) 18:59, 9 May 2008 (UTC)

Does a centrifuge work if it is not rotating?

David: Everybody will agree that the centrifuge has to rotate. But the point is "How do you describe what is happening?" You have two choices to describe the rotating centrifuge: 1) Sit in the lab frame: the stuff in the test tube tries to stay still while the tube rotates. Relative to the moving tube, the stuff moves. 2) Sit on the centrifuge: the tube isn't moving, but the mysterious fictitious forces push the stuff down the tube. Brews ohare ( talk) 13:34, 9 May 2008 (UTC)

Brews, et al: I think it's become clear that it's a waste of time trying to explain the subject to David (unfortunate as that is). I've given up trying. On the positive side, all this has resulted in a lot of group effort to make the articles clearer and better referenced. Silver lining, eh ? Plvekamp ( talk) 13:45, 9 May 2008 (UTC)

I'd add to the positives that the treatment of centrifugal forces benefits from the view that rotating frames are just as real as inertial frames. It's just that we choose to describe the laws in inertial frames, for various reasons, some of the time. Brews ohare ( talk) 19:24, 9 May 2008 (UTC)

"A centrifuge is a device consisting of a rotating container in which substances with different densities are separated by centrifugal forces on the substances." "This force is opposed by the frictional force of the fluid on the particle." Page 123 The Encyclopedia Of Physics, R. M. Besancon. This source says basically what Mr Tombe has been saying in his edits which you removed and eventually blocked. Since there is now a valid citation supporting Mr Tombe's claims, you need to remove your blocks and apologise to Mr Tombe. 72.64.55.233 ( talk) 13:50, 9 May 2008 (UTC)

I have no objections to this quotation, which I interpret as adopting the "sit on the centrifuge" choice of description. Brews ohare ( talk) 14:20, 9 May 2008 (UTC)

We'll do no such thing, of course. The block is for violating policy by repeatedly adding material without citations, despite many requests and warnings; the existence of a citation somewhere is not the issue, but rather the disruptive editing pattern. I will leave it for the community at this page to evaluate whether this source supports Mr. Tombe's claims; it seems to me more of a case of imprecise language than a statement that centrifugal force is caused by a physical mechanism. -- SCZenz ( talk) 14:58, 9 May 2008 (UTC)

I interpret your answer to mean that you would have blocked Mr Tombe unfairly even if he had provided this as a citation, because you are rude and nasty editors at wikipedia and your managemant supports your bad behavior, which you just exhibited in response to this. I really dont think you can fairly blame Mr Tombe for not providing the citation, since you have already rejected every one that he has previously provided. When he provides a citation you disagree with, you revert his edits anyway. This is an abuse of your authority. Your actions are unfair, and you should remove the block on Mr Tombe. 72.84.76.230 ( talk) 00:41, 10 May 2008 (UTC)

If you really believe that, you should either raise this issue with other administrators or go away. If we were that evil, there would be no point in continuing your efforts here. -- SCZenz ( talk) 08:00, 10 May 2008 (UTC)

Evidently the procedure of going to the administrators to seek justice from wikipedia is the equivalent of asking you to approve of a citation. You only approve of those that support your narrow prejudices. 71.251.176.68 ( talk) 20:15, 10 May 2008 (UTC)

Proposed addition

In the section "is centrifugal force real" the following appears

Despite the name, fictitious forces are experienced as very real by anyone whose immediate environment is a non-inertial frame. Even for observers in an inertial frame, fictitious forces provide a natural way to discuss dynamics within rotating environments such as planets, centrifuges, carousels, turning cars, and spinning buckets.

To this sentence I propose adding:

For example, a description of the centrifuge from this viewpoint is: "A centrifuge is a device consisting of a rotating container in which substances with different densities are separated by centrifugal forces on the substances.…This force is opposed by the frictional force of the fluid on the particle." ^[1] See, for example, the article Lamm equation.

Any objections or modifications to this addition? Brews ohare ( talk) 15:16, 9 May 2008 (UTC) I implemented this change. Brews ohare ( talk) 19:44, 9 May 2008 (UTC)

All this rotation business makes things unnecessarily complicated when one wants to understand why the rotating bucket has hydrostatic pressure that the non-rotating bucket doesn't. There is an equivalent, much simpler experiment that only requires one to think in one dimension. Imagine that you have a friend sitting with his bucket of water in his spaceship, which is "standing still" (in an inertial frame of reference). You are in your own spaceship, with your own bucket, and your spaceship is accelerating away from your friend's. From your ship's frame of reference, you don't seem to be moving, yet your friend seems to be accelerating away from you. You explain his acceleration by means of a fictitious force that acts on your friend's spaceship. This fictitious force only exists in your frame of reference. Yet, your bucket will have weight, pressure and all that, while your friend's bucket will be floating freely inside his ship. This just goes to show the difference between inertial and non-inertial frames of reference, and that real forces (of the sort that make your bucket have weight and hydrostatic pressure) only relate to acceleration with respect to the inertial frame.

I have to agree with the majority that centrifugal force is a fictitious force and that the hydrostatic pressure in the rotating bucket is due to inertia (or acceleration with respect to an inertial frame of reference), same as the hydrostatic pressure in the bucket inside the accelerating spaceship. Didn't Einstein say that force due to acceleration was indistinguishable from gravity, by the way? -- Itub ( talk) 15:52, 9 May 2008 (UTC)

Sir you must surely be as confused as those with whom you profess to be in agreement. It seems all of you have become deranged. In your thought experiment, which is basically just a fictitious situation which does not really exist and can not exist, you suppose that because your spaceship is accelerating, but you dont know that fact, that it is reasonable for you to suppose that there is some fictitious force acting to explain that the other spaceship is accelerating. That is certainly a curious state of affairs. What your fictitious example shows is that if you are ignorant of your physical state you are certainly entitled to make false conclusions regarding the actual state of affairs about which you are ignorant. But of course, your reasonable false conclusion results from the fact that you don't have accurate knowledge of your physical state. Hence the hypothesis of a fictitious force arises from ignorance of the actual state of affairs and not from any valid concept of physics. 71.251.176.68 ( talk) 20:36, 10 May 2008 (UTC)

Can an example be provided to show what this statement means? For example, a book on a table exerts a gravitational force on the table that certainly results in a Newton's third law reaction by the table. This statement either should be supported by a clarifying example, or removed. What does it mean? In this connection, notice that the centrifugal force often is referred to as "artificial gravity" e.g. for astronaut training. See also Taylor. Likewise the statement that "they cannot be felt by a person subject to them" seems far-fetched. See also the point of view in Sedimentation. Brews ohare ( talk) 19:20, 9 May 2008 (UTC)

uhh, I don't get it. What needs explaining? Why did you take out the part about reaction force? There is no reaction counterpart to a centrifugal or coriolis force, unlike real forces. Rracecarr ( talk) 21:46, 9 May 2008 (UTC)

I've reverted some of the recent edits. I agree that some examples are good, but they should illustrate rather than confuse. Rracecarr ( talk) 22:04, 9 May 2008 (UTC)

If you create a rotating frame of reference 6 feet above the surface of the Earth, there's a massive centrifugal force on the center of the Earth in the rotating frame. This force has no equal and opposite reaction force (in that particular case there's the coriolis force, but it's twice as big- and it's not a 3rd law reaction; and there are other cases where there's no coriolis.)- ( User) WolfKeeper ( Talk) 22:09, 9 May 2008 (UTC)

Not intending to be argumentative, but can you go into some more detail on this example? I am still not getting the point that there is no reaction. My analogy is to think of gravity as a fictitious force, and all engineering analysis of bridges, buildings etc. treat gravity just like any other force. Brews ohare ( talk) 00:00, 10 May 2008 (UTC)

Just create a rotating reference frame on the equator, six feet above the Earth, rotating at 1khz with the axis aligned parallel with the Earths axis. This force suddenly appears (a combination of coriolis and centrifugal) in that frame which holds the Earth in an 'orbit' around the axis at 1khz. It's quite a large force, and has no equal and opposite force anywhere else. ;-) Everything works out just fine, all the motions are precisely the same, only spinning around, is all.- ( User) WolfKeeper ( Talk) 04:14, 10 May 2008 (UTC)

First of all, let's set aside the idea that gravity itself can be considered a kind of fictitious force in the context of general relativity. Classically, real forces are the result of interactions between objects. If there's a (real) force on object A, some other object B must be exerting that force, and there is an equal and opposite force of the same type exerted by B on A along the same line. If you push on me, you are exerting a contact force (electromagnetic in origin) on me, and I exert an equal and opposite electromagnetic contact force on you. If A is you and B is the Earth on which you are standing, there are two pairs of action-reaction forces: the earth exerts a gravitational force on you (pulls you down), and you, equal and opposite, exert a gravitational force on the earth (pulling the earth toward you). You also exert a contact force on the earth, pushing on it with your feet, and the earth exerts and equal and opposite contact force back on you. Now, what about inertial forces? They come seemingly out of nowhere. Objects in rotating frames are influenced by them, but they are not exerted by any other object, and so there's nothing to push back against.

As for the bit about "you don't feel inertial forces/gravity, you feel what stops them from having their way" that's a bit semantic, I think. You "feel" gravity (and inertial forces) by noticing that they cause you to accelerate relative to your frame of reference. You are right that inertial forces and gravity are the same in this sense (what they feel like) but I think throwing that in without a careful explanation of the difference between the real force of gravity and fictitious forces like the centrifugal force could cause confusion. Rracecarr ( talk) 00:57, 10 May 2008 (UTC)

You can only notice differences in gravity- a completely constant gravity field is undetectable. As I understand it, in General Relativity gravity is essentially a fictitious force- that's why the gravitational mass and inertia are equal. It's not quite the same though, because gravity is always equal and opposite on something whereas centrifugal and coriolis aren't.- ( User) WolfKeeper ( Talk) 04:14, 10 May 2008 (UTC)

I will explain it for you. Because the example is imaginary, a fictitious force arises, because the reference frame is imaginary. There is no actual physical significance to the rotating reference frame, so you can say that the force that appears in the frame is fictitious. Which makes sense since the frame was fictitious. Did you get that reasoning? Problem is that the rotating frame is supposed to model an actual, physically real, situation, and not a fictitous situation. In this case the model of a fictitious force doesnt make sense any more. That is the source of the difficulty. 72.84.76.230 ( talk) 01:15, 10 May 2008 (UTC)

That's a really interesting point of view. Unfortunately, if you can't find any verifiable reliable sources that support it, we can't put it in the article. -- The Anome ( talk) 10:25, 10 May 2008 (UTC)

Hey that is not a problem. There are a multitude of classical physics textbooks, with very clear and excellent discussions, that do not lead to confusion and misunderstanding, that can be cited by the main article in order to clear up the confusion you have in it. You simply refuse to accept them. Even if they might have been written by a Nobel winner. You still would not accept them. I get that you dont understand. 72.64.54.70 ( talk) 15:26, 10 May 2008 (UTC)

Excellent! Since there are so many of these clear and excellent discussions available in a multitude of classical physics textbooks, possibly, as you hint above, including textbooks written by Nobel prizewinners, you will presumably have no problem providing a cite to some of them here... -- The Anome ( talk) 21:31, 10 May 2008 (UTC)

I think one way to resolve the difficulties regarding whether the rotating frame is 'fictitious' or not, is to use the equivalence principal - i.e., the physical phenomena are the same regardless of the coordinate system used. Any reference frame is as good as another; but the coordinates you use will depend on the choice. The simplest is an inertial, Cartesian reference frame in which straight-line uniform motion (no force) involves no 'fictitious' forces. Any other reference frame (accelerating, rotating, even polar) will include 'fictitious' terms due solely to a change of coordinates.

Another way to resolve it is to use coordinate-free vector notation, but to do any practical work we need to introduce coordinates.

There's a slightly subtle point about polar coordinates - Even in an inertial frame, motion will involve 'fictitious' terms due to coordinate transformation. Try describing straight line force-free motion in polar coordinates, you'll see what I'm talking about. Some of the arguments about inertial frames miss that point. Since we nearly always analyze orbital mechanics using polar coordinates, centrifugal and coriolis terms arise. One of David's examples above included the centrifugal term in orbital mechanics and he tried to say the force was 'real.' Nobody called him on it, and I think perhaps it was because we're so stuck on rotating frames in this article that the point was missed. Plvekamp ( talk) 15:14, 10 May 2008 (UTC)

I rewrote the discussion of "no reaction force" so it makes sense to me. I hope this revision accords with your meaning. Brews ohare ( talk) 17:36, 10 May 2008 (UTC)

Yes, I can go with that. The problem I'm seeing is that the intro says that fictitious forces only arise in rotating frames of reference, but the references don't go quite that far. They do say that fictitious forces appear in rotating frames, true. But that's not the only place they appear. Centrifugal terms also appear in orbital mechanics in inertial frames due to use of polar coordinates. I'll try to dig up a reference or two. Unfortunately, all my old college textbooks are in storage, so I'll try to find a reliable source online. The article on orbital mechanics skips the derivation of the orbit equation, which is where I'm fairly sure you'd find it. Plvekamp ( talk) 18:39, 10 May 2008 (UTC)

I found a derivation of rectangular to polar coordinate conversion [5], where the frame is stationary. The author points out the centrifugal and coriolis terms due to the transformation, and shows their presence in straight-line uniform motion, absent of forces.

I think there may be a section in Halliday and Resnick, but I'm relying solely on memory for that. - Plvekamp ( talk) 19:43, 10 May 2008 (UTC)

Mr Plvekamp, it apears you are confused. Feynman clearly states that it does matter which coordinate system that you use. He states that the pseudo forces "are due merely to the fact that the observer does not have Newton's coordinate syatem, which is the simplest coordinate system." page 12-11, Vol 1 of his Lectures. Your statement that one reference frame is as good as another evidently indicates you dont understand this topic. I suggest that you do go back and check up on your memory and stop pulling facts out of the air. 71.251.176.68 ( talk) 20:07, 10 May 2008 (UTC)

I'm not disagreeing with Feynman; on the contrary, I completely agree that the appearance of pseudoforces depends completely on the coordinate system. What I'm trying to say is that a rotating frame is not the only way you'll see them; you'll also see them if you use polar coordinates in a stationary frame - check the reference I linked to [6]. I provided it to show that I'm not "pulling facts out of the air." The introduction as it stands seems to concentrate solely on rotating frames.

My statement that one reference frame is as good as another was in reference to the Equivalence Principle. In other words, a change in coordinate systems does not change physical law. You may have misunderstood me, in which case I apologize for not explaining myself well.

In any case, I won't make any changes to the article unless there is consensus (unlike another recently). Plvekamp ( talk) 20:52, 10 May 2008 (UTC)

Unfortunately, Prof Kleitman's notes contain a very basic error: he has derived the acceleration of a particle in polar coordinates referred to an inertial frame, and then incorrectly refers to the terms as the centrifugal and Coriolis forces. In fact, what he calls the centrifugal force is actually the centripetal force (it is radially inward). His Coriolis force is zero if dr / dt is zero (motion in a circle). The Coriolis force in fictitious force is zero only for motion with zero apparent velocity in the rotating frame. It seems to me that circular motion with a slower rate of rotation than the coordinate system produces a Coriolis force, while that is not true for the notes cited. I suspect that one must treat a rigid body capable of rotation, and not a point particle, to properly account for Coriolis force. Brews ohare ( talk) 01:35, 11 May 2008 (UTC)

Brews, thanks for taking the time to read his derivation. I'm honestly trying to understand this better. The thing that confuses me a bit about your interpretation of it as a centripetal force - radially inward - is that the point particle, continuing in its straight line motion, continues toward infinity. How could it do that if it were a centripetal force? It's a positive acceleration, not negative, isn't it? About the "coriolis" term, the derivation in fictitious forces doesn't include a rigid body, and neither does the coriolis effect article, so I don't see your point there. However, Prof Kleitman's identification of the angular acceleration as coriolis doesn't seem right either, so I think I can agree with you. Maybe Prof Kleitman should talk to a physicist about his terminology (but you'd think an MIT mathematician would get it right).

Or maybe I'm just going off on a wrong tangent with this whole approach (pun intended)... - Plvekamp ( talk) 02:14, 11 May 2008 (UTC)

Hi Plvekamp: I paralleled Kleitman's approach at Centripetal force, and no restriction to straight-line motion is implied. However, an inertial frame and a point particle is implied. The problem with that is that the coordinate frame based upon u_r and u _θ is tied to the particle trajectory r(t) and is not free to have a trajectory-independent life of its own with its own rotation that doesn't depend on what the particle does (it should just be a rotating frame from which to view the particle). In fictitious force a moving and rotating reference frame is used explicitly, from which to observe a point particle. It would be desirable to try all the formulas on a standard problem or two to sort out what the differences are, but the formulas don't appear to be the same. Brews ohare ( talk) 05:29, 11 May 2008 (UTC)

Brews, There are a number of points to clear up.

(1) The edit war has been principally about the fact that these people here have been trying to deny that a centrifuge works BECAUSE it is rotating. They have been arguing that centrifugal force occurs when we view something from a rotating frame of reference. The two concepts are quite diffent.

I have been trying to insert the cause and effect aspect into the main article, but it gets deleted instantly every time.

These people think that a rotating centrifuge is equivalent to observing a stationary centrifuge from a rotating frame whose axis is on the axis of the centrifuge.

Clearly you can see that this is nonsense. A centrifuge will not be made to work in that manner. There is no equivalence principle involved in all of this.

However, there is a group here that are trying to promote the equivalence principle, and they are quite wrong. They are denying the age old Bucket argument.

(2) Orbital theory. Polar coordinates show up both the centrifugal force and the Coriolis force. However, Kepler's law of areal velocity eliminates the Coriolis force term. No Coriolis force is involved in the gravitational field.

We are then left with a radially inward gravity force and a radially outward centrifugal force which is absolutely real.

(3)Action - Reaction. In the real scenario, when actual rotation occurs, we get a radial centrifugal force, which as regards the issue of action-reaction, behaves exactly like gravity. However in the purely fictitious situation in which we observe a stationary object from a rotating frame, any effects are only fictitious and Newton's third law will be totally irrelevant. The group that are controlling this article are focused exclusively on the latter scenario. David Tombe ( talk) 04:13, 11 May 2008 (UTC)

David, if you can produce cites to multiple reliable sources that agree with your assertions, you will find that other editors will be happy to work with you in incorporating your assertions into the article, albeit as a minority viewpoint, unless you can also show that your assertions are supported by a majority of reliable sources. Please read the verifiability policy to see the requirements for citations. -- The Anome ( talk) 13:26, 11 May 2008 (UTC)

See centripetal force and John Robert Taylor (2005). Classical Mechanics. Sausalito CA: University Science Books. p. pp.28-29. ISBN  189138922X. {{ cite book}}: |page= has extra text ( help) for support for criticism of Prof Kleitman's notes. Brews ohare ( talk) 14:26, 11 May 2008 (UTC)

You are right that the Taylor book is a better source (in the very specific sense defined in WP:RS) than Professor Kleitman's notes, since while both are documents written by credentialed academics, the former has been through an editorial and publishing process, and thus presumably an extra process of proof-reading and fact-checking. However, as far as I can see, Taylor's expression for a in (1.47) is in agreement with Kleitman's derived expression for d²r / dt² apart from notational differences. -- The Anome ( talk) 15:33, 11 May 2008 (UTC)

Hi Anome: That is correct - the acceleration is the same as in Taylor. What is incorrect is the description of the terms as "centrifugal and Coriolis forces". That is not accurate. The term referred to as "centrifugal" is in fact "centripetal", as Taylor will support, and the term referred to as Coriolis is some bastardization of the negative of same for this particular case. The correct expressions are given in Taylor in his discussion on rotating frames much later in the book, as described in fictitious force. Brews ohare ( talk) 16:09, 11 May 2008 (UTC)

David, there is no "group ... controlling this article." It just happens that most editors disagree with you. If you can't get consensus for your edits, you're just being disruptive. It may help to remember that nobody owns the articles. Plvekamp ( talk) 14:37, 11 May 2008 (UTC)

Brews, I can assure you that it is not centripetal force. I have worked at great length with that derivation and done many calculations in orbital theory. The terms in that equation are centrifugal force, Coriolis force, and Euler force. That equation in its own right doesn't infer any kind of motion. However when we apply Kepler's law of areal velocity to the gravitational field, the two tangential terms vanish. That leaves us with the radial terms. The radial terms, in the absence of gravity expose the fact that inertia is centrifugal force.

David: This article is a subject in kinematics. For this discussion to take a different direction, perhaps you can explain to me what the errors are in, for example, Centripetal_force#General_planar_motion or in Fictitious_force#Rotating_coordinate_systems. The arguments agree with textbooks (which are cited and on-line so you can read them). They seem to be pretty straightforward results of differentiation to obtain acceleration. The directions of the forces are a direct outgrowth of the math. It is a red herring to drag in Kepler's laws and gravitational fields. They belong in orbits and Kepler's laws of planetary motion, not kinematics. Brews ohare ( talk) 05:32, 12 May 2008 (UTC)

Brews, the maths in both of those articles is perfectly correct and I am well familiar with it. In fact it is basically the same maths in both cases. But you must never lose sight of the physical meaning behind the maths symbols. Those equations tell us alot. But they don't tell us everything. We need to model a real physical situation before we can decide how those terms fit in, and what they mean in any given context.

I took the gravity orbit as being the most well known physical context in which those equations are applied. Kepler's law of areal velocity is highly relevant because it gets rid of the two tangential terms. We are then left with a gravity force radially inwards and a centrifugal force radially outwards.

You have been trying to read a physical meaning into those equations in their own right. In their own right, all they do is convert polar coordinates to Cartesian. Centripetal force is not determined by those equations alone. We need to know the physical model before we can apply them and obtain a differential equation to solve.

Interestingly, they do tell us some information in their own right. If there was no applied centripetal force such as gravity or tension T in a string, or no applied torque, then in a space vortex, we would have a curved path caused by the centrifugal force and Coriolis force. If there were no vorticity, then the Coriolis force would disappear and we would be left with a centrifugal force acting alone. This would lead to a hyperbola with infinite eccentricity, which is essentially straight line motion. David Tombe ( talk) 09:34, 12 May 2008 (UTC)

For the gravity orbit, we will additionally have gravity itself acting as the centripetal force inwards. The centrifugal term acts outwards in the opposite direction.

The centrifugal force and the gravitational force only balance in the special case of circular orbits. For the purposes of action-reaction pair we have to look at the two planets. The centrifugal force acting on the Moon will be equal and opposite to the centrifugal force acting on the Earth. And likewsie with the gravity force. David Tombe ( talk) 03:56, 12 May 2008 (UTC)

The thing is, you only get purely radial terms if you rotate the frame around with a particle that is not necessarily moving with constant angular velocity (in an orbit the angular velocity is inversely proportional to radius, under the ' areal velocity' rule or equivalently conservation of angular momentum). This article really deals with the case when the rotation frame is travelling at a constant angular speed, or more generally is moving with an independent speed than a particle. The equations for polar and for orthogonal axes are different. You can see that because the polar form cannot have a tangential coriolis term, whereas the general form of the equations does have.- ( User) WolfKeeper ( Talk) 04:17, 12 May 2008 (UTC)

If you look at a particle in an elliptical orbit from the point of view of a frame that rotates at constant speed, you find that there is a centrifugal force pointing away from the origin, as well as a coriolis force that points at 90 degrees to the particle's motion in the rotating frame. The maths is not the same as polar coordinates, and I do not understand how anybody can expect them to be in general. This article is not about polar coordinates.- ( User) WolfKeeper ( Talk) 04:17, 12 May 2008 (UTC)

Wolfkeeper, That's what is so interesting about Kepler's law of areal velocity. It means that there is no tangential acceleration. Of course we can still have a variable angular velocity.

No, that's not interesting. The fact that you have a variable angular velocity is why the coriolis force is not a central force in a steadily rotating frame of reference, but is in polar coordinates. THIS ARTICLE IS NOT ABOUT POLAR COORDINATES IT IS ABOUT ROTATING REFERENCE FRAMES- THEY ARE DIFFERENT. - ( User) WolfKeeper ( Talk) 05:29, 12 May 2008 (UTC)

Supposing we were to ignore Kepler's law of areal velocity. The polar coordinate conversion equations still wouldn't point us to any particular kind of motion. They would merely facilitate with the mathematical expressions that were needed in order to set up a differential equation modelling a real physical scenario.

Irrelevant.- ( User) WolfKeeper ( Talk) 05:29, 12 May 2008 (UTC)

Such a differential equation involving real tangential forces as well as real radial forces would almost certainly be non-analytical. David Tombe ( talk) 04:59, 12 May 2008 (UTC)

'Almost certainly'. We are talking about maths, not quantum mechanics. This isn't a probability question, the forces are analytic, and they work as described in the article. The article is not about polar coordinates. Did I mention that the article isn't about polar coordinates? Because .. it .. isn't about .. polar coordinates. Get it? No polar coordinates... not polar!- ( User) WolfKeeper ( Talk) 05:29, 12 May 2008 (UTC)

Wolfkeeper, I've lost track of the point that you are trying to make. I didn't bring the subject of polar coordinates up. But whoever did was correct to do so because it is relevant to the topic. David Tombe ( talk) 09:41, 12 May 2008 (UTC)

David, I just noticed your comment:

"However, there is a group here that are trying to promote the equivalence principle, and they are quite wrong."

Are you saying the equivalence principle does not apply here? Can you provide a cite supporting this assertion, or is this your own original opinion? -- The Anome ( talk) 19:53, 11 May 2008 (UTC)

Anome, Does a centrifuge work when it is rotating. Answer 'yes'.

Does a non-rotating centrifuge work if we observe it from a rotating frame of reference? Answer 'no'.

Conclusion. There is no equivalence principle for rotation.

But really, I should be asking you to provide a cite saying that the equivalence principle does apply in rotation, because I know that it doesn't, and I know that you would never be able to find such a cite.

You have been constantly misrepresenting this whole dispute. I am not adopting any minority or fringe viewpoint. I am trying to improve the article by explaining basic classical mechanics to the other editors.

If you check the rules, you will see that no citations are necessary unless the subject matter is challenged.

The appropriate course of action is then to insert a [citation needed] tag into the challenged clause.

This has not been happening. My edits have been getting wholesale deletion without any reason whatsoever. Take for example RRacecarr's deletion of my edits yesterday. I tidied that section up very well and made it more interesting, more coherent, and more accurate. No fringe viewpoints were included. Years ago I studied the whole artificial gravity issue and the problem relating to machines trying to fly in the rotating atmosphere. Those were interesting points that I put in. They were all correctly described and none of them were controversial.

I challenge you to point out a single controversial statement in the edits which I made yesterday. I'll bet that you won't be able to.

And as an administrator, it is your job to detect vandalism and wikistalking when you see it happening. This was a clear case of wikistalking on the part of RRacecarr. He removed perfectly good edits for no reason other than spite. And you as an administrator should act accordingly.

Show me the errors in those edits and we can move forward from there. David Tombe ( talk) 04:08, 12 May 2008 (UTC)

I honestly think this dispute ought to go to formal mediation. 69.140.152.55 ( talk) 09:33, 12 May 2008 (UTC)

David, you are attempting to solve this dispute by argumentation, rather than by providing cites for the material you want to include. Other editors have since added point-by-point cites for various statements in this article; if you'd like to provide cites supporting your assertions, I'd be delighted to see them. -- The Anome ( talk) 11:35, 12 May 2008 (UTC)

No Anome, this dispute has never been about cites. It has been about you and others falsely alleging that I have been adopting a fringe and unorthodox position.

I am waiting now for you to describe that position. David Tombe ( talk) 12:10, 12 May 2008 (UTC)

It appears that a digression is taking place to orbits and Kepler's laws of planetary motion. Is there a notion that something from those articles should appear here? Brews ohare ( talk) 05:16, 12 May 2008 (UTC)

Brews, it maybe wouldn't do any harm at all, because it is highly relevant. It involves a radially outward centrifugal force that is as real as the radially inward gravitational force. Furthermore, Kepler's law of areal velocity explains why their is no Coriolis force acting in space whereas there is a centrifugal force. Kepler's laws tell us that tangential acceleration is zero in space.

Hence a straight line motion across your kitchen contains an inbuilt centrifugal force which is exposed when measured in polar coordinates with reference to any fixed point, whereas there will be no Coriolis force.

Ideally, you need a space vortex to get Coriolis force. This only occurs in hydrodynamics such as in the oceans and the atmosphere. David Tombe ( talk) 09:22, 12 May 2008 (UTC)

I'm afraid you're wrong about this too. Here's an experiment you can perform at home. Sit on a rapidly spinning office chair or other rotating platform, and let go of the pen in your hand. It will (from your rotating viewpoint) fly away out of your hand (centrifugal acceleration) and also move (from your rotating viewpoint) tangentially to the side (Coriolis acceleration) as it flies away from you. (I've just carried out this experiment, and this is indeed what happens.) If you choose the point of view that the apparent accelerations are necessarily caused by forces, you have just witnessed centrifugal force and Coriolis force in action. No vortex required, and -- incidentally -- all also completely explainable as motion under Newton's laws of motion in an inertial frame, without the need to invoke pseudoforces. -- The Anome ( talk) 11:59, 12 May 2008 (UTC)

Anome, a straight line motion across your kitchen does not involve any Coriolis force. It is ruled out by Kepler's law of areal velocity.

The effect that you have just described is a tangential artifact as viewed from a rotating frame of reference. The rotating frame of reference in this case is fixed in the rotating person. That is not Coriolis force. David Tombe ( talk) 12:07, 12 May 2008 (UTC)

Yes! Yes! You've nearly got it! "The effect that you have just described is a tangential artifact as viewed from a rotating frame of reference." is exactly right: there is no Coriolis force required to explain this, if you are viewing the system from the basis of an inertial frame (your kitchen), rather, this "tangential artifact" is the explanation of the apparent Coriolis force. Now, you only need to go one step further, and see centrifugal acceleration/force as a radial artifact as viewed from a rotating frame of reference, and you're there!

(This last is a difficult mental step to make, because it requires you to let go of part of your common-sense interpretation of the world, but believe me, it's a great relief when you've done it. It is much easier to "let go" of the idea of Coriolis force, because the physical intuition for that is less firmly grounded that that for centrifugal force.) -- The Anome ( talk) 12:18, 12 May 2008 (UTC)

No Anome, the radial effect can never be an artifact of circular motion. Only the tangential effect can be an artifact of circular motion.

You missed the point entirely. Centrifugal force in a zero-curl field is the same thing as inertia. There is centrifugal force built into every straight line motion. But there is no Coriolis force because Kepler's law of areal velocity eliminates it. We need hydrodynamics to get the Coriolis force. David Tombe ( talk) 12:34, 12 May 2008 (UTC)

Your statements are false. There are three references in the article for the derivation of both the centrifugal and coriolis forces in the same manner, from transformation into a rotating frame. Mr. Tombe, you are unlikely to improve this article by continuing to make statements in contradiction to reliable sources. -- SCZenz ( talk) 13:19, 12 May 2008 (UTC)

Those derivations are correct, but they have got absolutely nothing to do with the point in question. The article is unlikely to be improved as long as SCZenz is involved in adjudicating. 118.175.84.92 ( talk) 16:44, 13 May 2008 (UTC)

FyzixFighter, I think we may now have identified the root cause of the edit war. You have just deleted my reference to the existence of two different kinds of scenario involving rotation.

(1) There is actual rotation. (2) And there is artificial rotation as when a stationary thing is observed from a rotating frame of reference.

Now I have been accused by Anome of adopting a minority or fringe viewpoint. Let's explore that so-called minority or fringe viewpoint.

My viewpoint, for which I will obtain cites if challenged, is that a centrifuge works BECAUSE it is rotating.

However, if we were to view a stationary centrifuge from a rotating frame centred on the centrifuge axis, the centrifuge would not work.

I do not believe that the "principle of equivalence" applies to rotation.

That is my viewpoint.

Is that a minority viewpoint? Do you think differently? Would you challenge it if I were to put that viewpoint into the main article? David Tombe ( talk) 09:48, 12 May 2008 (UTC)

I don't think you mean the same thing that other people understand by the term when you refer to the "principle of equivalence".

You are attacking a strawman here. Firstly, no-one doubts that a centrifuge works because it is rotating. Secondly, no-one is denying the reality of rotation as an entity independent of the frame of reference chosen (indeed, the whole concept of an inertial frame is based on it not accelerating or rotating, thus providing a basis against which rotation and acceleration can be measured). Thirdly, you seem to believe that the principle of equivalence denies this; it does not.

They do, on the other hand, assert (and this, I believe is the matter under dispute) that the motions of classical rotating objects can be described entirely by using Newton's laws within inertial frames, without invoking pseudoforces.

Other editors have since added point-by-point cites for various statements in this article; if you'd like to provide cites supporting your assertions about the disputed issues, I'd be delighted to see them. Providing cites that support undisputed statements, such as the need for a centrifuge to spin in order to work, would be less useful: nevertheless, please supply them as well, so we can at least pin down even the uncontroversial statements as common ground. -- The Anome ( talk) 11:30, 12 May 2008 (UTC)

Actually a stationary centrifuge in a rotating frame works perfectly fine. To see this you need either transformation equations given in this article or better you need to move to GR where changing to rotating coordinates adds terms to the Levi-civita connection and thereby inducing the same effect. ( TimothyRias ( talk) 13:07, 13 May 2008 (UTC))

Are you serious? You are saying that a stationary centrifuge will work if we observe it from a rotating frame of reference. 118.175.84.92 ( talk) 16:34, 13 May 2008 (UTC)

Anome, in that case, if nobody is denying it, can you please tell me exactly what the edit war is about. And can you tell me why you erased an edit which I made to that extent and then blocked me from editing for 31 hours, extended by a further 25 hours on a petty technicality. You blocked me on the false pretext that I hadn't supplied a cite. But the rules say that a cite is only necessary if the clause is challenged. And even then, the correct procedure is to insert a 'citation needed' tag.

The edit that you erased and blocked me for is contained in this exert,

the centrifugal and Coriolis forces can have real physical effects in situations where the object in question is co-rotating such as in the case of the centrifuge device. In situations in which the object in question is not co-rotating, these fictitious forces are merely artifacts of coordinate transformation. The distinction between these two aspects of fictitious forces is the subject of a long standing debate known as the Bucket argument.Classifying such forces as "fictitious" reflects the special

Can you please point out exactly what aspect of this exert is being challenged, and why I had to be blocked for over two days for having made this edit. David Tombe ( talk) 12:28, 12 May 2008 (UTC)

The issue here is that no magic occurs when the object and frame are "co-rotating": the fictitious forces do not suddenly become any realer in this situation. There is no distinction between these two scenarios: the bucket argument is not relevant to this particular case.

If you disagree with this, please provide a cite that supports your assertion. Your failure to provide a cite for assertions such as this is the entire dispute: you are not being blocked for merely disagreeing with other people.

For instance, you say "The distinction between these two aspects of fictitious forces is the subject of a long standing debate" -- can you provide any references to reliable sources which report this debate?

Incidentally, here's a thought experiment: consider an object rotating at 1Hz, considered within a coordinate frame rotating at 1.00000000001 Hz: would there be a sudden change in the actual physical regime between this and one considered within an exactly co-rotating frame rotating at precisely 1Hz? If so, how would you measure it? If not, how about 1.01 Hz? 1.1Hz? 2Hz? 0Hz? -- The Anome ( talk) 12:51, 12 May 2008 (UTC)

Anome, coordinate frames have got nothing to do with it. It is the actual rotation that induces the centrifugal force. So if there is no co-rotation of the object in question, then there is no rotation.

The centrifuge illustrates quite clearly that centrifugal force only occurs when there is actual rotation.

So as regards your question, there would be centrifugal force based on the actual rotation of the object in question irrespective of what reference frame we viewed it from. In other words, there would be a centrifugal force associated with a 1Hz actual rotation. The frame that you mention rotating at 1.00000000001 Hz would have absolutely no bearing on the matter. David Tombe ( talk) 13:15, 12 May 2008 (UTC)

Well, at least we agree on one thing: a coordinate frame rotating at 1.00000000001 Hz indeed would have absolutely no bearing on the matter, and cause no physical difference in the behavior of the system. I would go just one step further: nor would a frame "co-rotating" at precisely 1Hz. Indeed, I would assert that the actual physics of the situation is the same from all possible rotating frames, including the trivial case of frames rotating at 0Hz -- that is to say, inertial frames.

When you say "if there is no co-rotation of the object in question, then there is no rotation", what do you mean by "co-rotation", if not just "rotation"? "Co-rotation" implies that two things are rotating together; my understanding of this from your previous edits was that the two things rotating together were the object and the coordinate frame. If this is not the case, what are the two things that must "co-rotate" for this effect to happen? -- The Anome ( talk) 14:02, 12 May 2008 (UTC)

Anome, the two things in question for the purposes of co-rotation are the object in question that experiences the centrifugal force and the imaginary rotating frame of reference that you consider to be so important. If they are co-rotating, then there will be centrifugal force on the object as per the maths, and in a centrifuge that will cause a real effect.

If an object is not co-rotating with an imaginary rotating frame or even a real rotating frame, then nothing will happen to it. It will experience no real centrifugal force.

Does that point of view differ from the orthodox point of view? David Tombe ( talk) 14:11, 12 May 2008 (UTC)

So, when you say "co-rotating", you mean "rotating"? -- The Anome ( talk) 14:40, 12 May 2008 (UTC)

It can't go to mediation until we've discovered what the dispute is about. The evidence is that a team of vandals and wikistalkers have been falsely alleging that I am adopting a minority and fringe position.

We need to await a declaration of exactly what that fringe position is. David Tombe ( talk) 12:37, 12 May 2008 (UTC)

David, I'm not a mindreader, and I can only discuss specific cases. Since you raised it above, here's one specific example( diff).

Here are the sentences in question:

"...forces can have real physical effects in situations where the object in question is co-rotating such as in the case of the centrifuge device. In situations in which the object in question is not co-rotating, these fictitious forces are merely artifacts of coordinate transformation. The distinction between these two aspects of fictitious forces is the subject of a long standing debate known as the Bucket argument."

In my opinion, these articulate a position contrary to the consensus content of this article, without providing support from verifiable reliable sources, in spite of many, many requests to you, over the course of more than a year, to provide such cites. This goes against the Neutral Point of View policy, which states: "All Wikipedia articles and other encyclopedic content must be written from a neutral point of view (NPOV), representing fairly, and as far as possible without bias, all significant views that have been published by reliable sources." As the policy says "This is non-negotiable and expected of all articles, and of all article editors." The various finer points of this rules, including what is meant by "significant", and the need for verifiability of those reliable sources, are articulated in greater detail elsewhere. Original research is specifically excluded.

Your failure to provide a cite for assertions such as this is the entire dispute: you are not being blocked for merely disagreeing with other people.

Can you, for example, support the statement that "co-rotation" causes an alteration of the physical regime, between these phenomena being real forces and mere observation artifacts, using reliable sources as evidence? Or support the statement that "The distinction between these two aspects of fictitious forces is the subject of a long standing debate", using reliable sources as evidence? Note that you do not even have to demonstrate that these beliefs are true; just that they are beliefs which meet the criteria for significance, verifiability, and attributability required by Wikipedia's policies, so that they can be represented as such in the article, even if only as significant dissenting opinions. Of course, if you can demonstrate that these are mainstream opinions, all the better.

If you don't like the rules of editing here, you might want to try some other online forum for your views, such as a personal website, or a fork of Wikipedia that does not have these rules. How, other than by blocking you when you break them, do you propose that these rules be enforced? -- The Anome ( talk) 13:24, 12 May 2008 (UTC)

Anome, you know the answer fine well and the answer is not being challenged. Hence no cites are necessary. A centrifuge has real effects and it only works when it is rotating.

Your deletions and blockings have got nothing to do with cites.

I think you are labouring this citations issue and hiding behind bureacratic slogans. David Tombe ( talk) 14:05, 12 May 2008 (UTC)

Now we come to the crux of the matter. You say above "Hence no cites are necessary." Unfortunately, you have come to a place where cites are necessary, and wish to contribute without doing so. You can either play by the rules, or not. If you don't want to play by the rules, and continue to do so in the face of persistent courteous requests to do so, you will be blocked from editing. -- The Anome ( talk) 14:20, 12 May 2008 (UTC)

Anome, it says in the rules that cites are necessary when something is challenged. Are you challenging the idea that the real effects of a centrifuge only occur when the centrifuge is rotating?

Because if you are, I will get you a cite. If you are not, I will go ahead and put it in again without a cite. David Tombe ( talk) 14:24, 12 May 2008 (UTC)

No, that's not the way it works. Editors each have to supply cites for their own assertions, not strawman assertions attributed to them by other people. As I have said above, centrifuges only work because something rotates, or -- put more generally -- moves in an accelerating path: that is not in dispute. I have made quite clear above which assertions I am asking you to substantiate. -- The Anome ( talk) 14:30, 12 May 2008 (UTC)

OK RRacecarr, what was the problem with those edits? What would it be like for birds in an atmosphere in the absence of a gravitational field? David Tombe ( talk) 14:07, 12 May 2008 (UTC)

His opinion on that question is irrelevant, and so is yours. Is your statement based on any source, or was it simply original research? Also, how does speculation about birds in the atmosphere improve an article on centrifugal force...? -- SCZenz ( talk) 14:33, 12 May 2008 (UTC)

There is no inherent difference in what a bird would experience. Fictitious force doesn't "feel" any different from gravity. The strength and direction would change with location, but so does gravity. Given a big enough space station the birds wouldn't notice anything. A (massless) space station as big as the sun would only have to rotate once every 15 hours to create a "gravitational field" to match Earth's, and the Coriolis force would be no more noticible than on Earth. Of course a space station that big is not practical, but the point is there is no fundamental difference in what birds would experience--the weird Coriolis forces they would experience go away as the station gets larger. Rracecarr ( talk) 16:19, 12 May 2008 (UTC)

You're right that in a sufficiently large station it would be for almost all purposes the same. However, for practical stations, the birds flying around would feel the coriolis force as well. This tends to turn their velocity vector in the opposite direction to the real rotation. Flying parallel to the axis they would notice nothing out of the ordinary, but any motion at 90 degrees to that, up or down (i.e. towards or away from the rotation axis) or spinward or antispinward would cause their velocity to tend to rotate. It's actually a noticeable effect; I don't have the exact figures to hand, but IRC simply dropping an object from ~6 feet causes a movement of an inch or so in a 1g habitat of a few kilometer radius due to coriolis effects in the natural rotating reference frame. There's also variations in g-force proportional to distance from the axis (centrifugal force) but that has much smaller effects unless you climb quite high.- ( User) WolfKeeper ( Talk) 03:27, 13 May 2008 (UTC)

As long as the birds maintained a tangential path, things would seem normal. But they would have a hard job maintaining a tangential path as they got closer to the centre of the cylinder. So as they flew higher, they would begin to get disorientated.

There is also the issue of the fact that as they got closer to the center, the degree of co-rotation may reduce.This would effect the centrifugal force 118.175.84.92 ( talk) 16:52, 13 May 2008 (UTC)

David, you inserted the following text without a supporting citation:

"As regards trajectories however, the matter becomes somewhat more complex. Providing that an object begins on the floor and doesn't move too far away from the floor, the result will be a good approximation to gravity. For example, when playing catch, a ball that is thrown upwards will come down again due to centrifugal force. For longer range trajectories that go closer to the center of rotation, a noticeable deflection will occur due to the rotation of the space station."

This is [a] contrary to the predictions of the classical treatment of rotational motion (which is fully cited within the article), [b] uncited. You have persistently and consistently refused to provide cites, and this is just one more example. Accordingly, I am blocking you again. -- The Anome ( talk) 14:55, 12 May 2008 (UTC)

Note: I asked for this block to be reviewed at WP:AN/I: see there for discussion. -- The Anome ( talk) 15:29, 12 May 2008 (UTC)

Go on then Anome, block it permanently and get it over with. I played by the rules. You didn't. All your blocks have been totally unlawful. That statement that I made above is perfectly true and it doesn't need any citations because it is not being challenged. It doesn't even relate to the controversy in question.

And your reversion of my reference to rotation yesterday was done under the totally false pretext of something to do with distance. 61.7.167.79 ( talk) 16:08, 13 May 2008 (UTC)

Block evasion is also against the rules. The above IP is blocked for 24 hours. -- SCZenz ( talk) 16:27, 13 May 2008 (UTC)

SCZenz, it's a pity that you don't know anywhere near as much about physics as you do about abuse of administrative authority. As long as you are around pushing your fictitiousist views and denying the cause and effect aspect of centrifugal force, this article will remain a mess. 118.175.84.92 ( talk) 16:31, 13 May 2008 (UTC)

Wikipedia:Blocking policy#Evasion of blocks -- SCZenz ( talk) 17:09, 13 May 2008 (UTC)

I have reset User:David Tombe's block to 48 hours from now, and blocked the IP for a similar period of time. If block evasion continues, I recommend quickly escalating the length of the block to indefinite. As I judge consensus both here on this page, and on the recent WP:ANI thread, David Tombe has just about exhausted the patience of the community. So, if disruption continues after the block expires, I recommend the same thing: an indef block. This is a collaborative environment, and one disruptive editor can ruin the experience for many others. I've had enough. Anome, SCZenz, (among others) I know you've been trying to work with him, and if you really think you can bring David Tombe into the collaborative editing community, I'll back off on this, but otherwise, this needs to be his last chance. -- barneca ( talk) 18:27, 13 May 2008 (UTC)

Sir what is at issue here is the ability of a user to point out a mistake to the editors of wikipedia. This mistake has been pointed out and the community of editors, refuse to admit that they have made a mistake n interpretation of the references. This has resulted in the unfair blocking because the mistaken editors dont want ther error to be discovered. So what you have done is unfair and damaging to the reputation of wikipedia, since it implies that you support editors who make mistakes and refuse to admit it. 72.64.56.156 ( talk) 16:39, 17 May 2008 (UTC)

Let me try to state David's viewpoint in words I understand, and without digressions in six different directions.

David agrees that observation of events from a rotating frame leads to a description using fictitious forces, including centrifugal and Coriolis forces. He also agrees that in an inertial frame the same observations do not require these forces. So far, everybody is on board.

However, David has reservations. Here are some possible interpretations of David's remarks:

Although a bucket of water that is stationary in an inertial frame exhibits a flat surface for the water, David believes the article implies incorrectly that when viewed from a rotating frame the water would have a parabolic surface because a centrifugal force appears in the rotating frame.

I suppose equally he would say that observation of two globes tied with string and stationary in an inertial frame would reveal no tension in the string, while David feels that the article proposes incorrectly that observation of these same stationary globes from a rotating frame would predict tension in the string.

Here is an alternative view of David's position:

Although a rotating bucket of water exhibits a parabolic surface when viewed in an inertial frame, the article suggests incorrectly that the surface observed in an inertial frame is flat, because centrifugal forces are "fictitious" and do not appear in an inertial frame.

If David can draw such conclusions from the article, perhaps so can other readers. A clear statement of these confusions and their resolution should appear in the article. Brews ohare ( talk) 15:19, 12 May 2008 (UTC)

I agree: the article needs to be as thoroughly argued and cited as the 0.999... and waterboarding articles. This is a confusing topic, even if you follow the mainstream interpretation, since (a) centrifugal force is undoubtedly part of our common-sense perception, even if it's wrong, so intuition often leads one astray; and (b) if you think about it hard enough, the considerations in this article lead onwards towards deeper questions regarding, for example, the equivalence principle and Mach's principle. -- The Anome ( talk) 15:44, 12 May 2008 (UTC)

Anome, your talking total nonsense now. Show us all a citation that states that the equivalence principle applies to rotation. As for Mach's principle, that disproves your position because it highlights the reality of the need for actual rotation in order to induce centrifugal force. 118.175.84.92 ( talk) 16:19, 13 May 2008 (UTC)

Here you go: here's a test of the EP involving some extremely massive rotating objects: [7]. By the way, I see you appear to be editing from an IP address while blocked: please don't do that -- see barneca's comments above. -- The Anome ( talk) 23:55, 13 May 2008 (UTC)

David seems to use a different definition of centrifugal force from the rest of us. In the interests of helping people communicate better, I thought I would try to state clearly what I think David means. Take the example of a particle in a centrifuge: David and everyone else agree that in the coordinate frame rotating with the centrifuge, there is a centrifugal force, determined by the rotation rate and the distance from the axis, acting on the particle. Where David's definition parts from everyone else's is in reference frames other than that particular one.

David's method: pick a reference frame rotating with the particle you're interested in, and calculate the centrifugal force. Then define that to be the centrifugal force no matter what reference frame you're in. In an inertial frame, or in one rotating twice as fast as the centrifuge, David's centrifugal force remains the same. Analysis in other frames would clearly require other fictitious forces in addition to David's centrifugal force, but he would argue that analyzing in any but the most "natural" rotating frame is an "ultra mathematical game"--the centrifugal force that the particle cares about, the one that it "sees", is the one in the reference frame rotating with it.

Standard method: pick any reference frame you want, and then define the centrifugal force relative to that frame. In the frame rotating with the centrifuge, the force is the same as David's. In the inertial frame, there is no centrifugal force. The force felt by the particle is applied by the wall of the centrifuge, and it accelerates inward in response. In the frame rotating twice as fast, the centrifugal force is twice as large as David's, but (in this special case) it is perfectly cancelled by the Coriolis force, and again the observed circular motion (in the opposite direction as in the inertial frame) is due 100% to the force applied by the wall.

Ok, maybe that will help people understand where David is coming from. Now maybe I can get David to consider whether the standard method actually might make sense to use in some situations (whether or not I succeed, the article will continue to exclude David's method until some references are produced, in accordance with WP:NOR).

As long as you are dealing with a single particle in circular motion at constant speed, David's method is fine. But what if the speed changes? With David's method, that requires a change of reference frame, which may not be convenient--angular acceleration of a reference frame introduces even more fictitious forces. Even worse, what if you have a bunch of particles, all moving around with different velocities within some rotating environment? David's method requires a different reference frame for each particle, to match with its actual instantaneous angular speed about the axis. In the standard method, all the particles are treated in the same reference frame, subject to the same (position dependent) centrifugal force. Differences in the velocities of the particles do result in differences in the fictitious forces they experience, but that is described by the Coriolis force, rather than by assigning each particle its own individual centrifugal force (which wouldn't, by the way, get rid of the need for a Coriolis force). Doesn't the standard way seem easier? Rracecarr ( talk) 15:57, 12 May 2008 (UTC)

Racecarr, you have more or less defined my position correctly. The only time when centrifugal force has any meaning is when a particle is undergoing actual curved path motion.

That's not the way that the term is used. If I'm standing in a centrifuge and I let go of something the force that pulls it out of my hand and slams it into the wall is the centrifugal force. Once it has left my hand it is in fact moving in a straight line, but from the rotating frame that is moving with the centrifuge; it's the centrifugal acceleration/force that is still accelerating it. This is not arguable, nor debatable, essentially every physicist in the world uses this term in this way.- ( User) WolfKeeper ( Talk) 18:23, 13 May 2008 (UTC)

As regards extending the concept to situations in which stationary particles are observed from a rotating frame of reference, I am fully aware of this viewpoint. I was taught it many years ago in applied maths.

You have asked me to consider whether or not it has any merit. Well certainly it has merit in meteorology and oceanography. But we must remember that any real effects which occur in these situations are entirely due to elements of air or water which are co-rotating with the larger entrained bodies of air and water.

No. Cyclones and anticyclones do not (co)rotate with anything- they follow epicyclic motion due to two different rotations superimposed, the rotation of the surface of the earth and (anti)cyclone itself. They do not move in any rotation in any inertial frame. The theory in the article handles that, your half baked, broken version of the theory doesn't.- ( User) WolfKeeper ( Talk) 18:23, 13 May 2008 (UTC)

My main problem has been in trying to insert any mention of actual rotation into the main article. I'm going to do that now to prove the point.

How about no? How about you follow the policies of the wikipedia including: WP:POINT and WP:NPOV?- ( User) WolfKeeper ( Talk) 18:23, 13 May 2008 (UTC)

Anome has been totally misrepresenting the situation. He has been claiming that I am pushing some minority fringe viewpoint. I haven't.

OK, then you will be able to produce references then?- ( User) WolfKeeper ( Talk) 18:23, 13 May 2008 (UTC)

I have been trying to focus the article more on the aspects of centrifugal force that are caused by actual rotation. I have been trying to focus it on cause and effect.

At the moment, the article concentrates on the fictitious aspect as when we observe stationary objects from a rotating frame of reference. 61.7.167.79 ( talk) 16:03, 13 May 2008 (UTC)

Yes, because strangely enough, that's what the rest of the world uses the term to mean. And in fact, they go way out of their way to say it isn't what you say it is. Sucks to be you I guess.- ( User) WolfKeeper ( Talk) 18:23, 13 May 2008 (UTC)

What you don't seem to recognize is that the fictitious force described in the article is the same exact thing you're talking about, but defined in such a way that it is computationally useful. You think it is silly to analyze the motion of a single object, stationary in an inertial frame, from an arbitrary rotating frame. You're absolutely right. But no one is advocating that; no one does that. No one would try to calculate the best way to aim the cue ball in a game of billiards by analyzing the motion of the balls from a rotating frame in which they all seem to move in circles, and in which moving balls curve in even stranger trajectories. BUT, suppose you were playing a game of billiards on a special table that was ACTUALLY rotating. The surface of the table would be a paraboloid so that the balls would sit still on the surface. In that case, it would make a lot of sense to plan your shot by analyzing the situation in a frame rotating with the table. In an inertial frame the balls and pockets are all moving in circles, and in the rotating frame, conveniently, they all sit still. The only price you have to pay is that you need to consider the Coriolis force which tends to make moving balls follow circular paths (you won't even have to worry about centrifugal force--gravity and the shape of the table cancel it out). So far, I'm sure you will agree, but STAY WITH ME: suppose you decided to hit the cue ball tangentially with a velocity equal and opposite to the rotation speed of the table at that point. Now, the cue ball (for an instant) is stationary in an inertial frame, and you would argue that it is silliness to continue to consider it from a rotating frame, because that just imposes artificial circles on an object which is really at rest. But there is actually nothing special, in the rotating frame, about the particular speed and direction which makes a ball stationary in the inertial frame. It continues to behave according to exactly the same rules, same forces, as a ball moving any other direction. There is no reason at all to suddenly switch back from the rotating frame to an inertial one just because you notice the cue ball happens to actually be stationary. For one thing, it won't remain stationary--it will begin to roll downhill toward the center of the table--but more importantly all the other balls and pockets now move in much more complicated ways. It makes life much easier just to stay rooted in your rotating frame and forget about what the velocities might be in any other frame, inertial or otherwise. You can apply the equations of motion (for a rotating frame) to the cue ball and all the balls it strikes, happy happy joy joy. Meanwhile, according to your definition, the centrifugal force on each ball depends on its velocity--if it's moving in the same direction as the table is rotating, there's more centrifugal force because it's rotating faster, and if it's moving in the opposite direction, there's less centrifugal force. That means you are considering each ball from its own reference frame--one in which it is instantaneously only moving radially. That method of analysis is far more difficult. Besides needing a reference frame for each ball, the frames undergo angular acceleration as the balls move, introducing weird tangential fictitious forces in addition to the centrifugal and Coriolis. Then, to calculate how the balls will hit each other, you will have to do coordinate transformations from each ball's frame to all the others---it is an absolute mess.

I wrote all of this to try to show you that it makes sense that centrifugal and Coriolis forces apply to ALL particles viewed from a rotating frame of reference, irrespective of what their velocity might be in an inertial frame. Your definition may jive with your intuitive sense of what centrifugal force is, but the concept is really only useful if you can do calculations with it. And by far the simplest way to do calculations with the fictitious force produced in rotating reference frames is to break it up into a centrifugal force and a coriolis force which ARE NOT CONTINGENT upon any kind of "co-rotation".

Please read this post carefully before trying to refute it. Rracecarr ( talk) 18:54, 13 May 2008 (UTC)

That was awesome. Antelan ^talk 00:13, 14 May 2008 (UTC)

What you say here is an irrational confused rant and shows you are confused and are trying to justify that confusion by an illogical rationalization that really isnt physics, just nonsense. 71.251.177.97 ( talk) 14:59, 14 May 2008 (UTC)

That is a very good essay. With some minor modifications, it could be a general introduction to the usefulness of non-inertial frames and fictitious forces. Perhaps a bit lengthy for Wikipedia, but it definitely deserves better than ending up forgotten in a talk-page archive. Is there a wikibook project or something where this could go? -- PeR ( talk) 16:42, 14 May 2008 (UTC)

RRacecarr, Let me now reply to your above assessment of my position. Your first part is more or less correct. We are all agreed that real outward radial effects occur when something is actually undergoing curved path motion.

In that case, why all the fuss? What is the fringe viewpoint that Anome keeps alleging that I am pushing?

And why are we not allowed to have any mention of this aspect of centrifugal force put in the main article?

I have tried on many occasions to highlight the fact that a centrifuge involves real radial effects which arise exclusively because the centrifuge is rotating. But these edits get swiftly removed every time. Itub and Timothy Rias have even tried to tell us that a centrifuge doesn't need to be rotating to work.

I was blocked from editing by Anome for inserting comments to the extent that a centrifuge does need to be rotating. And if you go to the notice boards behind the scenes, you will see that there is all sorts of panic going on and discussions about possibly blocking me permanently.

On your specific question, I would agree with you that rotating frames are useful in hydrodynamics, with meteorology being a classic example.

But not for a rotating snooker table. That never happens and it wouldn't work. There is no Coriolis force acting on free trajectories. You need to have actual curl as in hydrodynamics where the many particles are actually bonded to each other by inter atomic forces that are not subject to Kepler's law of areal velocity.

Anyway, I intend to re-insert the bit about the centrifuge into the section entitled 'Is the centrifugal force real?'. If Anome, or any of his colleagues in the administration, block me permanently on that basis, then we will all know the truth.

The truth is that there has been efforts made to play down the layman's concept of centrifugal force and to play up a fictitious aspect that is associated with artificial circular motion as viewed on stationary objects from a rotating frame of reference.

Have you got any citations regarding that theory about Coriolis force acting radially on a stationary particle when it is viewed from a rotating frame? There is a whole section on it in the main article and it seems to be given a much higher priority than anything to do with actual centrifugal force. David Tombe ( talk) 03:58, 16 May 2008 (UTC)

No one is saying that a centrifuge doesn't need to rotate to work. A centrifuge doesn't need to rotate to have a centrifugal force--it is the reference frame that needs to be rotating for that. And a centrifuge doesn't need centrifugal force for it to work--it works just as well when seen from a non-rotating frame where there is no centrifugal force. Sure, it sucks that such an intuitive statement as "centrifuges work due to centrifugal force" turns out to be incorrect due to the way centrifugal force is rigorously defined in current physics, but that's just the way it is and we are not here to write what ought to be but what it is. This is certainly not the only case of a term that has a precise meaning in physics that is at odds with the intuitive "layman's" definition. -- Itub ( talk) 11:10, 16 May 2008 (UTC)

Itub, you said above, All this rotation business makes things unnecessarily complicated when one wants to understand why the rotating bucket has hydrostatic pressure that the non-rotating bucket doesn't.

The simple fact is that the hydrostatic pressure is induced because it is rotating. If we observe a non-rotating bucket from a rotating frame of reference, we do not get any hydrostatic pressure induced.

Hence there is no equivalence in the two situations. It is like the Faraday paradox.

So there are two distinct scenarios to be analyzed separately when answering the question 'Is centrifugal force real?'

And any attempts on my part to answer that question in relation to the actual rotation scenario are instantly erased, along with blocks and threats of permanent blocking. Such edits generate no end of panic on the notice boards behind the scenes.

So there is something seriously wrong going on. Some group here are totally intolerant of references to the real effects associated with actual rotation. David Tombe ( talk) 12:57, 16 May 2008 (UTC)

When I gave the linear example you are quoting, it was just with the intention of demonstrating fictitious forces in a simpler context that should be easier to understand. In the linear case, there is only one dimension and one fictitious force to worry about, unlike in the rotation case where there are multiple fictitious forces. Yet the essence is the same: fictitious forces come from using a non-inertial frame of reference. -- Itub ( talk) 13:14, 16 May 2008 (UTC)

Again, this cuts to the heart of the matter. The phenomenon which makes a centrifuge work is the interplay of the forces that induce the inwards acceleration of the edge of the centrifuge, (as considered from the viewpoint of an inertial frame), not centrifugal force.

A rotating centrifuge will work, whether analyzed from the viewpoint of an inertial frame (see previous sentence), or from the viewpoint of a frame rotating about its center at the same speed as the centrifuge, in which case the effect can be regarded as being caused by centrifugal force. Indeed, any analysis of the phenomenon, from the viewpoint of any frame, inertial, rotating or accelerating, (with the addition of pseudoforces to Newton's laws as appropriate to deal with apparent accelerations induced by coordinate transformation effects), will show it working: which is just as well, because that is what experiments show.

A non-rotating centrifuge will not work, whether analysed from the viewpoint of the inertial frame (in which case there is no acceleration), or from the viewpoint of a frame rotating about its center at the same rate as in the case above (in which case, there is a centrifugal force caused by the rotation of the frame, of the same magnitude as above, but this is balanced out by the presence of a Coriolis force caused by the apparent backwards rotation of the centrifuge, sufficient to cause the motion as seen from within the rotating frame.) Indeed, any analysis of the phenomenon, from the viewpoint of any frame, inertial, rotating or accelerating, (with the addition of pseudoforces to Newton's laws as appropriate to deal with apparent accelerations induced by coordinate transformation effects) will show it not working: which is just as well, because that is what experiments show.

To reiterate: there is nothing special or privileged about the "co-rotating" frame. -- The Anome ( talk) 13:27, 16 May 2008 (UTC)

Anome, will a centrifuge work if it is not rotating? It's a yes or no answer. No need for all the hokum about reference frames. David Tombe ( talk) 13:55, 16 May 2008 (UTC)

Anome already said: "A non-rotating centrifuge will not work". Go and read his comment again. -- Itub ( talk) 13:58, 16 May 2008 (UTC)

Yes. But he then tried to qualify it with a load of irrelevant hokum about frames of reference.

A centrifuge works BECAUSE it is rotating. End of story. There is nothing more to say on the matter. But this fact is not allowed in the main article and I was blocked for trying to put it in. So somebody has been abusing their administrative authority. David Tombe ( talk) 14:39, 16 May 2008 (UTC)

I agree. A centrifuge works because it is rotating. However, that has nothing to do with centrifugal force. -- Itub ( talk) 15:06, 16 May 2008 (UTC)

I'd like to request semi-protection for this article, and preferably for the talk page also. Both seem to be under attack from a POV-pushing anonymous from different IPs. Now there's nothing wrong with pushing POV, provided they include reliable refs, but this isn't.- ( User) WolfKeeper ( Talk) 03:53, 14 May 2008 (UTC)

p.s. I removed some anonymous comments from this page, it seems that they're David Tombe, and he's currently suspended, so that's vandalism in my book.- ( User) WolfKeeper ( Talk) 03:53, 14 May 2008 (UTC)

I've semi-protected the article; Tombe evidently is on a dynamic IP. I really don't want to protect the talk page, as then legitimate IP and new users are locked out of the article completely. In my opinion, feel free to just delete IP trolling on this talk page while he's blocked. We'll see what happens when the protection expires; may have to look into a range block, though i hate that too. Let's see how it goes. -- barneca ( talk) 04:22, 14 May 2008 (UTC)

I just removed three more edits. David, if you want to appeal the block, feel free to follow the instructions that were given to you on your talk page. -- Itub ( talk) 08:32, 14 May 2008 (UTC)

Note that FyzixFighter and PeR appear to be correct, and User:71.251.177.97 is very likely not David Tombe, but instead a troll trying to impersonate Tombe. Also agree with Anome that stuff like that, from that general IP range, can be removed by anyone as trolling. -- barneca ( talk) 17:59, 15 May 2008 (UTC)

This page is for discussing the article. Although the some of the discussions with David Tombe are related to the subject, I would really appreciate it if they could be kept on his talk page. One reason is I'd like to be up to date with the general discussion on this page, and it simply takes too long to read all the debates. Another reason is that he is currently blocked, and tempting him to answer via IPs is unfair, as that could have consequences for him. (He is allowed to edit his own talk page while blocked.) -- PeR ( talk) 15:12, 14 May 2008 (UTC)

P.S. I know I haven't always kept to this myself in the past. -- PeR ( talk)

This is a fair request. For everyone's information, discussions with no prospect of contributing to this article may be summarily archived. It seems increasingly unlikely that discussions with Mr. Tombe have any such potential, so if they get in the way... See also WP:TALK. -- SCZenz ( talk) 16:53, 14 May 2008 (UTC)

In all the presentations of the fictitious forces, the Coriolis term and the centrifugal term appear with the same sign. Yet in the example in the section entitled "Fictitious Forces" claiming that a fictitious centripetal force acts on a stationary object as viewed from a rotating frame of reference, the two terms suddenly take on opposite signs.

Could we have a citation which explicitly states that the rotating frame of reference transformation equations apply to particles which don't themselves physically connect to the ω term.

It strikes me that someone somewhere has lost the connection between the maths symbols and the physical reality to which they are supposed to relate to. David Tombe ( talk) 13:30, 16 May 2008 (UTC)

Itub, we need the exact page number and paragraph and preferably we would like to see the exact quote. David Tombe ( talk) 13:38, 16 May 2008 (UTC)

I did give the page number. Feel free to check out the book. It's even available on Google. -- Itub ( talk) 13:46, 16 May 2008 (UTC)

Itub, can we please have the exact quote. David Tombe ( talk) 13:51, 16 May 2008 (UTC)

No. Go and do your own homework. -- Itub ( talk) 13:56, 16 May 2008 (UTC)

In other words Itub, there is no quote that backs up your point and the citation is bogus. David Tombe ( talk) 13:59, 16 May 2008 (UTC)

Go here [8]. Click on the top hit for that search. Read page 233. -- The Anome ( talk) 14:01, 16 May 2008 (UTC)

Anome, Page 233 wasn't available. We need to see an exact quote which explicitly states that the transformation equations apply to particles which don't themselves physically connect to the ω term.

What do you mean "physically connect to the ω term"? That doesn't make any sense. Here is the direct link to page 233: [9] -- Itub ( talk) 14:21, 16 May 2008 (UTC)

The examples on page 234 relate to co-rotation so it doesn't look very promising. David Tombe ( talk) 14:16, 16 May 2008 (UTC)

Itub, I've seen page 233. It disproves your point. It doesn't state anywhere that those equations apply to particles that are not co-rotating with the frame. The only example given is an example involving co-rotation. And the Coriolis force term and the centrifugal force term both have the same sign. In the example in the 'fictitious forces' section in the main wiki article on centrifugal force, you have reversed the sign of the centrifugal force in order to try and make your theory make sense.

There is no such theory. The artificial circle idea is the original research of one of the editors here. And you have all been destroying this article in the name of serving that original research. David Tombe ( talk) 14:31, 16 May 2008 (UTC)

The sign is correct. The equation in the book is a vector product. Note that ω (ω r) = –ω²r. This is trivial (vector) algebra. -- Itub ( talk) 14:39, 16 May 2008 (UTC)

Plus, the book (like all the others) doesn't mention co-rotation, because it is meaningless. It just mentions the coordinate transformation. -- Itub ( talk) 14:41, 16 May 2008 (UTC)

There is no negative sign on your centrifugal force in the section in question in the main article. And your book doesn't say that those equations apply to particles that don't have the angular velocity ω. Where did that theory about the artificial circle come from? It's not in your book. David Tombe ( talk) 14:45, 16 May 2008 (UTC)

Of course it is, when it says that the particle may be moving with respect to your reference frame, you can generalize it to all cases, including having the particle fixed in the inertial frame. The negative sign just results from the change of notation used in this article. It is exactly equivalent. -- Itub ( talk) 14:47, 16 May 2008 (UTC)

Now you are just talking nonsense. If the particle is stationary in the inertial frame, then it relates in no way to ω. The entire derivation of those equations was based on a particle whose tangential speed is related to ω. As for the signs, you have cooked the books in the main article by making the centrifugal force have a positive sign. David Tombe ( talk) 14:49, 16 May 2008 (UTC)

David, please read Wikipedia's civility policy. -- The Anome ( talk) 14:59, 16 May 2008 (UTC)

If they are talking nonsense, you will be able to give us a proof that the coriolis and centrifugal forces/accelerations, when applied together give incorrect results when applied to a non corotating body. We don't require a general proof, a single, worked numeric example will do. Body x is at (3,4,5) moving with speed (-3,4,5)... Either you can do that, or you can't. Everyone here says you can't, because the equations are general, and correct. But if you think you can prove us wrong. Go right ahead. Indeed, I personally will be only too happy to learn something new.- ( User) WolfKeeper ( Talk) 00:13, 17 May 2008 (UTC)

Do they have a "gun-boat diplomacy policy" too, to deal with administrators who engage in debates while continually threatening to permanently block those who they disagree with? David Tombe ( talk) 17:44, 16 May 2008 (UTC)

See WP:ADMIN for the relevant policy on this and on how to resolve it. Specifically, Wikipedia:Administrators#Grievances_by_users_.28.22Administrator_abuse.22.29 where it gives the avenues for handling allegations of "gun-boat diplomacy". If you believe admins have misused their privileges, then bring it up on the relevant noticeboards ( WP:ANI or WP:RFC/ADMIN). Cheers. -- FyzixFighter ( talk) 17:56, 16 May 2008 (UTC)

Absolutely. You are welcome to ask for my actions to be reviewed at any time: this is one of the reasons why I requested a review by other admins when I blocked you earlier. -- The Anome ( talk) 00:36, 17 May 2008 (UTC)

David: The Coriolis term depends on the velocity vector, so it flips sign if the velocity flips sign. If you look at Centrifugal_force#Examples you will see that the Coriolis force is opposite to the centrifugal force if the velocity has the appropriate direction. Brews ohare ( talk) 15:12, 16 May 2008 (UTC)

Brews, look at my reply to FyzixFighter below. It might help solve alot of your queries about the A vector in EM. David Tombe ( talk) 15:26, 16 May 2008 (UTC)

FyzixFighter, that was an interesting reference and it actually was relevant unlike the one supplied by Itub. It brought attention to the point that I have been driving at.

I have noticed that you in particular have been very interested in examining these effects starting with the coordinate-less velocity vector. We are agreed that this results in a vXω acceleration at right angles to the direction of motion and it is identical in principle to the qvXB force in electromagnetism.

This fact alone should direct you to the Faraday paradox and tell you clearly that the principle of equivalence does not apply to rotation.

Anyway, the expression vXω is the parent term for both the Coriolis force and the centrifugal force. Can you now see how Maxwell derived vXB from his sea of vortices? It's centrifugal force which he believed to be real and to be the cause of magnetic repulsion.

Anyway, those diagrams on P349 that you referred to correctly show that it doesn't matter what direction v is in to get the vXω deflection.

But I can assure you that if you split vXω into two mutually perpendicular components in polar coordinates, one being the Coriolis force and the other being the centrifugal force, then the Coriolis force will be the tangential component. The two can never act along the same line.

It was an interesting reference, but I want a reference which explicitly states that the transformation equations apply to particles that are not related to the ω vector, because the derivation explicitly requires that the particle in question possesses ω as its own angular velocity. David Tombe ( talk) 15:28, 16 May 2008 (UTC)

Hi David: It would help me to know whether we are on the same page if you would answer this question: Do you have any quarrels with the examples given? Several of them involve the Coriolis force. For example, the Centrifugal_force#Dropping_ball example clearly invokes the Coriolis force, but the ball is not co-rotating. Brews ohare ( talk) 16:03, 16 May 2008 (UTC)

David. can you provide a reference that states that the transformation equation applies only to co-rotating objects? Also the reference in Marion&Thornton says (literally, I'm pretty sure, I'll check when I get home.) that if you modify Newton's second law by the terms in the transformation equation, that you get the EoM for a particle as described in a rotating frame. This means any particle including those that are not co-rotating. ( TimothyRias ( talk) 15:36, 16 May 2008 (UTC))

Timothy, G David Scott of the University of Toronto wrote about centrifugal force. He said,

"The centrifugal forces must be recognized for what they are --- Non-Newtonian forces acting on masses at rest in a rotating frame."

I'll try and get you the full name of the publication. David Tombe ( talk) 16:36, 16 May 2008 (UTC)

Here is the link to GD Scott – however, this article requires a subscription – I cannot access it. [ [10]] Brews ohare ( talk) 16:55, 16 May 2008 (UTC)

Brews, none of your examples involved the Coriolis force. The final example did involve a tangential deflection as viewed from the rotating frame, but that is not a Coriolis force.

Take a look at these two situations.

(a) Imagine a pole sticking up from the ground. An electrically charged projectile passes it at ten yards in straight line motion in the horizontal plane.

We will have the vXω (parent force for centrifugal and Coriolis) acting on the projectile due to its inertia. If the gravitational attraction of the pole is negligible, the straight line motion follows exactly as the solution to motion in a zero-curl field. Kepler's laws get rid of the Coriolis force and we are left exclusively with centrifugal force (inertia). The solution is a hyperbola of infinite eccentricity which is a straight line.

Now consider a particle at rest. Rotate the pole and nothing will happen.

(b) Consider the pole now to be a bar magnet with the magnetic axis along the length of the pole. This puts a curl into the field.

The Lorentz force is vXω (remember, Maxwell derived the Lorentz force with B being related to angular velocity).

This time the projectile describes a curved path due to the curl in the field.

However, rotate the pole on its magnetic axis and nothing happens.

The Faraday paradox and the Bucket argument are the same thing.

In your examples there is no curl and so there is no Coriolis force.

To get Coriolis force we need hydrodynamics. Maxwell showed that the magnetic field was hydrodynamics.

In meteorology, we get Coriolis force because elements of air move relative to the larger entrained body of rotating atmosphere. Kepler's laws don't apply on the inter molecular scale and we can see that the Coriolis force is a real effect simply by observing the spiral cyclones from space. David Tombe ( talk) 17:14, 16 May 2008 (UTC)

Hi David: Well, you haven't directly answered my question about the Dropping Ball example, although your statement "In your examples there is no curl and so there is no Coriolis force." seems to mean you disagree with it. I'd like to track down how we might differ on this example – that might help me to understand your viewpoint. To reprise the article's approach, the rotating observer sees the falling ball trace out a circular path. As with any student of mechanics, he concludes a centripetal force must be at work – otherwise the ball should follow a straight line, and obviously it does not do that. That is about as far as he gets with this problem. However, if he does a bit more study, looks at balls falling at different rates and radii, he will come up with an explanation based upon the forces F = –2mΩ × v – mΩ × ( Ω × r). Call them what you will, if these forces are put into Newton's laws the correct trajectories emerge. Where would you fault this process? Brews ohare ( talk) 18:03, 16 May 2008 (UTC)

Brews, I'll summarize my points of disagreement and then we'll have to go into to them each in more detail.

(1) The circular motion as viewed from the rotating frame is only an artifact. There is nothing real about it. No forces are acting at all. There is no inertia. There is no centripetal force.

(2) Coriolis force never acts in the radial direction. Coriolis force and centrifugal force are mutually perpendicular components of a parent vXω force. The former causes an east-west deflection on north-south motion. The latter causes a radially outward deflection on tangential motion.

(3) Even if we were to accept that the Coriolis force could act radially, we still end up with a net inward acceleration. That is not circular motion. The radial acceleration for circular motion must be zero.

This is borne out by orbital theory. The radial acceleration is the sum of the inward acting gravity force, which is the centripetal force, and the outward acting centrifugal force. When we have a circular orbit, these two cancel and the radial acceleration is zero.

(4)The signs in the transformation equations are based purely on the vector notation. We cannot know the actual signs until we know the real physical situation. And in this case, there is no real physical situation.

(5) I don't know where you found that theory about a fictitious centripetal force being composed of a fictitious outward centrifugal force and a fictitious inward Coriolis force twice as strong. Did you find it here on wikipedia? I can assure you that it is badly wrong.

(6) the transformation equations only apply to objects that possess the angular velocity in question. The derivation insists upon that. David Tombe ( talk) 18:38, 16 May 2008 (UTC)

Hi David: Thanks for the list. It provides a good starting point. To begin, I have innumerable sources that provide the force as F = –2mΩ × v – mΩ × ( Ω × r). Among them are Georg Joos & Ira M. Freeman (1986). Theoretical Physics. New York: Courier Dover Publications. p. p. 233. ISBN  0486652270. {{ cite book}}: |page= has extra text ( help) and Vladimir Igorevich Arnolʹd (1989). Mathematical Methods of Classical Mechanics. Berlin: Springer. p. §27 pp. 130 ff. ISBN  0387968903.. They also are derived at Fictitious_force#Rotating_coordinate_systems. Can we agree that these forces apply? Brews ohare ( talk) 19:04, 16 May 2008 (UTC)

Brews, OK, we'll start with that one. I was never denying that mathematical expression. I was saying that nobody as yet has provided a citation which explicitly states that the above equation can be applied to objects that do not physically possess the angular velocity ω. The derivation of that equation begins by considering a particle which possesses that angular velocity. David Tombe ( talk) 04:31, 17 May 2008 (UTC)

Hi David: Glad you decided to respond. My interpretation of the variable ω is as the rate of rotation of the frame, not the object to which the force is applied. To support this view, see Joos above (p. 232) and Arnolʹd as cited above. For example, in Section 26 Arnolʹd says (p. 126): "We first consider the case when our point is at rest in K and the coordinate system K rotates. In this case the motion of the point q is called a transferred rotation. Example. Rotation with fixed angular velocity ω... Theorem At every moment of time t, there is a vector ω (t) such that the transferred velocity is ... The vector ω is called the instantaneous angular velocity ; clearly it is defined uniquely by Equation (4).. Then, on the cited page (p. 130) he refers us back to this Section for the definition of ω. See also derivation.

Assuming this interpretation of ω, the actual motion of the body with mass m as seen in the rotating system can have any trajectory, and in particular, can be stationary as viewed in an inertial frame. The fictitious forces apply regardless. That is how the dropping ball example is handled. This view appears to agree with Arnolʹd (p. 130):"This [centrifugal] force does not depend on the velocity of relative motion, and acts even on a body at rest in the coordinate system K" {My emphasis: I interpret this as also saying "even on a body not at rest"}.

If you wish to argue that I am misinterpreting these authors, one approach to discussion would be to argue using the derivation, as that is very much available to us, and it is not necessary to hunt through pages of reference to find the definitions. Brews ohare ( talk) 17:25, 17 May 2008 (UTC)

To quote from the article:

To answer this question, let the coordinate axis in B be represented by unit vectors u_j with j any of { 1, 2, 3 } for the three coordinate axes. Then

${\displaystyle \mathbf {x} _{B}=\sum _{j=1}^{3}x_{j}\ \mathbf {u} _{j}\ .}$

The interpretation of this equation is that x_B is the vector displacement of the particle as expressed in terms of the coordinates in frame B at time t. From frame A the particle is located at:

${\displaystyle \mathbf {x} _{A}=\mathbf {X} _{AB}+\sum _{j=1}^{3}x_{j}\ \mathbf {u} _{j}\ .}$

In this quotation frame A is inertial and frame B is accelerating. The derivation then carefully distinguishes between the motion of the particle and the change in the coordinates and unit vectors in the accelerating frame. The result is the equation for forces that is agreed upon. The definition of ω is as below:

If the rotation of frame B is represented by a vector Ω pointed along the axis of rotation with orientation given by the right-hand rule, and with magnitude given by

${\displaystyle |{\boldsymbol {\Omega }}|={\frac {d\theta }{dt}}=\omega (t)\ ,}$

then the time derivative of any of the three unit vectors describing frame B is: ^{[1] [2]}

${\displaystyle {\frac {d\mathbf {u} _{j}(t)}{dt}}={\boldsymbol {\Omega }}\times \mathbf {u} _{j}(t)\ ,}$

and

${\displaystyle {\frac {d^{2}\mathbf {u} _{j}(t)}{dt^{2}}}={\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {u} _{j}+{\boldsymbol {\Omega }}\times {\frac {d\mathbf {u} _{j}(t)}{dt}}={\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {u} _{j}+{\boldsymbol {\Omega }}\times \left({\boldsymbol {\Omega }}\times \mathbf {u} _{j}(t)\right)\ ,}$

These unit vectors are attached to the rotating frame, not to the object under observation.

This discussion has motivated me to be more careful in my derivation, so I've added a few words and a Figure to make this point inescapable. So, kudos, David: a better article has resulted. Brews ohare ( talk) 19:16, 17 May 2008 (UTC)

First of all, the Coriolis term should be at right angles to the centrifugal term, but you have decided that it can act along the same radial line. Next, you reverse the sign on the centrifugal term arbitrarily in order to make it act in the opposite direction from the Coriolis term. You then conclude that the difference between the two is the net inward centripetal force. But that is yet another mistake, because in circular motion, there is no net radial force. You have got it all so wrong in so many respects. If you look on the main article, you will see a section entitled 'Fictitious Forces'. This is the section that contains your incorrect theory about the fictitious forces adding up to give a fictitious centrieptal force on an object that is stationary in the rest frame. But notice how you have taken the centrifugal force out of its vector format and given it a positive sign. If you had left it as it appears in the transformation equations, it would have had the same sign as the Coriolis force and your theory wouldn't work. But somebody has cooked the books and taken the negative sign away from the centrifugal force. Hence it appears that what is claimed to be true seems not to be the case. Hence you appear to be mistaken. 72.64.56.156 ( talk) 20:04, 17 May 2008 (UTC)

Tell me; oh wise anonymous one, if the coriolis is always at right angles to the centrifugal force, how come in the atmosphere, the circling winds are acted on by the coriolis centered on the high pressure or low pressure zone, rather than the center of the rotating frame (i.e. the Earth's axis). Centrifugal force always acts away from the axis of the frame, but the coriolis in the atmosphere acts radially to the circular motion- it acts at 90 degrees to the motion of the air, not the rotation of the planet/frame!!!!!! The only reason you get those nice circular patterns is because you're wrong about this. - ( User) WolfKeeper ( Talk) 21:29, 17 May 2008 (UTC)

Hi 72.64.56.156: Of course, you can take up this argument as simply a statement of your prejudices, but that only leads to my doing the same thing. To advance, what is needed is to actually "look under the hood" and decide where in the math some hidden assumption has occurred, or some stupid algebraic error.

As of now, my view is that the math is tight as a drum, the logic impeccable and the assumptions all out in the open. The result of this exemplary work: the exact same forces espoused by all the references that I can find. Brews ohare ( talk) 22:03, 17 May 2008 (UTC)

Hi again 72.64.56.156: I apologize for my truculence above. You have suggested that an error in sign has been made in evaluating the vector cross-products. This matter is somewhat subtle, because the velocity entering the Coriolis force is the velocity seen from within the rotating frame. The centrifugal term is straightforward: −Ω × (Ω × r ). Vector r is radially outward,(Ω × r ) is tangential to the orbit, and Ω × (Ω × r ) is normal to the orbit and inward. Hence, with the − sign the centrifugal force is outward, as perhaps you agree. The Coriolis term is −2(Ω × v_rot ) =+2(Ω × (Ω × r )! The plus sign comes because the velocity of a body in the rotating frame is the negative of (Ω × r ). Consequently, (Ω × (Ω × r )) points inward, and the sum 2m(Ω × (Ω × r )) –mΩ × (Ω × r ) =mΩ × (Ω × r ) is the necessary inward centripetal force.

An example is the dropping ball problem. Here the centrifugal force is outward (as always). However, (Ω × r ) points oppositely to the observed velocity in Figure 3. Consequently the Coriolis force is inward.

It's confusing, I agree. I've edited the article to make the evaluation clearer. Thank you. Brews ohare ( talk) 02:47, 18 May 2008 (UTC)

For Huygens and Newton centrifugal force was the result of a curvilinear motion of a body; hence it was located in nature, in the object of investigation. According to a more recent formulation of classical mechanics, centrifugal force depends on the choice of how phenomena can be conveniently represented. Hence it is not located in nature, but is the result of a choice by the observer. In the first case a mathematical formulation mirrors centrifugal force; in the second it creates it.

The primary aim of this paper is to show that in the eighteenth century centrifugal force was a problematic notion in many respects. Moreover, I intend to show that current views concerning the ideas on centrifugal force expressed by Newton in the Principia mathematica are severely affected by the projection of modern methods and ideas that are found neither in the Principia nor in works contemporary with it. I hope that my analysis will stimulate a fresh reflection on Newton's mechanics and its reception.

The Relativization of Centrifugal Force Author(s): Domenico Bertoloni Meli Source: Isis, Vol. 81, No. 1, (Mar., 1990), pp. 23-43 Published by: The University of Chicago Press on behalf of The History of Science Society.

David Tombe ( talk) 17:33, 16 May 2008 (UTC)

Thank you! This is an interesting piece of research, and it's actually verifiable [11]. We can build on this. Can you find any similar historical research? If you can, this would definitely be a good basis for writing a section on historical views of centrifugal force, which, as the quote above suggests, were probably quite different to modern views. -- The Anome ( talk) 17:48, 16 May 2008 (UTC)

Anome, the point remains, can you tell me exactly what is the fringe point of view that you keep accusing me of trying to push?

Here in essence, as far as I can remember, was my introduction which started the war,

When an object undergoes curved path motion, it experiences a force directed away from the center of curvature. This force is known as the Centrifugal force (from Latin centrum "center" and fugere "to flee").

Centrifugal force should not be confused with the inward acting centripetal force which causes a moving object to follow a circular path.

In the days of Newton, Bernoulli, and Maxwell, centrifugal force was considered to be a real force, but the official position nowadays is that centrifugal force is only a fictitious force which acts in rotating frames of reference.

Where is the fringe viewpoint contained within this very basic and easy to read introduction? David Tombe ( talk) 18:22, 16 May 2008 (UTC)

I'd describe the fringe viewpoint as follows: "An object undergoing curved path motion experiences a force directed away from the center of curvature. The previous sentence is true in any reference frame." Do you agree that in your introduction you are promoting this viewpoint? If so, then that's the answer to your question, because this is a fringe viewpoint. If not, perhaps you should have written more clearly. :-) -- Steve ( talk) 19:02, 16 May 2008 (UTC)

Yes. The modern interpretation would rephrase your sentence as: "In classical mechanics, [w]hen an object undergoes curved path motion, it experiences a force directed away from the center of curvature it is because it is subject to a force component orthogonal to its direction of motion. "

Also, you haven't provided any cites that state that Bernoulli (1700–1782) and Maxwell (1831–1879) believed anything other than the current interpretation; or provided any evidence that Meli's paper supports the position articulated in your quote above; as far as I can see, the quote you give above only supports the assertion that Newton (1643–1727) and Huygens (1629–1695), according to Meli, a modern scholar, arguably believed that "centrifugal force was the result of a curvilinear motion of a body; hence it was located in nature, in the object of investigation."

Additionally, as far as I can see, I the fourth sentence of the quote from Meli's paper can only be interpreted in context as follows (comments mine): "In the first case" [ie in Newton and Huygens' formulation, see the first sentence] "a mathematical formulation mirrors centrifugal force; in the second" [ie in the modern formulation, see the second and third sentences] "it creates it." The exact terms used to describe this modern position, in the second and third sentences, are "centrifugal force depends on the choice of how phenomena can be conveniently represented. Hence it is not located in nature, but is the result of a choice by the observer." Which is in accordance with the description of the modern formulation in the current consensus version of this Wikipedia article. -- The Anome ( talk) 19:38, 16 May 2008 (UTC)

Sounds like total confused justification of what you want to believe to me. All you have done is demonstrate that you are closed minded and prejudiced against any provable views which you disagree with. Hence you reject all citations by MR Tombe that supports his position. That is basically a reflection of your bias and prejudice against him. He could cite a hunderd papers that support his position and you would reject every one of them and remove his justified edits made according to your rules, because you dont want to believe his views are correct. Thus your personal opinions are prejudicing the information found on wikipedia. This sems to be in violation of your own rules. Maybe you should read them and follow them yourself. So far I see no proof that what you say in the, now locked, main article regarding centrifugal force is correct. 72.64.40.215 ( talk) 13:03, 18 May 2008 (UTC)

Anome,

Here is a quote from Bernoulli out of the ET Whittaker book on the history of aethers.

"The elasticity which the Aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools."

And here is a quote from Maxwell's paper 'On Physical Lines of Force' in relation to the mutual repulsion that occurs between adjacent magnetic field lines,

"The explanation which most readily occurs to the mind is that the excess of pressure in the equatorial direction arises from the centrifugal force of vortices or eddies in the medium having their axes in directions parallel to the lines of force"

When you first denied that these quotes indicate that Maxwell and Bernoulli believed centrifugal force to be real, you lost all credibility.

A few hours ago somebody put in a bogus citation in reply to a 'citation needed' request. When pressed to give the actual quote, they began to drag their feet. In the end, we saw that there was nothing in the citation that was relevant.

When I removed the citation, I got a warning in my tray from you not to remove valid citations.

This has been your characteristic gun-boat diplomacy style all along.

You are steering this article to support a fringe viewpoint which does not appear in any textbook, and to that end, you are abuisng your administrative powers.

The fringe theory in question was probably the original research of one of these wikipedia editors.

I will remove it now. Feel free to block me permanently if you so wish, but your intervention in this debate along with the behaviour of the others has turned the whole page into a circus. David Tombe ( talk) 04:47, 17 May 2008 (UTC)

It comes down to the community's reading of the citations, actually; I see clear consensus that your point of view remains essentially unsupported, whereas the article's current text is supported. Mr. Tombe has been blocked for one week for removal of cited material despite many warnings; see his talk page for more details. -- SCZenz ( talk) 06:20, 17 May 2008 (UTC)

As I said previously, using the term "centrifugal force" in a scientific paper is perfectly respectable: it is entirely legitimate to use the concept of centrifugal force to explain motions from the viewpoint of a particular rotating reference frame -- indeed, the current version of the article goes to great lengths to make this clear -- and does not necessarily imply that the author is using the term in a way that is different from the modern usage. If you had a quote from Maxwell or Bernoulli defining centrifugal force in a way that conflicts with the modern usage, or a published peer-reviewed paper such as Meli's -- better yet, several such sources -- that held that Maxwell and Bernoulli believed that it meant something different, you might have a basis for making that assertion; but in the absence of such a source, drawing such a conclusion from the mere use of the term is original research. -- The Anome ( talk) 10:07, 17 May 2008 (UTC)

Although I personally disagree with David Tombe on the points he has raised, response to his points has led to the tightening of the arguments in the articles and the addition of two figures, one in fictitious force and one in centrifugal force and a clarification of sentences and phrasing that make both articles much clearer. In my opinion, this improvement would not have occurred without David's input. Debate is useful, despite a tendency to boil over. Brews ohare ( talk) 16:56, 18 May 2008 (UTC)

Absolutely. This is why I have not been eager to have David indefblocked, I see blocking as a last-resort sanction to help enforce Wikipedia's rules of engagement, and not as a measure for suppressing dissenting opinions. Providing he can work within the WP:NOR/ WP:V/ WP:NPOV rules, and keep the discussion oriented towards improving the article according to those principles, I believe that the debate is extremely useful as a way of improving the article.

As you say, he has driven the article towards a much more closely-argued structure, and, albeit indirectly, helped improve it from a B-class article to an A-class article. If he wants to work within the rules, I think he can help more directly; his discovery of Meli's paper arguing that early ideas of centrifugal force did not match the modern interpretation is particularly valuable: if he, or any other editors, can find other verifiable supporting sources showing other scholars support this view, this could be the basis for a really interesting section on historical views of centrifugal force.

Having said which, the rules of engagement remain non-negotiable: if any editor refuses consistently to abide by the community norms over a long enough period of time, they will sooner or later end up permanently blocked from editing, as an unfortunate last resort. I still hope this won't need to happen. -- The Anome ( talk) 19:36, 18 May 2008 (UTC)

We now have a fairly good, well referenced, account of the modern treatment of the concept of centrifugal force in classical mechanics. I'm sure it can be improved in the long term from a pedagogical viewpoint, but it's an excellent start. However, I think there are several ways in which this article could be improved further.

Firstly, it would be useful to have a section on the development of the concept of centrifugal force in the history and philosophy of science. For example, there appears to be some literature (see above) to suggest that the concept of centrifugal force held by Newton and Huygens differed somewhat from the modern concept.

Secondly, it would be useful to have a section on the everyday conceptualization of centrifugal force from the viewpoint of naive physics. There appears to be a fair amount of research on this, particularly from the viewpoint of research into science education, where it is a major stumbling block for students. There is also some research devoted to the concept as an example of metaphor formation in the artificial intelligence literature.

Thirdly, it would be interesting to have a section on how these problems are overcome in science education: there also appears to be some literature on this topic, including studies of the effectiveness of different approaches.

With these sections in place, based on reliable sources and cited to the same standards as the rest of the article, I think we would be in a good position to push towards featured article status.

Would anyone be interested in developing these topics further? -- The Anome ( talk) 10:35, 21 May 2008 (UTC)

Thoughtful suggestions. I do not intend to pursue these matters just now, but they would make a beautiful article. Brews ohare ( talk) 13:18, 22 May 2008 (UTC)

One of three key objections to the extrapolation of the transformation equations to fictitious situations surrounds the issue of 'net radial force'.

These transformation equations are claimed to produce a net centripetal force on a particle that is at rest in the inertial frame but viewed from a rotating frame.

However, in circular motion, it is quite obvious that the net radial force is zero.

Consider the general equation for a central force orbit. It takes the form,

Applied Centripetal Force + Induced Centrifugal Force = Resultant Radial Force

This is the equation used for the gravity orbit.

We can also apply it to any orbital motion. Consider an object being swung around in a circle on the end of the string.

T for tension goes into the centripetal force slot. mv^2/r is the centrifugal force. The resultant radial force is zero and hence we end up with the equation,

T = mv^2/r

If we try to apply this equation to the artificial circle according to the theory being pushing by the fictitiousists, we will have a net centripetal force mv^2/r. The radial accleration is zero and so the equation will not be balanced.

SBharris and others seem to think that the net radial acceleration in circular motion is not in fact zero. They base this on the fact that the centripetal force has supplied an inward radial force which causes the particle to continually change its direction.

Of course such a force does exist and does produce that effect. But the net radial acceleration is still zero and so the only conclusion can be that there is also an outward centrifugal force. And this outward centrifugal force can be observed inducing Archimedes' principle in a centrifuge. It can be felt reacting against the centripetal force as like weight in the case of gravity. It can even be observed in straight line motion in the absence of any centripetal force. And most importantly of all it is used in the complex analysis of planetary orbital motion.

Consideration of the more general elliptical and hyperbolic situations makes centrifugal force an essential tool in the analysis. If we restrict our studies to circular motion where centripetal force, induced centrifugal force, and reactive centrifugal force are all equal then the induced centrifugal force becomes obscured.

Elliptical situations can be compared to weight variations in an accelerating elevator. The normal reaction and the weight change, but gravity doesn't. Likewise in elliptical motion, the induced centrifugal force (analgous to gravity) is not cancelled by the centripetal force (analgous to normal reaction) and hence the reactive centrifugal force (analgous to weight) is not generally equally to the induced centrifugal force. David Tombe ( talk) 07:26, 24 May 2008 (UTC)

We must distinguish between applied and induced effects. The transformation equations tell us no physics. They merely tell us the mathemtical form of a force that acts at right angles to a motion. They tell us nothing about the source of either a centrifugal force or a Coriolis force.

We need actual physical situations in which to apply these equations to.

One good example is a rotating turntable with a radial groove in which a marble can roll along freely.

This situation demonstrates induced centrifugal force as a real radial effect.

But there is no naturally occuring induced Coriolis force in curl-free space.

When the marble rolls out radially, it is constrained to a co-rotating radial path by an 'Applied Coriolis' force in the tangential direction. This applied Coriolis force is directly analgous to centripetal force.

The marble in turn will cause an equal and opposite tangential force on the turntable. This will be a "Reactive Coriolis Force" by analogy with reactive centrifugal force.

This article has totally played down "induced centrifugal force" and relegated it to "colloquial centrifugal force" and more recently to the classic newspeak terminology "Centrifugal Tendency".

Rotation as the cause of induced centrifugal force has been censored in the main article. David Tombe ( talk) 08:00, 24 May 2008 (UTC)

Hi David:

Point 1. In a kinematic discussion, the only forces are force requirements. They are independent of the actual cause of the trajectory, and accelerations are determined strictly by the second derivative of the displacement vector. That leads to the equation:

${\displaystyle \mathbf {a} _{B}=\mathbf {a} _{A}-2{\boldsymbol {\Omega }}\times \mathbf {v} _{B}-{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {x} _{B})-{\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {x} _{B}\ ,}$

that is very well cited, and to which you have agreed earlier. We all can assume this equation is completely correct.

Point 2: Applied to the example cited, that of a body at rest in an inertial frame, but viewed from a rotating frame, it leads to the results in the article.

Consequently, the only recourse you have in arguing for a change is to show that the terms in this equation have been misapplied. That is a discussion in the form of a term-by-term mathematical counter assessment employing the displacement vector for the example. Mere verbiage is not appropriate. Neither is a digression outside the kinematical framework. Brews ohare ( talk) 13:46, 24 May 2008 (UTC)

Brews, the point that I was making was that in the case of the marble rolling out the radial line, the Coriolis term in the above equaion applies and so does the centrifugal force term.

But the equation above doesn't tell us why they apply. We know that they apply simply by observing the scenario. We know that the centrifugal force is induced in the radial direction. We know that there is an applied and a reactive Coriolis force in the tangential direction. The equation on its own tells us absolutely nothing in the absence of a real physical scenario within which to apply it. David Tombe ( talk) 14:10, 24 May 2008 (UTC)

The equation on its own tells us the acceleration acting upon the object in order for it to follow its path. It tells us "why" by stating the acceleration required for the path to occur. Assuming a point mass, no torque is possible, and given the mass, the acceleration dictates the force requirement. Anything outside of this framework also is outside the scope of the article. So, does your term-by-term mathematical counter assessment employing the displacement vector for the example disagree with that of the article? Brews ohare ( talk) 14:23, 24 May 2008 (UTC)

Brews, it's not even a transformation equation. It tells us nothing. It is modern physics gone mad. It gives us the mathematical form of the centrifugal force (and/or the centripetal force) and the Coriolis force and nothing more.

If you think that that equation contains real physics, then can you tell me exactly what trajecory it describes?

It's supposd to describe effects as viewed from a rotating frame. But it will only do that if those effects actually exist. David Tombe ( talk) 14:42, 24 May 2008 (UTC)

The effects exist. All you have to do is move the objects in a straight line and then rotate the coordinates by a time dependent angle, and you get a strange path out, which very much is due to centrifugal and coriolis in the rotating frame- these two accelerations explain what you see perfectly. Just try it, get a spreadsheet, like the google one and try it. I've done it before, it's as clear as your nose.- ( User) WolfKeeper ( Talk) 16:20, 24 May 2008 (UTC)

Wolfkeeper, we're going to have induced radial centrifugal force anyway in straight line motion relative to the origin, unless that motion is already absolutely radial. On top of that, you'll get an artifact circular motion. Those equations above might apply to the centrifugal force if the synchronization is correct. David Tombe ( talk) 16:55, 24 May 2008 (UTC)

Nothing was synchronised when I did it, I plugged in all manner of random velocities and angles, completely independent of the rotation rate. I got two self-evident accelerations, a radial one outwards and the coriolis that always curved the velocity in the opposite direction to the frame rotation. Plain as day. It's trivial, any spreadsheet can plot it. Just do it.- ( User) WolfKeeper ( Talk) 15:40, 25 May 2008 (UTC)

David: Pick an example, for example, the dropping ball. The analysis based upon the formula is described in the article using the above equation. The question then is: does your term-by-term mathematical counter assessment employing the displacement vector for the example disagree with that of the article? Brews ohare ( talk) 16:24, 24 May 2008 (UTC)

Brews, in the dropping ball example, all I can see is an artificial circular motion imposed upon the actual motion when it is viewed from the rotating frame.

I don't see either a centrifugal force or a Coriolis force at work. From the rotating frame of reference, we would need to see a tangential acceleration before we could start talking about Coriolis force. And we would need to see some radial acceleration before we could start talking about centrifugal force.

Those so-called transformation equations don't even describe the artificial circle.

The dropping ball is quite simply not a demonstration of either centrifugal force or Coriolis force.

I gave you the best demonstration. It is a marble rolling along a radial groove on a rotating turntable with a wall at the edge to hold it in.

That gives you everything,

(1) Induced centrifugal force

(2) Applied centripetal force

(3) Reactive centrifugal force

(4) Applied Coriolis force

(5) Reactive Coriolis force

The only thing it doesn't give you is induced Coriolis force and applied centrifugal force.

Induced Coriolis force is a tricky one, but applied centrifugal force would occur if an engine were to accelerate an object radially outwards along a groove on a rotating turntable. David Tombe ( talk) 16:38, 24 May 2008 (UTC)

The marble rolling along a radial groove on a rotating turntable is another example that shows how centrifugal force only exists in the rotating frame. In the inertial frame, there is just one force: the wall of the groove pushing tangentially on the marble (and of course, its reaction, the marble pushing on the wall). On the rotating frame, there are two fictitious forces: the centrifugal force pushing the ball outwards and the Coriolis force pushing the marble against the wall of the groove. The Coriolis force is balanced by the real force that the groove produces on the marble, so there is no tangential motion in the rotating frame. In this case, the Coriolis force is tangential. But if the groove were not radial, the Coriolis force would be perpendicular to the groove, and the Coriolis force would not be tangential. -- Itub ( talk) 09:20, 26 May 2008 (UTC)

No Itub, if the groove were curved, any radial force would be centripetal and centrifugal. Centrifugal force is a radial effect caused by actual tangential motion, no matter how we look at it. David Tombe ( talk) 09:56, 29 May 2008 (UTC)

In the inertial frame, the diplacement is

${\displaystyle \mathbf {r} (t)=h\mathbf {u_{z}} -v_{z}t\mathbf {u_{z}} }$

${\displaystyle {\frac {d^{2}}{dt^{2}}}\mathbf {r} (t)=0}$

In the rotating frame the ball drops veritcally in the same way, but appears to rotate:

${\displaystyle \mathbf {r} (t)=h\mathbf {k} -v_{z}t\mathbf {u_{z}} +R\mathrm {cos} \theta (t)\mathbf {u_{x}} +R\mathrm {sin} \theta (t)\mathbf {u_{y}} }$

This equation is the displacement of the ball as recorded by the rotating observer in their reference system. In the rotating frame the unit vectors appear stationary, so their estimate of the acceleration is

${\displaystyle {\frac {d}{dt}}\mathbf {r} (t)=-v_{z}\mathbf {u_{z}} -R\omega \mathrm {sin} \theta (t)\mathbf {u_{x}} +R\omega \mathrm {cos} \theta (t)\mathbf {u_{y}} }$

${\displaystyle {\frac {d^{2}}{dt^{2}}}\mathbf {r} (t)=-R\omega ^{2}\mathrm {cos} \theta (t)\mathbf {u_{x}} -R\omega ^{2}\mathrm {sin} \theta (t)\mathbf {u_{y}} =-\omega ^{2}\mathbf {r} _{\perp }(t)}$

that is, an inward centripetal force. Having no physical means of supplying this force. such as a tether or gravity, these observers resort to the fictitious forces of the article. When these fictitious forces are considered, the rotating observer agrees with the inertial observer that there is no real force on the ball, only the ubiquitous forces that they see everywhere, forces without apparent origin in gravity, electromagnetism etc.. Brews ohare ( talk) 17:21, 24 May 2008 (UTC)

David: I'll intersperse my comments among yours:

Brews, In circular motion there is no net radial acceleration. But if you resolve the motion along a diameter that is fixed in a Cartesian frame then you will get a simple harmonic motion.

You have just given the equations for simple harmonic motion above in terms of an X axis and a Y axis in a Cartesian system.

But there is no net radial acceleration otherwise the radius would be changing. David Tombe ( talk) 17:54, 24 May 2008 (UTC)

David: These remarks are incorrect. Circular motion when projected on an axis does become simple harmonic motion along the axis. That does not mean that circular motion IS simple harmonic motion. It means its PROJECTION is simple harmonic motion. Your remarks about radial acceleration have been dealt with completely and authoritatively by other commentators in earlier exchanges. Your idea here is plain and simply a misconception. Please re-read what has been said about this. For example, by SCZenz below. Brews ohare ( talk) 04:21, 27 May 2008 (UTC)

I've completed the argument below. It is all a straightforward application of derivatives. I'm sorry I haven't the opportunity to pursue this matter just now - I'll be away a few days. Brews ohare ( talk) 18:01, 24 May 2008 (UTC)

David, you continue to assume that the "net radial acceleration" is equal to ${\displaystyle d^{2}r/dt^{2}}$. That idea is inconsistent with position, velocity, and acceleration as vector quantities; you won't find any source that supports it. Lacking such support, as you know, you can't put any reasoning based on your assertion in the article. -- SCZenz ( talk) 19:20, 24 May 2008 (UTC)

SCZenz, we are exclusively looking at the radial component of the acceleration. That is all that is involved in central force analysis. Any advanced classical mechanics textbook will confirm that fact.

The only equation which is relevant for this entire article is,

applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

It is a second order differential equation and r is the variable. The centrifugal force is naturally induced by tangential motion and all we have to do is insert the applied centripetal force.

When we have circular motion, ${\displaystyle d^{2}r/dt^{2}}$ will be zero and hence the centripetal force will be cancelled by the centrifugal force.

That is all there is to it.

You can use that equation to analyze any central force situation.

But in your artificial circle example, you have a net inward centripetal force and so the equation is unbalanced. David Tombe ( talk) 07:45, 25 May 2008 (UTC)

You can't make false statements about vectors calculus true by fiat, no matter how many times you repeat yourself or say "that's all there is to it." -- SCZenz ( talk) 08:41, 25 May 2008 (UTC)

SCZenz, have you never seen the orbital equation being solved in an applied maths textbook? That equation that I have cited is a scalar equation. We are only interested in the radial component of the acceleration and variations in the radial magnitude. David Tombe ( talk) 10:38, 26 May 2008 (UTC)

David: It is your reading of the math books that is faulty here. If you wish to challenge the orthodox treatment of the article, you'll have to get mathematical yourself. I'm of the opinion that you are completely wrong and what you claim cannot be proven. You'd be more useful as a contributor if you focussed on matters other than the rigor of the approach, which is in good shape as it is now. Brews ohare ( talk) 04:21, 27 May 2008 (UTC)

To proceed, the fictitious force is:

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\Omega }}\times \mathbf {v} _{B}-m{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {x} _{B}).}$

Vector Ω describes the rotation of the rotating frame. If they observe the ball to be moving counterclockwise, this rotation is clockwise so:

${\displaystyle {\boldsymbol {\Omega }}=-\omega \mathbf {u_{z}} }$

Hence, Ω × v is:

${\displaystyle {\boldsymbol {\Omega }}\times \mathbf {v} _{B}={\boldsymbol {\Omega }}\times \left(-v_{z}\mathbf {u_{z}} -R\omega \mathrm {sin} \theta (t)\mathbf {u_{x}} +R\omega \mathrm {cos} \theta (t)\mathbf {u_{y}} \right)}$

${\displaystyle =-v_{z}{\boldsymbol {\Omega }}\times \mathbf {u_{z}} -R\omega \mathrm {sin} \theta (t){\boldsymbol {\Omega }}\times \mathbf {u_{x}} +R\omega \mathrm {cos} \theta (t){\boldsymbol {\Omega }}\times \mathbf {u_{y}} }$

${\displaystyle =0+R\omega ^{2}\mathrm {sin} \theta (t)\mathbf {u_{y}} +R\omega ^{2}\mathrm {cos} \theta (t)\mathbf {u_{x}} }$

${\displaystyle =\omega ^{2}\mathbf {r} _{\perp }}$

Consequently, the Coriolis force (related to -2 × the above) is inward radial with twice the value of the outward radial centrifugal force, leading to the rotating observer's requirement of an inward centripetal force, as calculated above. Brews ohare ( talk) 17:59, 24 May 2008 (UTC)

Hi David: I'll intersperse comments between yours:

Brews, you have just repeated the argument in favour of the artificial circle idea. I follow the argument perfectly. But I have four important objections to it.

(1) The velocity term in the Coriolis force is restricted by the derivation to be the radial velocity. Hence the Coriolis force can never swing around into the radial direction and work along the same line as the centrifugal force. The two are mutually perpendicular components of the one parent force mvXω which can be yielded directly from the velocity vector.

I do not understand how the derivation is so restricted. Please spell out the mathematical assumptions that are the supposed source of such restriction. Brews ohare ( talk) 04:07, 27 May 2008 (UTC)

Brews, the derivation begins with a vector triangle involving two components of a displacement vector for an actual particle. The first component leads to a fixed point on the rotating frame. In the limit, it becomes the tangential component and takes on the form ωXr. The other component is the velocity of the particle relative to the fixed point in the rotating frame. Hence, in the limit, it must be the radial component of the velocity.

The first component leads to a centrifugal force at that fixed point. The second component is the expression for a tangential Coriolis force if such were to be applied. David Tombe ( talk) 07:06, 27 May 2008 (UTC)

David: This is your derivation, not that above nor that of the article itself. So, maybe your derivation is limited, not those. Brews ohare ( talk) 13:59, 27 May 2008 (UTC)

(2) There can be no naturally induced Coriolis force in free space. We can only have an applied and a reactive Coriolis force, and both acting equally and oppositely in the tangential direction. No such Coriolis force exists in the artificial circle.

This is simply an assertion on your part with no support. Brews ohare ( talk) 04:07, 27 May 2008 (UTC)

Brews, it's not an assertion on my part. It follows directly from Kepler's law of areal velocity.

David: Kepler's law has absolutely nothing to do with this analysis, which is purely kinematic and has no necessary connection to Kepler's laws. Brews ohare ( talk) 13:59, 27 May 2008 (UTC)

That's not correct. The same situation is described at the very end of this web page

http://www.mathpages.com/home/kmath428/kmath428.htm

and it shows exactly the same thing, i.e., the Coriolis force is inward along the radial direction, opposite to the centrifugal force, and twice the size. This net inward inertial force is the force that holds the particle in its circular orbit with respect to the rotating coordinate system. TstoneT ( talk) 19:21, 26 May 2008 (UTC)

Tstone, if you had been following this from the beginning you would have seen all the reasons why what you say is wrong. To begin with, let's concentrate on the new section at the bottom about the scalar orbital equation. David Tombe ( talk) 07:09, 27 May 2008 (UTC)

(3) The centrifugal force is only induced on particles that actually possess the angular velocity ω. The entire derivation is based on a stationary anchor point on the rotating frame and it is at that anchor point that the centrifugal force acts.

Again, I fail to see any such restriction in the mathematics. Please point out mathematically where your viewpoint comes from. Brews ohare ( talk) 04:07, 27 May 2008 (UTC)

Brews, it's because the centrifugal force term evolves from the fixed point on the rotating frame that is the anchor point in the derivation. David Tombe ( talk) 07:15, 27 May 2008 (UTC)

David: This statement of yours is not a mathematical answer, but gobbledygook. Rephrase it in terms of the mathematics of the formulation in use in the article. Brews ohare ( talk) 13:59, 27 May 2008 (UTC)

Timothy Rias tried to wriggle out of that restriction by allowing the anchor point to slide all over the place. But if we do that, we have to change the ω accordingly, and the v term for the velocity relative to the anchor point will no longer refer to the velocity relative to the rotating frame.

(4) You continue to ignore the fact that in circular motion, the net radial force must be zero. In your example, you end up with a net inward centripetal force.

This notion is your own, and has no basis. Brews ohare ( talk) 04:07, 27 May 2008 (UTC)

Brews, it's not my own notion. In a gravity orbit, when there is circular motion, the radial acceleration absolutely has to be zero. See the new section below. David Tombe ( talk) 07:15, 27 May 2008 (UTC)

David: Gravity cannot enter into a kinematic argument, which is based entirely on trajectory, not on the kinetics. Brews ohare ( talk) 13:59, 27 May 2008 (UTC)

The central force equation is a second order differential equation on the radial distance. It takes the form,

Applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

When applied to the artificial circle and your above theory, it does not balance.

Why are you so keen to focus on artifacts rather than actual cases of centrifugal force? David Tombe ( talk) 07:58, 25 May 2008 (UTC)

David: two problems as I see it. Problem 1 is that you are so far off the beam that it may well be impossible for you to understand the presented arguments at all. Problem 2 is that you are unwilling to adopt the perspective of the article and show how it runs amok. Instead you flail away at it from premises that are of your own invention, thereby completely disconnecting yourself from any viable conversation. I have taken the time to outline in mathematical detail the approach of the article (which is also the approach of all published articles on the subject that I have read to date, and certainly that of the most reputable ones). In contrast, you have not undertaken to go through this math and point out what you consider to be its deficiencies. I find that reluctance on your part to be a failure to engage in responsible argument. If you were to do that, I believe you would rapidly identify your mathematical errors and abandon your viewpoint. Brews ohare ( talk) 04:28, 27 May 2008 (UTC)

Brews, see the new section at the bottom about the scalar orbital equation. I have pointed out the maths errors in the transformation equations on many occasions. Let's concentrate on that one issue for the meantime. David Tombe ( talk) 07:00, 27 May 2008 (UTC)

SBharris, the derivation of the transformation equations is essentially the same maths that is involved in polar coordinates. All we are doing is obtaining mathematical expressions in the radial and tangential directions for a force that acts at right angles to a motion.

The Coriolis force term is unequivocally a tangential term.

Whoever was first to apply that Coriolis term to radial motion made a big mistake and it doesn't surprise me at all if Feynman fell for it too, or for all I know maybe even originated it.

On radial motion there is only one important equation. It is,

Applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

Hence if we have a circular motion, then ${\displaystyle d^{2}r/dt^{2}}$ will necessarily be zero and the centrifugal force will be exactly balancing the centripetal force.

It has got nothing to to with frames of reference. We can see radial motion in a system perfectly well without having to rotate with that system.

Your big problem is that just because you have seen that a centripetal force is acting radially inwards, you then assume that there must be a net radially inward acceleration. Yet it is obvious that there isn't.

It is obvious that there is. Acceleration is change in velocity, not change in speed, and velocity along that radial vector is always changing in direction. Thus, the object is being accelerated. Any time you have an object moving along a straight line in space, and you apply a momentary force tangentially to it (for the briefest time you can imagine) you'll get the same thing: a change in direction, but no change in speed. But you can tap it this way on the side as many times as you like, until finally it is going entirely the opposite direction from before, yet still with the same speed! ${\displaystyle d^{2}s/dt^{2}}$ = 0 in all this, but ${\displaystyle d^{2}r/dt^{2}}$ if r is a vector, is obviously changed, because now the velocity vector is pointed oppositely. Are you going to claim no acceleration has taken place just because the speed hasn't changed? That's exactly what happens when something moves in a circle. S B H arris 02:57, 26 May 2008 (UTC)

So you look at ${\displaystyle d^{2}r/dt^{2}}$ = zero yet still claim that there is a net radial acceleration. This is because you don't want to involve the centrifugal force which is a critical aspect of the entire central force analysis.

And now having realized that since gravity and centrifugal force are both radial and that hence if one is real, the other must also be real, you have decided to opt for the ludicrous conclusion that they are both fictitious. David Tombe ( talk) 08:21, 25 May 2008 (UTC)

You know, when you get the Nobel Prize in Physics, you can mention how Feynman was wrong during your acceptance lecture. Then we can cite that and it won't be considered original research by Wikipedia. -- Itub ( talk) 15:48, 25 May 2008 (UTC)

The orbital equation,

Applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

is a scalar equation. The only variable is the radial distance. It is solved as a scalar equation in standard university applied maths textbooks such as Goldstein's.

If you would only apply that equation to any non-circular scenario, then all your problems regarding centripetal force, reactive centrifugal force and induced centrifugal force would be explained. But by confining your studies to circular motion, the ensuing equality of the three blurs the distinction between them.

On another matter, there are only two directions in space. There is radial and tangential. That is clear on both the microscopic and the cosmological scales. Cartesian coordinates and Newton's law of inertia are only good in the limited close-up context as like inside a cuboid kitchen where hyperbolic motion appears like straight line motion.

And because of Kepler's law of areal velocity, there is no naturally occuring Coriolis force and we don't need to do a full vector analysis of the problem.

"The unnatural, that too is natural".- ( User) WolfKeeper ( Talk) 10:35, 26 May 2008 (UTC)

Look, the bottom line is, go sit on a roundabout, and wave a ball about in your hand. You can feel the coriolis effect, and I guaranteed you that it's not always, or even mostly radial. I don't care what your polar coordinate maths says, you don't live in a polar coordinate world, you live in a 3D world, that's the way the human brain is wired.- ( User) WolfKeeper ( Talk) 10:35, 26 May 2008 (UTC)

And it's a pity that Itub doesn't pay as much attention to what Maxwell says as he does to what Feynman says. Feynman contributed nothing towards either classical mechanics or classical electromagnetism. You'll have to learn to move out of that 'Feynman worship' attitude whereby scientific progress ends forever at the mistakes that Feynman didn't spot. David Tombe ( talk) 10:08, 26 May 2008 (UTC)

Oh I wouldn't say that. He showed how classical mechanics, particularly Fermat's principle arises out of quantum mechanics for example; and he contributed knowledge of how the classical limit arose out of quantum mechanics in general.- ( User) WolfKeeper ( Talk) 02:30, 27 May 2008 (UTC)

I've now started a section on the historical development of the modern conception of centrifugal force in this article. I am by no means an expert in the history of science, and I'm unsure about how the references I've cited hold together: could an expert please review the material I have added so far? There appears to be significant work on this topic by Domenico Bertoloni Meli (for example, [12], [13]), however, most of the interesting papers on this subject are behind a paywall and inaccessible to me. -- The Anome ( talk) 12:23, 25 May 2008 (UTC)

Anome, before we do the history of centrifugal force, we still have to address the fact in the introduction that engineers today adopt a different attitude towards centrifugal force than do the applied mathematicians.

I am in the latter category by training but I have adopted the engineers attitude in the last few years. Since this debate began a few weeks ago, I have realized that the applied maths attitude to centrifugal force is actually worse than I had originally imagined.

Your introduction does pretty well explain the applied maths attitude correctly. My own opinion now, having scrutinized it in depth over the last few weeks is that it is total nonsense and that it doesn't explain centrifugal force at all.

But if it is the official opinion today amongst applied mathematicians, then so be it. That's what has to be stated under wikipedia rules and regulations.

But there is no need for you to excise the engineers's attitude from the introduction and remove key clauses like 'caused by rotation' or to demote it to merely a colloqiual viewpoint as would be held by the village idiots.

I would tend to extend the introduction something along the lines of,

The effects described above become real in situations where actual rotation induces actual outward radial acceleraion. This aspect can be seen in engineering devices such as the centrifuge and the centrifugal clutch.

Would you see any original research or fringe theory in such an extension? David Tombe ( talk) 10:25, 26 May 2008 (UTC)

You are basically saying that in engineering, centrifugal force has a different definition in "applied math". Can you provide a few references of engineering textbooks (preferrably written in the last 100 years) to back up that claim? If the definitions are truly different and incompatible, we can then create Centrifugal force (engineering), just like we have Energy (spiritual) for one of the definitions of energy that is different from Energy (physics). -- Itub ( talk) 11:08, 26 May 2008 (UTC)

I would say that "even" engineers know that velocity is a vector quantity, and the time derivative of a velocity (as a function of time) is nonzero if the V vector changes direction, EVEN if it does not change length. Give us all a break, Mr. Tombe. S B H arris 01:34, 27 May 2008 (UTC)

SBharris, even engineers know that a component of a vector is a scalar, and that the central force equation is a scalar equation in radial distance. Are you denying this scalar equation which is in all texbooks about orbital theory,

Applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

We are only concerned with the radial direction. You have consistently reminded us all that the centripetal force acts radially inwards and that it changes the direction of the particle even when the tangential speed remains constant. You seem to think that you are educating people that don't know the difference between speed and velocity.

But you are the one who has failed to tell us all why it follows that, if there is an inward radial centripetal acceleraion, that there must be a NET inward radial acceleration. In circular motion, there clearly isn't a net inward radial acceleration because ${\displaystyle d^{2}r/dt^{2}}$ has to be zero.

Are you denying the above equation? David Tombe ( talk) 06:25, 27 May 2008 (UTC)

Yes, and I told you why. The fact that a scalar dx^2/dt^2 in some direction is zero, does NOT mean, or imply, that there's no acceleration AT ALL, since the acceleration may be acting at right angles to direction of motion, in which case it does not change the scalar, and the accleration is never in the direction of the vector or the velocity, therefore does NOT change its length. Which is EXACTLY what is happening here. S B H arris 09:02, 27 May 2008 (UTC)

After reading [14], I'm starting to think that David Tombe is stuck in the 17th century. That paper shows nicely how the modern concept of centrifugal force as a fictitious force evolved. BTW, I wasn't comparing Feynman with Maxwell. I was comparing him with David Tombe. I think that a Nobel Prize winner who was also a notable physics educator is more likely to get it right than him. Even if Maxwell agreed with David Tombe about centrifugal force (something that I doubt), it could still represent an outdated view of the topic. Many key concepts from 19th century physics have changed their definitions since (for example, heat). The Wikipedia article should focus on the current view, outside of the "historical development" section. In that respect Feynman has one advantage over Maxwell--he lived one century later. -- Itub ( talk) 08:52, 27 May 2008 (UTC)

Speaking of historical development, here's an interesting Google search: http://books.google.co.uk/books?q=%22vis+centrifuga%22+%22vis+inertiae%22. -- The Anome ( talk) 10:03, 27 May 2008 (UTC)

SBharris, that is the exact equation which is used in advanced classical mechanics textbooks. It is a scalar equation and the variable is the radial distance. There is no tangential acceleration involved in any of the problems that we have been discussing. In a circular orbit, we have an inward radial centripetal force balanced by an outward radial centrifugal force and hence ${\displaystyle d^{2}r/dt^{2}}$ will be zero.

It is now clear that you are stuck in the limited high school mode where they emphasized only a part of the overall picture. They emphasized the fact that velocity has both magnitude and direction and that a centripetal force changes the direction of the particle while leaving the speed unchanged (in cases of uniform circular motion).

You have not moved on from that. I have taught that myself. But I am showing you the equation that is used in planetary orbital theory. It is in the advanced textbooks and you are simply denying it. It shows clearly that ${\displaystyle d^{2}r/dt^{2}}$ must be zero in a circular orbit. However in your artifact circle, this equation is not balanced because the application of the transformation equations to that scenario is a nonsense. David Tombe ( talk) 10:50, 27 May 2008 (UTC)

Wolfkeeper, You said above that,

I got two self-evident accelerations, a radial one outwards and the coriolis that always curved the velocity in the opposite direction to the frame rotation.

The centrifugal force will have been real and dependent on the exact angular velocity of the particle in question.

Regarding your observed Coriolis artifact, did it ever act in any direction other than the tangential direction? David Tombe ( talk) 10:16, 26 May 2008 (UTC)

Wolfkeeper, and regarding your latest statement,

Look, the bottom line is, go sit on a roundabout, and wave a ball about in your hand. You can feel the coriolis effect, and I guaranteed you that it's not always, or even mostly radial. I don't care what your polar coordinate maths says, you don't live in a polar coordinate world, you live in a 3D world, that's the way the human brain is wired.- (User) WolfKeeper (Talk) 10:35, 26 May 2008 (UTC

I guarantee you that all applied Coriolis effects and all reactive Coriolis effects will be in the tangential direction. And if you lost hold of the ball, the artifact would also be in the tangential direction. David Tombe ( talk) 10:42, 26 May 2008 (UTC)

No, not even. If the ball goes outwards, coriolis effect pushes you anti-spinward. If you go inward, if forces you spinward. If the ball goes spinward, coriolis forces you outward. If you go antispinward, coriolis forces the ball inward. Don't give us any dopey mathematical 'proof's. Just Go Do It. You'll see.- ( User) WolfKeeper ( Talk) 10:49, 26 May 2008 (UTC)

In Physics, which this is, experiment is the ultimate decider.- ( User) WolfKeeper ( Talk) 10:49, 26 May 2008 (UTC)

Wolfkeeper, a purely tangential motion will never go inside the circle. If you see anything going inside the circle, it means that there was a radial motion to begin with.

I have absolutely no idea what you are talking about here.- ( User) WolfKeeper ( Talk) 10:26, 27 May 2008 (UTC)

Once again, you are too focused on artifacts to actually see what centrifugal force really is. David Tombe ( talk) 06:58, 27 May 2008 (UTC)

No, the focus is on experimental support for the theoretical proof. And I've actually done it, I've sat on a roundabout and felt the coriolis as well as the centrifugal effects. Centrifugal force is what you feel when you are stationary relative to a rotating frame of reference (when you don't move around on a roundabout). Coriolis is an additional vector you add on when you move. That's all. Go do it, and get back to us if it isn't like that, but if do that, if you're truthful and attentive to what actually happens, we will never see you here again.- ( User) WolfKeeper ( Talk) 10:26, 27 May 2008 (UTC)

Wolfkeeper, well at least you are now admitting that the centrifugal force only acts on co-rotating objects (although it's not quite as simple as that). The Coriolis force on a roundabout will be an applied force which acts tangentially on co-rotating radial motion and it is likely to trip a walker up if he decides to walk a radial line on a roundabout.

I am 'admitting' to no such thing. I'm saying that centrifugal and coriolis effects can be easily observed in a particular physical situation. In other situations the effects cancel. Either you have tried the experiment or you have not. Go try it and stop bothering us with this nonsense.- ( User) WolfKeeper ( Talk) 11:28, 27 May 2008 (UTC)

No tangential motion on the roundabout can possibly cause a deflection to act such as to move the object inside the circle of which it forms a tangent. David Tombe ( talk) 11:10, 27 May 2008 (UTC)

I can't see any counterexamples. But I can't see any relevance either. So, so what?- ( User) WolfKeeper ( Talk) 11:28, 27 May 2008 (UTC)

We need to get to the point here. Is everybody denying this scalar equation,

Applied centripetal force + induced centrifugal force = ${\displaystyle d^{2}r/dt^{2}}$

It's a second order differential equation in radial distance and it is used to solve planetary orbital problems. It can also be used for any central force scenario.

Are you all denying this equation? It is found in any advanced classical mechanics textbook.

It contains one out of at least four reasons why the artificial circle idea is nonsense.

I have been accused of not having pointed out the maths errors in the transformation equations despite having done so on numerous occasions. The equation above relates to a very important one of those maths errors.

So do you all accept this equation or not? David Tombe ( talk) 06:54, 27 May 2008 (UTC)

The equation is correct. However, by using the radius a coordinate you are using a rotating reference frame, which explains the presence of the centrifugal force term. You can perfectly well describe orbital motion from an inertial frame using x and y as coordinates and without any centrifugal force. -- Itub ( talk) 08:32, 27 May 2008 (UTC)

A point of clarification: The use of "radius" as a coordinate need not imply a rotating reference frame. A stationary polar coordinate system can be used, and in fact this seems to be what Mr Tombe has in mind. However, inertial forces appear when working in stationary polar coordinates too, just as they do in rotating coordinates. This is explained in some of the linked articles. TstoneT ( talk) 16:55, 27 May 2008 (UTC)

TstoneT, I'm not sure what you mean about stationary polar coordinates. Does that mean no tangential motion? We need the tangential motion to induce radially outward centrifugal force. Stationary polar coordinates would only be useful if we were focusing exclusively on gravity problems where things fell straight downwards. David Tombe ( talk) 07:23, 29 May 2008 (UTC)

Thanks, that is correct. I assumed David Tombe referred to a rotating frame because he keeps talking about radial and tangential components, which to me means a couple vectors--one is the rotating radius and the other is a vector orthogonal to the radius (the "tangential component"). But as you say, even if you transform Newton's equations to polar coordinates (r and θ), the fictitious force appears. Here's a link to a book that shows the derivation: [15] -- Itub ( talk) 09:21, 28 May 2008 (UTC)

I just noticed there was some discussion about this above: Talk:Centrifugal force#Polar_coordinate_system. -- Itub ( talk) 09:28, 28 May 2008 (UTC)

Itub, in your artificial circle example, you also use the radial direction and that's what we're comparing it with. No need to play the old trick of hiding behind Cartesian coordinates.

Your so called centripetal force that derives from the Coriolis force is in the radial direction. At least that is what you have been trying to argue, so you can't have it both ways. In your artificial circle example you have a net inward radial force. That is impossible in circular motion. In circular motion ${\displaystyle d^{2}r/dt^{2}}$ is zero because the centrifugal force balances the centripetal force in the radial direction. Your artificial circle example causes a total imbalance in the central force orbit equation. David Tombe ( talk) 10:58, 27 May 2008 (UTC)

Nope, in the "artificial circle" one does not use the radial direction. One uses a set of orthogonal vectors that are rotating with respect to the inertial frame. If you measure the radius vector to the object (which is at rest in the inertial frame), you'll see that the vector is constantly changing. It is moving in an apparent circle, as per the apparent centripetal acceleration. On the other hand, in the "real rotation" example, using your equation, the object is at rest in the rotating frame, which is why the radius doesn't change. It does not change because the orthogonal vectors are rotating together with the radius. You are trying to be in two reference frames at the same time, by implying that you want to measure the "radial acceleration" and yet be in a non-rotating frame. You are the one who can't have it both ways. -- Itub ( talk) 11:09, 27 May 2008 (UTC)

No Itub, the entire transformation theory which you are basing it all on is done in polar coordinates and your Coriolis force supposedly swings into the radial direction. You have a net radial force for a circular motion and so your theory is a nonsense.

You cannot keep jumping out of polar coordinates when it suits you. David Tombe ( talk) 11:19, 27 May 2008 (UTC)

David, I agree completely with Itub's comments above. They go directly to the heart of the matter. Please read them again; particularly the part about the necessity for the consistent use of a single reference frame at any given time. -- The Anome ( talk) 11:23, 27 May 2008 (UTC)

Here's a summary of the two examples, from each of the two consistent viewpoints:

Example:	Inertial frame viewpoint	Rotating frame viewpoint
"Real rotation"	Object moves in a circle, accelerating towards the centre. Distance from centre does not change. Centripetal force pushes it into that path. No centrifugal force exists.	Object is stationary. There is no acceleration or rotation in any direction. Distance from centre does not change. Centrifugal force balances centripetal force precisely.
"Artificial circle"	Object is stationary. There is no acceleration or rotation in any direction. Distance from centre does not change. No force is exerted. No centrifugal force exists.	Object moves in a circle, in the reverse direction to the frame's rotation, accelerating towards the centre. Distance from centre does not change. Acceleration is caused by the inwards Coriolis force overwhelming the outwards centrifugal force.

-- The Anome ( talk) 11:37, 27 May 2008 (UTC) [Updated The Anome ( talk) 00:18, 28 May 2008 (UTC)]

I like that table, perhaps we should add it to the article. -- Itub ( talk) 11:44, 27 May 2008 (UTC)

It could do with a bit of tidying up, though, to make everything line up better and more consistently ordered. -- The Anome ( talk) 11:46, 27 May 2008 (UTC)

And "co-rotating" needs to be clarified, perhaps to "Viewpoint from rotating frame (constant rate)"... since nothing is "co-rotating" in the "arificial circle" example. --

Anome, it doesn't at all surprise me that you agree with Itub. But your boxes above completely ignore the fact that if centrifugal force and centripetal force both act in the radial direction, then we either have them both or we have neither. In your first box you acknowledge radially inward centripetal force while denying radial outward centrifugal force even though we know that in circular motion, ${\displaystyle d^{2}r/dt^{2}}$ must be zero.

And it is that latter fact which is the key point in the dispute. Your boxes are just sheer obfuscation. In the artificial circle, the radial length remains constant, hence ${\displaystyle d^{2}r/dt^{2}}$ must equal zero. But in your theory, you are ascribing to it a net inward radial force.

On the issue of consistency, I am the one that has been totally consistent. I talk only about the radial dircection. You are the ones that keep jumping between Cartesian and polar coordinates like stage magicians, and switching off centrifugal force when you think that nobody has noticed. David Tombe ( talk) 03:04, 28 May 2008 (UTC)

David, as several others have already pointed out, you continue to make the mistake of equating ${\displaystyle d^{2}r/dt^{2}}$ with the radial component of the net acceleration - it's not. The radial component of a vector is found by taking the dot product with the unit vector, ${\displaystyle {\hat {r}}}$ (see Protter and Morrey, Intermediate Calculus, pg 63 for finding the component of a vector along another vector). You are correct that the net radial force is proportional to the net radial acceleration, but since ${\displaystyle {\ddot {\vec {r}}}\cdot {\hat {r}}}$ (the radial component of the the acceleration vector) is not zero for circular motion, then the net radial force is also not zero. And every reliable source will agree with that statement. -- FyzixFighter ( talk) 04:05, 28 May 2008 (UTC)

FyzixFighter, you are telling me something that I already know. I know all about polar coordinates and their derivation. But when we get to central force problems, it all reduces to a scalar equation in the radial length.

${\displaystyle d^{2}r/dt^{2}}$ is to all intents and purposes the radial acceleration in the context. If you don't want to call it that, then so be it. But the physical realities will not change.

The term ${\displaystyle d^{2}r/dt^{2}}$ has to be zero for a circular motion. Hence, the artificial circle example fails because it talks about a net centripetal acceleration in the radial direction. In a proper circular motion, the centrifugal force and the centripetal force will cancel and ${\displaystyle d^{2}r/dt^{2}}$ will be zero. David Tombe ( talk) 07:12, 29 May 2008 (UTC)

Again, no one is arguing that ${\displaystyle d^{2}r/dt^{2}}$ is not zero - of course it's zero for circular motion. One of the principal disagreements here (as I see it) is on the proper expression for the radial component of a vector, specifically the acceleration vector. You claim that it's ${\displaystyle d^{2}r/dt^{2}}$, while everyone else and every reliable physics and vector calculus textbook says that it is ${\displaystyle {\frac {d^{2}{\vec {r}}}{dt^{2}}}\cdot {\hat {r}}}$. (1) Are you saying that ${\displaystyle {\vec {u}}\cdot {\hat {r}}}$ is not the radial component of an arbitrary vector ${\displaystyle {\vec {u}}}$? (2) Do you have a reliable source that backs up your expression/definition for the radial acceleration? (3) For circular motion, which direction does the net acceleration vector point? -- FyzixFighter ( talk) 18:01, 29 May 2008 (UTC)

Here's a quote from the wikipedia verifiability policy,

Editors should provide a reliable source for quotations and for any material that is challenged or is likely to be challenged, or the material may be removed.

Let's see if the administrators abide by the rules or not. I have added into the introduction that centrifugal force in the so-called colloquial sense (not my choice of terminology) occurs in connection with rotation.

Is anybody challenging this fact? If so can they give me an example of colloquial centrifugal force that is not connected with rotation?

If my insertion is deleted, it proves that you are merely throwing pies, and that you are not in the least interested in centrifugal force. David Tombe ( talk) —Preceding comment was added at 07:23, 27 May 2008 (UTC)

A moment's Googling yields these: [16], [17], [18], [19], [20], [21]. -- The Anome ( talk) 09:48, 27 May 2008 (UTC)

No Anome, the article is about centrifugal force in physics not in politics. Are you being serious, or are you just being silly? David Tombe ( talk) 10:52, 27 May 2008 (UTC)

I'm being completely serious. The whole point of that sentence is to emphasize that (a) the term is also commonly used in senses completely different from the usage in physics (hence the use of the words "any influence, real or metaphorical"), but (b) that this article is solely about the usage in physics. -- The Anome ( talk) 11:02, 27 May 2008 (UTC)

In that case, we need to clarify that in the introduction. David Tombe ( talk) 11:20, 27 May 2008 (UTC)

Which is what that sentence is there to do. -- The Anome ( talk) 11:24, 27 May 2008 (UTC)

Well now you've got Wolfkeeper claiming that the articles are on topics and not terms. I suggest we remove the reference to political centrifugal force. David Tombe ( talk) 11:26, 27 May 2008 (UTC)

David: I am now convinced that you are interested primarily in debate and not in resolving any issue about centrifugal force, and certainly not in the education of David Tombe. Brews ohare ( talk) 14:04, 27 May 2008 (UTC)

Brews, so what have you got to say about Anome's introducion of 'political centrifugal force' into the introduction? Would you delete it? David Tombe ( talk) 03:45, 28 May 2008 (UTC)

I'd say that it does not belong in the article. Brews ohare ( talk) 04:58, 28 May 2008 (UTC)

Since we now seem to have a consensus from both sides of the argument to remove this "what this article is not about" section as leading off-topic, I've now removed it. -- The Anome ( talk) 07:46, 28 May 2008 (UTC)

Anome, that doesn't mean that you have to remove the other part with it. You blended your political centrifugal force idea with colloquial centrifugal force as a means of being able to deny the need for rotation. Now that you realize that you can't do that, it is no excuse to remove the whole sentence. I'm going to put the original sentence back again as it was before you added the political bit. David Tombe ( talk) 05:50, 29 May 2008 (UTC)

It is saddening to see what terrible shape articles like planetary motion are in, where 1/10 the effort spent on the recalcitrant D Tombe would improve Wikipedia by several orders of magnitude. Brews ohare ( talk) 16:33, 27 May 2008 (UTC)

Brews, from what I can see, nobody here knows anything about planetary orbital theory and they don't want to know about it. If the people here start dabbling with the planetary motion page, I don't want to look at it. David Tombe ( talk) 03:14, 28 May 2008 (UTC)

But the debate with Tombe has sharpened the arguments quite a lot, and produced the useful table above, which neatly summarizes things. Many of the arguments here should be incorporated into the centrifugal and Coriolis force articles, so that they are understandable to high school students. This whole thing has clarified MY thinking, if not yours! S B H arris 23:24, 27 May 2008 (UTC)

SBharris, the boxes above are sheer obfuscation and they totally neglect the fact that if centripetal force and centrifugal force both act radially then we can't switch one off and leave the other on.

In a circular motion, the radius remains constant. Hence the scalar quantity ${\displaystyle d^{2}r/dt^{2}}$ must be zero. We know that there is a radially inward centripetal force. But there must also be a radially outward centrifugal force. That's how the planetary orbital equation works.

Your boxes above were downright deceit to mask out the truths behind the planetary orbital equation and the fact that the artificial circle is a nonsense concept. David Tombe ( talk) 03:11, 28 May 2008 (UTC)

David, please don't accuse other editors of "downright deceit". Please read WP:CIVIL, and abide by that policy. -- The Anome ( talk) 07:50, 28 May 2008 (UTC)

If there were a "centrifugal force" canceling the centripetal force when you are in an inertial frame, the object would be moving in a straight line! (or not moving at all). Newton's first law. -- Itub ( talk) 08:08, 28 May 2008 (UTC)

Hi Itub: Of course you are right, and David has been told this several times already with no apparent result. Brews ohare ( talk) 14:16, 28 May 2008 (UTC)

Itub, and how exactly do you reason that out? If the particle were moving in a straight line, it would already have an outward centrifugal force relative to the point origin in question. The centripetal force compounds with it to cancel it and cause curved path motion. When the two are exactly balanced we get circular motion and zero radial acceleration.

Can you not see that a straight line motion contains an outward centrifugal force realtive to any point that does not lie in its path? This is known as inertia. David Tombe ( talk) 05:55, 29 May 2008 (UTC)

A straight line motion implies absolutely no net Newtonian force. There's no way around that. Of course, if you look at it in a non-Newtonian reference frame (whether polar or rotating) and yet you want to be able to use Newton's laws in this frame, you will need to introduce non-Newtonian (aka fictitious) forces to explain why the particle seems to be accelerating. -- Itub ( talk) 08:30, 29 May 2008 (UTC)

Itub, the centrifugal force is in the radial direction. Your artificial circle uses the radial direction. You are trying far too hard to write off the centrifugal force by looking at the real example in the limited context of Newton's law of inertia. Newton's law of inertia is only god for cuboid kitchens. When we go to the cosmic scale or the microscopic scale, then the radial direction is the only direction that has any meaning. David Tombe ( talk) 09:39, 29 May 2008 (UTC)

I noticed yesterday that quite a bit of deceit went on. I added a clause to the introduction stating that centrifugal force had to be considered in conjunction with rotation.

Anome, knowing fine well that that is a true fact, for some reason doesn't want that fact mentioned.

So in order to obfuscate it, he blended the sentence in with the totally unrelated topic of 'political centrifugal force' as a cheap way of being able to claim that centrifugal force doesn't have to be connected with rotation.

This was a very cheap and pathetic tactic and it is totally contrary to wikipedia's rules.

So in order to expose what was going on, I split the sentence into two to clarify that we were talking about two totally unrelated topics.

Wolkeeper then comes in and reverts, citing the wikipedia rules that the pages are on topics and not terms.

But if Wolfkeeper had been genuine, he would simply have removed the political reference.

Instead, in an act of wikistalking and total hypocrisy, he retained the very subject that he was objecting to.

Wolfkeeper and Anome were clearly on opposite sides of the fence on this issue, but there would be no question of Wolfkeeper wanting to demonstrate any cracks in the united front.

So Wolfkeeper actually restored Anome's edit and the reference to political centrifugal force still remains, contary to wikipedia's rules.

Wolfkeeper was made fully aware of why I then re-reverted, but he just ignored it and reverted again.

That in my opinion suggests that there is no longer a serious scientific debate going on and that it has merely degenerated into the throwing of pies.

To clear this matter up, could we have a united statement from Wolfkeeper and Anome as to whether or not the political centrifugal force references should remain in the introduction?

I would imagine that any united decision will be totally steeped in politics, and neither in science nor wikipedia rules and regulations. David Tombe ( talk) 03:26, 28 May 2008 (UTC)

David, please don't accuse other editors of "wikistalking" and "total hypocrisy". Please read WP:CIVIL, and abide by that policy. -- The Anome ( talk) 07:53, 28 May 2008 (UTC)

Hi David. Your edits yesterday had no policy violations that I saw... but that doesn't mean that others can't edit the wording. That's how Wikipedia works. I don't see any conspiracy here. -- SCZenz ( talk) 11:58, 28 May 2008 (UTC)

I think there's a problem with this article, beginning in the first sentence, where centrifugal force is defined as follows:

"Centrifugal force is a fictitious force that is associated with the centrifugal effect, which is an apparent acceleration that appears when describing physics in a rotating reference frame; centrifugal force appears to act on anything with mass considered in such a frame."

One problem with this attempted definition is that it refers to "rotating reference frames", whereas it should really refer to non-inertial coordinate systems, which need not be rotating. (I see there has been some discussion of this point previously - "polar coordinates" - but the point doesn't seem to have been absorbed or reflected in the article.) Perhaps it would be more paletable to replace "rotating reference frame" with "rotating or curved coordinate systems". TstoneT ( talk) 18:13, 28 May 2008 (UTC)

At present the scope of the article evidently is only centrifugal force as it applies to rotating reference frames. There may be a case for also covering polar coordinate systems in the article as well, but they behave slightly differently. I don't consider the current article to be wrong or problematic per se, it simply has a scope that excludes it at present. If it is decided that it should be covered, then the question would then be whether that should be covered in this article or a separate article.- ( User) WolfKeeper ( Talk) 18:43, 28 May 2008 (UTC)

TstoneT, you can find a detailed generalized treatment of the general non-inertial-frame case at fictitious force#Mathematical derivation of fictitious forces. -- The Anome ( talk) 00:19, 29 May 2008 (UTC)

Nope, the article on fictitious force doesn't address the point in question, because it talks only about the time-dependent frame, using phrases like "the movement of the frame-B coordinate axes" and "derivatives of these vectors express only rotation of the coordinate system B". My comment concerns the appearance of inertial forces in stationary coordinate systems. For example, a fixed polar coordinate system does not change with time, but it is nevertheless not an inertial coordinate system, because the axes are curved, and hence both centrifugal and Coriolis terms appear in the equations of motion expressed in terms of a stationary polar coordinate system. Neither this article nor the "fictitious force" article gives an account of this, and therefore neither article gives a complete and comprehensive account of inertial or even just centrifugal forces. On the other hand, very few published references do either, and since Wikipedia is supposed to represent the general level of presentation in secondary sources, I guess the scope of the current article is defensible - not on the technical merits, but per Wikipedia policy. TstoneT ( talk) 01:04, 29 May 2008 (UTC)

In polar coordinates, you get a term that looks like the centrifugal acceleration term in a rotating coordinate system, but it is not the same thing, because theta-dot denotes a different quantity. (Angular velocity of the object, vs angular velocity of the coordinate system.)

However, you can have a centrifugal force in polar coordinates if the polar coordinate system is rotating. If the system only contains one object, then it might be convenient to fix the theta coordinate of that object to zero, and instead use another theta to denote the amount of rotation of the coordinate system. (Using the same symbol theta in order to confuser the reader.) You then get an equation of motion that looks exactly the same, but where the centrifugal acceleration term is the one described in this article.

Now, if you write the equations of motion of a second object in this coordinate system, you will get two centrifugal-looking terms. One involving the angular velocity of that object relative to the coordinate system, and one involving angular velocity of the coordinate system itself. The first one is not considered a centrifugal effect, but the second one is.

Hope this helps. -- PeR ( talk) 05:39, 29 May 2008 (UTC)

Centrifugal forces (like all inertial forces) are essentially defined as certain components that appear in the equations of motion when those equations are expressed in terms of non-inertial coordinates. In general, if we allow the coordinates to be curved in both space and time, several inertial terms appear in the equations of motion of a particle, and we call some of these terms “centrifugal”, some “Coriolis”, and some are given less familiar names, or aren’t named at all. If f is the mapping function to inertial coordinates, then all the inertial terms are of the form f_mn x^m/dt dx^n/dt with the understanding that the time coordinate is also one of the indexed “x^n” coordinates. It’s customary (and entirely reasonable) to call the diagonal terms “centrifugal” and the off-diagonal terms “Coriolis”. When you assert that stationary polar coordinates give something that looks like a centrigual force but really isn’t, you are sort of posing a zen riddle (like “Wagner’s music is better than it sounds”). It “looks” like a centrifugal force because it’s a diagonal term, it’s a fictitious force in non-inertial coordinates, and it points radially outward – all of which are essentially the definition of a centrifugal force.

You objected because you say the “theta dot squared” term refers to angular speed of the coordinate system in the case of centrifugal force, whereas it refers to angular speed of the particle in the case of stationary polar coordinates, so these are two different things. However, the motion of the particle and the motion of the (non-inertial) coordinates are defined relative to each other. In terms of stationary polar coordinates the value of theta is really just the angular position of the particle with respect to the coordinate system, and if that system is rotating, it simply adds to theta. In other words, if the coordinates have angular speed W and the particle has angular speed w relative to those coordinates, then the term that you claim should not be called centrifugal force is mr(W + w)^2, and of course this is the force that we would measure if we were holding the particle with a thread. It seems to me we would have to weave a fairly tangled web to claim that part of this is centrifugal force and part of it isn’t. We could expand the square, and call the W^2 term a centrifugal force and the 2Ww term a Coriolis force, but what would we call the w^2 term? A pseudo-centrifugal force? Or a double-secret-probation force? Bear in mind that all of these are purely fictitious forces, arising only because of the non-inertial coordinates. Anyone who doesn't like the "diagonal versus off-diagonal" criterion for classifying inertial forces as either cenrtifugal or Coriolis should propose a better one. TstoneT ( talk) 10:21, 29 May 2008 (UTC)

The main problem here is that most of the editors don't want to look at elliptical, hyperbolic, or general curved path motion. They want to focus exclusively on circular motion. That has been the cause of alot of the confusion.

Centrifugal force is something that is much more general than that which is associated with rotating frames of reference.

It is best to study the phenomenon from the perspective of polar coordinates in the inertial frame and to view centrifugal force as an absolute induced radial effect, induced by tangential motion.

If we are going to insist on clouding the issue with rotating frames of reference, then it will get confusing for cases of partial co-rotation because in reality we are only interested in the actual angular velocity of any particle in question.

The planetary orbital equation is about the best and most useful demonstration of centrifugal force in its general form. But from what I can see, there is a great reluctance on the part of the editors here to face up to elliptical or hyperbolic motion. David Tombe ( talk) 06:03, 29 May 2008 (UTC)

The only confusion I see here is yours. Everyone here knows all about polar coordinates, particularly as it applies to orbital motion.- ( User) WolfKeeper ( Talk) 09:48, 29 May 2008 (UTC)

Wolfkeeper, you are too biased and too involved in maintaining a united opposition to everything that I say, for your opinions to be worth anything. David Tombe ( talk) 09:51, 29 May 2008 (UTC)

Polar coordinates yield very useful mathematical expressions. They yield the radial and the tangential forms of acceleration when it applies at right angles to the direction of motion.

But they don't describe any particular motion. They don't tell us if the effects are applied or induced or if the radial term is a centrifugal force or a centripetal force. It is only the vector convention which causes the radial convective force to point inwards.

In order to make full use of polar coordinates, we need to use them in conjunction with a real known physical situation.

The gravity orbit is a prime case in point. We select the expressions from the polar coordinates and apply them in the direction which we know makes physical sense. The radial convective term becomes an induced outward centrifugal force and we use Newton's gravity expression for the radially inward centripetal force.

Once we have applied the polar coordinates correctly to a real physical situation, then they become an excellent tool for analysis. They become considerably superior to the limited bastardization of the exact same maths, which is known as "rotating frames of reference".

A further example of the need to introduce physical reality before applying polar coordinates is the case of Kepler's law of areal velocity. It's an observed physical law. It means that we can eliminate the tangential terms. It means that there is no naturally occuring Coriolis force in free gravitational space. David Tombe ( talk) 06:57, 29 May 2008 (UTC)

Trouble, is; that's completely wrong. Consider a spacecraft trying to dock with the ISS. Using the ISS (which is in an largely circular orbit) as a reference frame, it's trivial to work out how to guide your spacecraft to meet it. Doing it in polar coordinates... gah... Rotating reference frames tell, pretty straightforwardly, what happens at all points in space, using polar coordinates only give you one point at a time. Vectors aren't used because they're harder, they're used because they're much easier. You can't meaningfully add or subtract polar coordinates, but vectors add just fine.

Wolfkeeper, introducing a specific three body example doesn't get you off the hook regarding the nonsense of applying the rotating frame transformation equations to objects that aren't co-rotating.

We all know that the three body problem is very tricky. Rotating reference frames certainly don't solve it. David Tombe ( talk) 09:44, 29 May 2008 (UTC)

I'm saying with knowledge of rotating reference frames, it's possible to solve common problems, like docking. It was relatively easy even. I found in simulators, I was able to dock without any special instruments. I doubt very much that expressing things in polar coordinates centred at the Earth could in any way way be helpful. With vectors, you can express the forces differentially and you get lovely smooth potential and force fields on which you can act.- ( User) WolfKeeper ( Talk) 10:15, 29 May 2008 (UTC)

Wolfkeeper, in your docking scenario you will have to introduce another angular velocity. It will be a three body problem.

The bottom line is that the three body problem is non-analytical and we do not need to consider it in order to understand what centrifugal force is about. In practice, it will all be done numerically on the computer.

It's interesting how keen you, Anome, and Timothy Rias are to introduce the three body problem which can't be accurately analyzed, yet you are totally averse to looking at the two body problem in planetary motion.

I can only conclude that none of you can understand two body planetary orbital theory and so you all sweep it under the carpet.

You much prefer to introduce the three body problem knowing that nobody can understand it. David Tombe ( talk) 05:07, 30 May 2008 (UTC)

(I think the following section was posted to the article by mistake (it is argumentative, lacks sources, and is signed), so I'm moving it here. -- PeR ( talk) 08:58, 29 May 2008 (UTC))

Centrifugal force can be understood in its most general form in conjunction with planetary orbits. The general equation for any central force motion is a scalar equation and it takes the form,

Applied centripetal force + centrifugal force = m${\displaystyle d^{2}r/dt^{2}}$

where r is the radial length. In the case of planetary orbits, the centripetal force is the inward acting force of gravity.

The centrifugal force and the centripetal force that act on the same body are not necessarily balanced, and they should not be considered as an action-reaction pair. When they are balanced, we will have a circular motion, but even then the centrifugal force and the centripetal force should not be considered as an action-reaction pair because this is just a particular situation.

Newton's third law of motion is satisfied across two interacting bodies. For example, in the case of the Earth and the Moon, the centripetal force (gravity) that acts on the Earth is balanced by an equal and opposite centripetal force acting on the Moon. Likewise, the outward centrifugal force acting on the Moon is balanced by an equal and opposite centrifugal force acting on the Earth.

The reaction to a centripetal force across two bodies is sometimes called a reactive centrifugal force. The centripetal force and the reactive centrifugal force are always equal and opposite and they form an action-reaction pair. The reactive centrifugal force is essentially the centripetal force from the perspective of the other body.

In the gravity orbit, in the general case when the centripetal force and the centrifugal force are not balanced, the term ${\displaystyle d^{2}r/dt^{2}}$ will be non-zero and we will have an elliptical, parabolic, or hyperbolic orbit. David Tombe ( talk) 06:35, 29 May 2008 (UTC)

I would strongly disagree with the statement that "Centrifugal force can be understood in its most general form in conjunction with planetary orbits." Unless you only consider one planet at a time, it is quite cumbersome to describe the equations of motion in a rotating frame of reference.

In addition, the section is based on the implied assumption that the coordinate system is rotating at the same rate as the planet, which is very confusing. (See my comment under "Rotating versus Non-Inertial", above.) -- PeR ( talk) 09:08, 29 May 2008 (UTC)

PeR, it's straight out of the advanced applied maths textbooks such as Goldstein's. Have you ever studied planetary orbital theory?

The whole point of polar coordinates is to concentrate exactly on the particle under consideration which in general will have a variable angular velocity.

I see absolutely nothing argumentative about this section. Your deletion of it from the main article was just a further example of your continual efforts to deny what centrifugal force is all about.

And it's strange how you were happy enough with the other sentence until I added the clause 'in connection with rotation'. It is your denial of the connection between actual rotation and centrifugal force which is the sole cause of this edit war. And the support you are getting from the crowd and the administration is a combination of corruption, bonding, and ignorance. David Tombe ( talk) 09:31, 29 May 2008 (UTC)

A few days ago, I predicted that the reference in the introduction to colloquial centrifugal force would soon vanish once you guys realized the implications of it.

It seems that I was correct. Anome's technique was to first mix it all up with 'political centrifugal force'. That was the obfuscation stage. The next stage was to remove the whole lot on the grounds that political centrifugal force was inappropriate.

Clearly we have group corruption going on in order to present a totally false and fictitious view of what centrifugal force is about.

Any whisper of centrifugal force being a real radial effect, is swiftly erased. David Tombe ( talk) 10:02, 29 May 2008 (UTC)

The sentence that I removed did not say "colloquially". It said "in common understanding", which is not the same thing. -- PeR ( talk) 10:13, 29 May 2008 (UTC)

Then change it back to colloquial again. David Tombe ( talk) 10:16, 29 May 2008 (UTC)

Wolfkeeper, you are a wikistalker and a hypocrite and an absuser of administrative authority.

That edit of mine was already there for a long time and it didn't worry you before. I have got absolutely no confidence regarding your knowledge about this topic.

It is clear that you are here to push one big lie. David Tombe ( talk)

I'm discovered at last!!!!! ;-)- ( User) WolfKeeper ( Talk) 10:30, 29 May 2008 (UTC)

Wolfkeeper, you do not have the right to restrict this article to centrifugal force solely in connection with rotating reference frames. You have already created a dog's dinner by separating reactive centrifugal force to a separate page.

This article should mention centrifugal force in it's most general sense.

But it is quite obvious to everybody that you are just a wikistalker who is ganging up with a crowd who know nothing whatsoever about planetary orbital motion.

And because you know nothing about it, then nobody's allowed to know anything about it.

You are a totally corrupt editor who is being backed up by a crowd who need to learn a bit about centrifugal force before they are in a position to edit these pages David Tombe ( talk) 10:27, 29 May 2008 (UTC)

WP:AGF. It's off-topic. The paragraph covered reactive centrifgual forces for example.- ( User) WolfKeeper ( Talk) 10:29, 29 May 2008 (UTC)

Wolfkeeper, the paragraph covered centrifugal force and nobody had objected to it when somebody else inserted it. It was only because I re-inserted it, after Anome deleted it in conjunction with his nonsense political centrifugal force idea, that you deleted it.

I get warnings in my tray not to accuse people of wikistalking even though it's quite permissible to go to the administrator's noticeboard and file a complaint of wikistalking.

You lot have broken the rules so many times that you can't be taken seriously.

You are a wikistalker if ever there was a wikistalker. And so is PeR. You are both top grade wikistalkers. And so are Anome and SCZenz.

Now if you don't like being exposed to the truth, then go ahead and do the honours, but I can assure you that you are a wikistalker.

It wouldn't matter what I put in the main article, whether it was sourced or not. You would routinely come along and delete it on the basis of a lie in the full knowledge that you are being supported by a crowd. You have a chip on your shoulder because you have been pushing a nonsense theory that has been exposed. David Tombe ( talk) 06:19, 30 May 2008 (UTC)

So what is the scope of this article? My intention was that it should only include D'Alembert forces as with this NASA page for example, but there's a <cough>persistent</cough> minority that want to include polar coordinate 'centrifugal forces' as well. I'm of the opinion that they're somewhat different, and certainly the associated coriolis terms are rather different. I think that if we integrate them the connectivity to other articles becomes problematic.- ( User) WolfKeeper ( Talk) 10:29, 29 May 2008 (UTC)

My opinion is that there's no such thing as "polar coordinate centrifugal forces". See my reply under "Rotating versus Non-Inertial", above. I might be persuaded otherwise by references to reliable sources, but I will revert any unsupported and questionable material on the matter. -- PeR ( talk) 11:05, 29 May 2008 (UTC)

And as a manifestation of clairvoyance, I predict that my next answer on this thread will be: I don't care about that. References to reliable sources is the only thing that will make me change my mind. -- PeR ( talk) 11:10, 29 May 2008 (UTC)

Hmm. I'm not sure considering polar coordinates would add anything to the article: the physics still works out the same in all cases, but the equations are more complex without making anything any clearer for the reader. -- The Anome ( talk) 16:52, 29 May 2008 (UTC)

Anome, you must be joking. Analyzing two body planetary orbital theory is much easier in polar coordinates that it is in Cartesian coordinates. David Tombe ( talk) 05:10, 30 May 2008 (UTC)

A generalization of centrifugal force beyond a rotating frame would be to a frame in complicated motion. The general case is covered by this equation from fictitious force:

${\displaystyle \mathbf {F} _{\mbox{fictitious}}=-m\ \mathbf {a} _{AB}-2m\ \sum _{j=1}^{3}v_{j}\ {\frac {d\mathbf {u} _{j}}{dt}}-m\ \sum _{j=1}^{3}x_{j}\ {\frac {d^{2}\mathbf {u} _{j}}{dt^{2}}}\ .}$

The article on centrifugal force treats the case of a fixed direction for the axis of rotation of the frame. A more general case would allow the frame Ω to vary in time both in direction and magnitude. If the observer moves in an elliptical or hyperbolic trajectory, the acceleration of the origin becomes a factor, as well as the rotational terms. The fictitious forces due to acceleration of the origin of the frame are not normally considered to be centrifugal or Coriolis terms.

It should be kept in mind that centrifugal force is not related to kinetics, but kinematics; therefore, introduction of mechanism is out of place, I'd say, and the role of planetary motion would be only as an example of a general approach for observational frames moving with time-dependent speed along 3-D curves with arbitrary Ω (t). So a frame fixed to the Earth has rotational aspects that include the precession of its Ω (t) (actually changing direction with time) and accelerations resulting from its elliptical rather than circular path around the Sun. The analysis of this case introduces secondary issues that possibly exceed the scope of an introductory article, and should be in another article. Brews ohare ( talk) 15:49, 29 May 2008 (UTC)

There are countless references for the fact that the radial fictitious force arising in stationary polar coordinates is called centrifugal force. Just to give two examples, with the relevant quotes:

(1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press. "In this chapter we have faced the fact that there is something of a crisis in intuition that arises from the introduction of the polar coordinate system, even in a non-rotating system or reference frame. When we first use rectilinear coordinates to understand the dynamics of a particle, we commit our minds to the simple expressions x" = F_x, y" = F_y. We think of the accelerations as time rate-of change [per unit mass] of the linear momentum X' and y'. Then we express the same situation in polar coordinates that partly restore the wanted form. In the case of the radial component of the acceleration we move the r(theta')^2 term to the right hand side and call it a "centrifugal force."

(2) Statistical Mechanics By Donald Allan McQuarrie, 2000, University Science Books. "Since the force here is radial, it is convenient to use polar coordinates. Taking x = r cos(theta) and y = r sin(theta) [i.e., stationary polar coordinates] then... If we interpret the term [r(theta')^2] as a force, this is the well-known centrifugal force..."

Many more references can be provided it required. Frankly, this is not a particularly controversial point (aside from the editors of this wikipedia article, apparently). As I said before, centrifugal forces (like all inertial forces) are essentially defined as certain components that appear in the equations of motion when those equations are expressed in terms of non-inertial coordinates. In general, if we allow the coordinates to be curved in both space and time, several inertial terms appear in the equations of motion of a particle, and we call some of these terms “centrifugal”, some “Coriolis”, and some are given less familiar names, or aren’t named at all. If f is the mapping function to inertial coordinates, then all the inertial terms are of the form f_mn x^m/dt dx^n/dt with the understanding that the time coordinate is also one of the indexed “x^n” coordinates. It’s customary (and entirely reasonable) to call the diagonal terms “centrifugal” and the off-diagonal terms “Coriolis”. When you assert that stationary polar coordinates give something that looks like a centrigual force but really isn’t, you are sort of posing a zen riddle (like “Wagner’s music is better than it sounds”). It “looks” like a centrifugal force because it’s a diagonal term, it’s a fictitious force in non-inertial coordinates, and it points radially outward – all of which are essentially the definition of a centrifugal force.

PeR objected because he says the “theta dot squared” term refers to angular speed of the coordinate system in the case of centrifugal force, whereas it refers to angular speed of the particle in the case of stationary polar coordinates, so these are two different things. However, the motion of the particle and the motion of the (non-inertial) coordinates are defined relative to each other. In terms of stationary polar coordinates the value of theta is really just the angular position of the particle with respect to the coordinate system, and if that system is rotating, it simply adds to theta. In other words, if the coordinates have angular speed W and the particle has angular speed w relative to those coordinates, then the term that you claim should not be called centrifugal force is mr(W + w)^2, and of course this is the force that we would measure if we were holding the particle with a thread. It seems to me we would have to weave a fairly tangled web to claim that part of this is centrifugal force and part of it isn’t. We could expand the square, and call the W^2 term a centrifugal force and the 2Ww term a Coriolis force, but what would we call the w^2 term? A pseudo-centrifugal force? Or a double-secret-probation force? Bear in mind that all of these are purely fictitious forces, arising only because of the non-inertial coordinates. Anyone who doesn't like the "diagonal versus off-diagonal" criterion for classifying inertial forces as either cenrtifugal or Coriolis should propose a better one. I've provided references to reputable sources supporting my claims. TstoneT ( talk) 18:54, 29 May 2008 (UTC)

Here are a couple more references that discuss the centrifugal (and Coriolis) forces arising in stationary polar coordinate systems:

(3) Essential Mathematical Methods for Physicists By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.

(4) Methods of Applied Mathematics By Francis B. Hildebrand, 1992, Dover, p 156.

Since no one is voicing any objections, I go ahead and think about how to incorporate the more complete definition of centrifugal force into the article, hopefully correcting the mis-impression that it pertains only to rotating coordinate systems. TstoneT ( talk) 23:25, 29 May 2008 (UTC)

The centrifugal term in the polar coordinate form of the Newtonian equations of motion is, in general, best regarded as part of a generalized force, and leads us on to a whole other topic. This article is about the much more well known case of the fictitious force that exists in the case of a reference frame rotating at a constant rate about a fixed axis. However, since you have references from reliable sources for this usage, please feel free to add a section to the article describing this usage of the term, but please don't mix it up with the simpler case of the coordinate-free fictitious force that occurs in rotating reference frames. -- The Anome ( talk) 23:30, 29 May 2008 (UTC)

A few comments: First, a generalized force is just a linear function of the real applied forces, converted to some other basis of generalized coordinates, i.e., Q_i = SUM F_i dx/dq. In contrast, centrifugal and Coriolis forces are not linear combinations of the real applied forces, they are inertial forces (also called fictitious forces) arising due to the non-inertial character of the coordinate system. (Please note that generalized forces are not fictitious forces, nor are they inertial forces.) Second, I don't think it's valid to tout the current article as being focused on the "much more well known case of fictitious force...rotating reference frame", because surely the simplest and most well-known meaning of centrifugal force is for cases when some object is actually moving on a curved path. Very few people ever ponder the enormous centrifugal forces to which their sleeping dog is being subjected at this very moment... when described in terms of a rapidly rotating system of coordinates. So let's face it, the current article has set itself the task of describing a fairly abstract concept, and is giving short shrift to common usage. Given this fact, it's a bit disengenuous to then turn around and say "whoa, let's keep it simple". Third, just for my edification, what the heck is a "coordinate-free fictitious force"? Fourth, just for fun, note that the definition of reference frame from (for example) the McGrath-Hill Dictionary of Physics and Mathematics is "A coordinate system for the purpose of assigning positions and times to events". So, when you commented "Absolutely. What matters is the frame, not the coordinate system.", what exactly did you mean (considering that a frame IS a coordinate system)? If I didn't know better I'd think you held the intuitive (but long ago discredited) idea that there are such things as metaphysical "frames" independent of coordinate systems. TstoneT ( talk) 01:28, 30 May 2008 (UTC)

Please note my objection to including this material. As indicated in the section below, although the terms centrifugal etc. are applied in the context of a particle described in polar coordinates, it is not the same thing as the subject of this article, for the reasons given below. Brews ohare ( talk) 03:09, 30 May 2008 (UTC)

I read your explanation, but I think it needs some clarification. Your statement of the article's purpose is: “This article refers to observational frames of reference and how trajectories described in such a frame are to be compared to those in an inertial frame.” Presumably by “observational frames of reference” you intended to contrast these frames with the frames you mention at the end of the sentence, namely, inertial frames. Now, a frame of reference is, by definition, a system of space and time coordinates, and an inertial frame of reference is by definition a system of space and time coordinates in terms of which Newton’s laws of motion, particularly F = m(d^2x/dt^2), are explicitly valid. In other words, the net applied force equals the mass times the second derivative of the position coordinates. So, I would interpret your sentence to mean something like this: “This article refers to non-inertial coordinate systems and how the descriptions of trajectories in terms of such systems are related to the descriptions of those same trajectories in terms of inertial coordinate systems.” If this is what you mean, then we’re in full agreement! In fact, it’s essentially a paraphrase of one of my initial statements here. I trust you’ll be supportive of my efforts to amend the article to reflect this statement of the article’s objective. (Hopefully it goes without saying that stationary curvilinear coordinate systems, e.g., polar coordinates, are not inertial coordinate systems, so a description of those is central to the article’s objective.) TstoneT ( talk) 07:22, 30 May 2008 (UTC)

It is important to differentiate between frames of reference and particular coordinates. You can certainly use polar coordinates to describe an inertial coordinate system; it's just a change of variables, e.g. you define ${\displaystyle r={\sqrt {x^{2}+y^{2}}}}$. By contrast, in changing from one reference frame to another the vectors change, just not their representation (although the physics, of course, does not). -- SCZenz ( talk) 07:37, 30 May 2008 (UTC)

Also, a stationary curvilinear coordinate system is still an inertial reference frame. As you noted, a reference frame is inertial if Newton's laws of force apply, and even using polar coordinates ${\displaystyle \Sigma {\vec {F}}=m{\ddot {\vec {r}}}}$. However, only in Cartesian coordinates does this vector equation reduce to the statement "the net applied force equals the mass times the second derivative of the position coordinates". For rotating frames, Newton's laws do not hold, and hence the addition of pseudo-forces and this is what for me differentiates the centrifugal force described in the article from the centrifugal-like terms within ${\displaystyle d^{2}r/dt^{2}}$ when described with polar coordinates. -- FyzixFighter ( talk) 17:32, 30 May 2008 (UTC)

Brews, he's given citations for the very things that I have been arguing about. Polar coordinates in the inertial frame are the correct and standard way to analyze planetary orbital motion and the best way of elucidating centrifugal force as an outward radial effect.

The section that I put in yesterday was standard textbook planetary orbital theory. I mentioned Goldstein's.

I can only conclude that most of the editors here are schoolboys who have done the basic circular motion theory and are totally unwilling to examine the general cases of curved path motion such as ellipses and hyperbolae and the role of the radially outward centrifugal force.

I would say that my section was erased yesterday for no other reason than that nobody here could understand it since they have never done planetary orbital theory in advanced applied maths at university.

And in true schoolboy style, anything that they can't understand must go to the trash can. David Tombe ( talk) 05:22, 30 May 2008 (UTC)

Well, like I said, I can be persuaded by references to reliable sources, like the ones that TstoneT has given. However, it should be pointed out that when we call the thetadot-squared term in polar coordinates a "force", we can no longer say things like "if the sum of all forces that act upon an object is zero, then that object will move in a straight line at constant speed". -- PeR ( talk) 12:29, 30 May 2008 (UTC)

---

I think there is one "trick" when trying to show a centrifugal force in polar coordinates. Look at eq. 1.48 in [22].

${\displaystyle F_{r}=m({\ddot {r}}-r{\dot {\phi }}^{2})}$

Here F_r is the "real" Newtonian force, which in the case of circular motion (that is, at constant r) is pointing constantly inwards and equals ${\displaystyle -mr{\dot {\phi }}^{2}}$. That is, the only force is the centripetal force. However, if we say "wait a second, there is a term here, ${\displaystyle m{\ddot {r}}}$ which looks just like Newton's equation for r!", we can rewrite equation 1.48 as (introducing the definition F′ for convenience):

${\displaystyle F'=m{\ddot {r}}=F_{r}+mr{\dot {\phi }}^{2}}$

This is exactly what McQuarry did. The problem is that F′ looks like a force for r, but it's not the "real" Newtonian force. So curiously enough, the centripetal force term from eq. 1.48 "changes sign" and turns into the centrifugal force term for Newton's force in a rotating frame. I argue that by insisting in treating F′ like a force, defined as ${\displaystyle F'=m{\ddot {r}}}$, we are effectively "hopping on" to the rotating frame. That is, like SCZenz said above, just changing the coordinate system does not make the frame non-inertial. What makes it non-inertial is pretending that the product of mass and the second derivative of a coordinate is a force.

However, unlike a frame of reference that is rotating at a constant rate, the polar coordinates are always "following" the object in question. That is why, when cast in terms of polar coordinates, the Coriolis force is always tangential. There is no way of "moving tangentially"--if the object tries to move tangentially, φ speeds up or slows down to follow along, which results in a change of the centrifugal force term instead of a radial Coriolis term (the net effect is the same, of course). -- Itub ( talk) 09:58, 30 May 2008 (UTC)

When discussing a point particle as in the article planar motion, the equation for acceleration arises:

${\displaystyle \mathbf {a} ={\frac {d^{2}\rho }{dt^{2}}}\mathbf {u} _{\rho }+{\frac {d\rho }{dt}}{\frac {d\mathbf {u} _{\rho }}{dt}}+{\frac {d\rho }{dt}}\mathbf {u} _{\theta }{\frac {d\theta }{dt}}+\rho {\frac {d\mathbf {u} _{\theta }}{dt}}{\frac {d\theta }{dt}}+\rho \mathbf {u} _{\theta }{\frac {d^{2}\theta }{dt^{2}}}\ .}$

${\displaystyle =\mathbf {u} _{\rho }\left[{\frac {d|\mathbf {v} _{\rho }|}{dt}}-{\frac {|\mathbf {v} _{\theta }|^{2}}{\rho }}\right]+\mathbf {u} _{\theta }\left[{\frac {2}{\rho }}|\mathbf {v} _{\rho }||\mathbf {v} _{\theta }|+\rho {\frac {d}{dt}}{\frac {|\mathbf {v} _{\theta }|}{\rho }}\right]\ .}$

where the coordinate axes are attached to the particle and the radial direction is that of the displacement of the particle from some origin in an inertial frame. Using this formula, one can refer to a Coriolis force, an Euler force and a centrifugal force by adopting the moving reference frame attached to the particle.

This problem and its associated terminology although similar to that of this article, are not the same. This article refers to observational frames of reference and how trajectories described in such a frame are to be compared to those in an inertial frame. That objective is different from following a single particle from an inertial frame and describing its components of acceleration along various directions rather arbitrarily selected. I say arbitrarily selected, because the radial direction selected depends upon the origin of the observer, and will change even within the same inertial frame if the origin is chosen differently. This radial direction is not along the radius of curvature of the path, and its magnitude ρ is not the radius of curvature of the path (except for the very specific case of a circular path around the selected origin of coordinates), and so connection with centrifugal force cannot be made. The other component also is arbitrary as u_θ is chosen orthogonal to the arbitrary direction of the displacement vector, and is not tangent to the path (except by accident). Brews ohare ( talk) 21:43, 29 May 2008 (UTC)

Absolutely. What matters is the frame, not the coordinate system. There's nothing very special about the polar treatment, since the physics is exactly identical to that in the Cartesian treatment; the generalized coordinates, generalized forces and Lagrangian mechanics articles cover everything needed to understand this. -- The Anome ( talk) 21:57, 29 May 2008 (UTC)

No Anome, what matters is the correct matching up of the maths to physical reality, and the polar coordinate system is the one that is tailor made to deal with concepts such as centrifugal force and Coriolis force.

The centrifugal force is a radial effect and the Coriolis force is a tangential effect.

But before we can use the expressions in polar coordinates we must construct a physical model of a real situation and then construct a differential equation around it, usually in the scalar variable of radial distance.

If you were in the slightest genuine about this topic, you would have read the section which I added to the main article yesterday. You would have blocked PeR for vandalism and wikistalking for having erased it on specious grounds.

It hardly needed sourced since it is standard planetary orbital theory which obviously none of you know anything about. In fact I did mention Goldstein's Classical Mechanics.

The picture that I am getting here is that the article has been hi-jacked by a group who have had a basic introduction to circular motion but who would be incapable of handling elliptical or hyperbolic motion and so they will all make sure that no such generalizations appear in the main article.

Your group has indulged in a number of deceitful tactics which I will now list.

(1) Making arguments in polar coordinates but jumping into Cartesian coordinates to conceal the flaws. The main example is circular motion, which is all that you seem to be capable of considering. You accept one moment that there is a radially outward centrifugal force balancing a radially inward centripetal force. But as soon as the centrifugal force becomes inconvenient for you, you claim that it vanishes in the inertial frame, even though the centripetal force remains. That is just a nonsense.

(2) Trying to drag in the three body problem while totally sweeping the two body problem under the carpet. This is because you feel more comfortable in a field that nobody can understand. It is good cover for talking nonsense.

(3) Introducing Lagrangian mechanics.

(4) Introducing Hamiltonian mechanics.

(5) Introducing matrix algebra.

(6) Quoting Feynam.

We have seen all these tactics used in a pathetic attempt to deny the fact that centrifugal force only occurs when a particle actually possesses an angular velocity relative to a point.

The section which I put in yesterday contained partically all that you need to know about centrifugal force. But that was too good for you. You much prefer that big mindless waffle of an introduction that tells us absolutely nothing about centrifugal force. David Tombe ( talk) 05:43, 30 May 2008 (UTC)

User:David Tombe has been blocked for a week for incivility and personal attacks. It is my strong recommendation that people not engage in discussion with him about his latest comments; it is extraordinarily unlikely to contribute to the project. If you must, please use his talk page. -- SCZenz ( talk) 06:34, 30 May 2008 (UTC)

You sir are a vindinctive and nasty person. You have harbored a personal animonisity towards Mr Tombe and your actions reflect your nasty character. You have consistently refused to treat him in a fair and civil manner in your efforts to block a full and objective discussion on these pages. You sir are the problem here, not Mr Tombe. Again I demand that you formally apologise to Mr Tombe for your personal animonisity and bias towards Mr Tombe. Your refusal to comply with past demands to do this demonstrates your personal lack of civility and personal mean spiritedness. You should be blocked from future actions of this nature and that would greatly improve the quality of discussions conducted here with wikipedia editors. It is my informed judgement that Mr Tombe has contributed more than you could possibility appreciate. The subject article is a dreadful mess. It reflects the ignorance of wikipedai editors and their continued resistence to learning the facts by educating themselves instead of repeating nonsense as if it were fact. 72.84.67.168 ( talk) 13:52, 30 May 2008 (UTC)

The equation for planar motion of a particle derived in planar motion:

${\displaystyle \mathbf {a} =\mathbf {u} _{\rho }\left[{\frac {d^{2}\rho }{dt^{2}}}-\rho \left({\frac {d\theta }{dt}}\right)^{2}\right]+\mathbf {u} _{\theta }\left[2{\frac {d\rho }{dt}}{\frac {d\theta }{dt}}+\rho {\frac {d^{2}\theta }{dt^{2}}}\right]\ }$

is discussed by Taylor using the example of circular motion to introduce the notions of centripetal acceleration and what he calls "tangential" acceleration. The case of circular motion is unique however, because in this coordinate system polar coordinates actually are normal and tangential to the trajectory. Consequently, forces normal to and tangential to the trajectory, which have actual physical meaning, happen to be picked up by the polar coordinate system. However, to treat an elliptical path, for example, an elliptical coordinate system is necessary to make the coordinates tangential or normal to the path. If one were to do this, the tangential and centripetal forces could be picked out in this case too.

However, the application of polar coordinates to an elliptical path does not have this property. Consequently, determining the centripetal and tnagential forces in such a case is not straightforward, and attempts to cook it up are doomed to complexity.

Also, in a kinematic discussion, an elliptical orbit does not have to be traversed in the manner prescribed by the inverse square law. It is a perfectly proper application of kinematics to inquire what forces are necessary to traverse an elliptical path with position on the path an arbitrary function of time. Thus, the discussion of elliptical orbits can be divorced entirely from planetary motion for a kinematic discussion.

In the case of planetary motion, the force of gravity is always radially directed toward the Sun. That gives polar coordinates a special place in kinetics, but the connection of this radial force to the centripetal and tangential forces of kinematics is (a) complicated and (b) specific to this particular dynamic arrangement.

In sum, from the viewpoint of fictitious forces, polar coordinates are only special for circular motion, and for any other trajectory their value is moot. Brews ohare ( talk) 16:09, 30 May 2008 (UTC)