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Does the centrifugal force that causes stuff to move to the outer edge of a centrifuge come under the real or fictitious category? If it is real, it is certainly not a reactive force. If it is fictitious, it has got a very real effect.

I suggest that the introduction be tidied up such as to define centrifugal force without splitting it into a real kind and a fictitious kind. 203.115.188.254 ( talk) 11:01, 4 April 2008 (UTC)

There happen to be two competing (and incompatible) uses of the term, and lack of perception of the differences continues to cause many confusions and even disputes in academia. Thus, how do you propose to do such "cleaning up" without recreating the kind of confusion that this article gets rid of from the start?

About your example: There is no real direct force that causes stuff to move to the outer edge; such a hypothetical force can have no real effect. However, moving objects resist changing their trajectory, and that causes a very real reactive force against the centrifuge wall. Do you think that it may be useful to add this example? Harald88 ( talk) 16:19, 6 April 2008 (UTC)

Harald88, In planetary orbital theory, an elliptical orbit is the result of an inward radial force of gravity and a very real outward radial force which is the centrifugal force.

In the centrifuge, gravity is neglible and so we only have the centrifugal force.

The orbital solution to a centrifugal force acting in isolation without gravity is an infinitely eccentric hyperbola. This translates into a straight line in the laboratory.

In the centrifuge, a very real effect occurs, but you say that this is simply due to the tendency of moving objects to resist changing their trajectory. This tendency is known as inertia and it is equivalent to centrifugal force in the laboratory. It is a very real effect.

Hence, I do not accept that centrifugal force is a fictitious effect. If it can bring about a real effect in a centrifuge, then it is real. David Tombe ( talk) 07:29, 16 April 2008 (UTC)

You did not answer my question. Do you think that it may be useful to add this example? Harald88 ( talk) 09:21, 20 April 2008 (UTC)

Harald88, By all means put in a section about the centrifuge. It totally undermines the existing introduction which tries to claim that centrifugal force applies to two different things, one real and one fictitious, which just happen to act in the same place at the same time.

In the centrifuge, would they try to argue that the centrifugal force only becomes real at the moment when the heavy particles hit the edge?

That would be the same as saying that gravity for a man falling over a cliff only becomes real when he hits the ground. David Tombe ( talk) 13:28, 21 April 2008 (UTC)

The main article seems to be hedging its bets. It claims that there are two kinds of centrifugal force, with one kind being real and the other kind being fictitious. It then gives examples of each kind but goes on to admit that both of these kinds are the same thing.

The problem seems to be that modern literature presents centrifugal force to be a fictitious force, whereas classical literature presents it as a real force.

Even in the absence of a resolution of this controversy, the main article needs to be tidied up. We need to explain what centrifugal force is, without mentioning whether it is real or fictitious.

There then needs to be sections giving reasons for suggesting that it is fictitious, and sections giving reasons for suggesting that it is real.

But in its current form, the article is unsatisfactory because it talks of two kinds of centrifugal force when in fact there is only one kind. David Tombe ( talk) 05:45, 18 April 2008 (UTC)

No, the two uses are entirely incompatible, and I thought that the article makes that clear - one of the purposes of this article is to end such confusion and misjudgment. Where did you get that idea, which sentence needs to be improved?

Note also that the article refers to a modern encyclopdia (edition of 2007) that defines centrifugal force as a reaction force.

Thanks, Harald88 ( talk) 09:19, 20 April 2008 (UTC)

Harald88, the example of the swerving car in the so-called consensus version totally undermines what you have just said. It is trying to make out that the fictitious centrifugal force and the real centrifugal force are the same thing depending on how you view it.

The version which I put in, which you didn't see because it was changed by Thermochap, merely states the facts as regards what centrifugal force is. It then points out that it used to be regarded as real, but that it is now regarded as fictitious. If you say that a 2007 encyclopaedia states that it is real, then that is a clear sign that there is no consensus on the matter within the physics community. David Tombe ( talk) 12:31, 20 April 2008 (UTC)

Thermochap, I thought that the middle paragraph of your new introduction was unnecessarily complicated. It involved the Affine connection. Overall, I'm not happy with it because you have acknowledged that centrifugal force is a real reaction to a centripetal force and then brushed that fact under the carpet as being history. What do you call that real reaction effect now if it is no longer considered to be centrifugal force?

Meanwhile, you have emphasized the modern view that centrifugal force is only a fictitious effect as viewed from a rotating frame of reference, when in fact you are perfectly aware yourself that the effect is real.

I had deliberately worded the article in such as way as to point out that nowadays, centrifugal force is considered to be fictitious, whereas in days of old, it was considered to be real. David Tombe ( talk) 08:14, 20 April 2008 (UTC)

David, we have been through all this long ago. It is clear to everybody that you don't understand the first thing about this article's subject. Please do not try to edit it, your attempts to do so invariably make the article wrong and completely out of tune with established physical understanding. I have reverted it. – Henning Makholm 08:19, 20 April 2008 (UTC)

Indeed, the use of the term as reaction force is less common nowadays, but that "old" meaning is related to Newtonian mechanics which led to the derivation of centripetal acceleration; which in turn is necessary for understanding the fictitious use of the term. Thus, although at a time I went along with putting the fictitious meaning first because of its greater popularity, for a logical and comprehensible explanation to the reader it is certainly better as it is now.

In spite of that, as long as people like David turn up, it appears that it is still not well enough explained - or perhaps the topic is just to difficult? I'm not sure. David, what should be changed so that you won't find it confusing anymore?

Thanks, Harald88 ( talk) 09:14, 20 April 2008 (UTC)

I actually think that the introduction is better off without any reference to the archaic use of the term "centrifucal force" to denote the reaction force to a centripetal force. That could still be in the article, but somewhere nearer the end. I also think that it needs to be made clear early in the article that the term "fictitious force" has a very specific meaning. It is not the same as "fictional". It is not the opposite of "real". It is a force that enters the calculations when a non-inertial reference frame is used. -- PeR ( talk) 17:28, 20 April 2008 (UTC)

I agree with these points, mostly. However, we should be careful not to move the reaction force so far down that it appears to be merely a historical curiosity that can safely be skipped. That's what it is, of course, to one who groks the fictitious force, but it seems to me that regrettably often people confuse the two forces. Therefore readers deserves to have the difference between them explained in some detail. And it is far nicer to do that by saying, "here is an older meaning of the word, but beware that it is different from the mainstream meaning in such-and-such way", than to have to say "here is a stupid misconception that you must disabuse yourself of". Of course we can only do this because we have sources to show that the achaic sense of the term is not complete fuction -- but given that we do have those, grabbing the chance sounds like a good idea. – Henning Makholm 22:25, 20 April 2008 (UTC)

Actually, because the reaction force is precisely a historical curiosity that can safely be skipped, I think it does more harm than good to give it a prominent position. Lots of people just read the first paragraph, and they should get as good info as possible. We should keep the text as clear as possible, and keep distractions to a minimum. -- PeR ( talk) 20:49, 21 April 2008 (UTC)

Henning, In the so-called consensus version, you talk about two kinds of centrifugal force. You talk about a real kind, and then you talk about a fictitious kind.

Below that, you then describe a scenario in which centrifugal force is either real or fictitious according to how you look at it.

This is entirely unsatisfactory.

The version which you reverted was not mine. In the version which I put in yesterday, I merely described centrifugal force and then pointed out the fact that it used to be considered to be real, but that nowadays it is considered to be fictitious. David Tombe ( talk) 12:35, 20 April 2008 (UTC)

No. The consensus version describes that the term "centrifugal force" has two different possible meanings, and then goes on to describe a situation that happen to illustrate both meanings. But even in the described situation the two meanings of "centrifugal force" refers to two different forces. – Henning Makholm 22:11, 20 April 2008 (UTC)

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)

Thermochap pointed out this nice animation from commons:

which nicely shows the difference between the two meanings described in the article. The red arrow is the centripetal force; the magenta one is the reactive centrifugal force, and the blue one is the fictitious force. I think this would make a good illustration for this article, if only the blue arrow had been decomposed into centrifugal and Coriolis terms after the green ball is let go. Names, aside, the force shown in magenta is and always was considered to be real; that shown in blue is and always was considered to be fictitious. – Henning Makholm 22:45, 20 April 2008 (UTC)

Henning, centrifugal force has only one meaning. The controversy lies in whether or not it is real or fictitious. The official position today is that it is fictitious. However, in former times, it was considered to be real.

I don't quite follow PeR's logic that if I were to provide a quote from an old paper confirming that centrifugal force was believed to be real, that this would have to be dismissed on the grounds that it was my original research.

The present introduction is totally unsatisfactory because it is trying to fudge the controversy by stating that the term centrifugal force has two different possible meanings.

The new introduction which I put in yesterday simply stated what centrifugal force is, and then further stated that the modern consensus is that centrifugal force is fictitious, whereas previously it had been regarded as real. David Tombe ( talk) 07:11, 21 April 2008 (UTC)

If you don't understand what I said, then read WP:OR. Then read what I said again. I'm tired of repeating myself. -- PeR ( talk) 07:57, 21 April 2008 (UTC)

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)

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)

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)

PeR, I'm glad that you agree that the introduction should be re-written. So let's take it one step at a time.

First of all, I assume that we are both agreed that somewhere in the introduction there should be a statement clarifying that we should not be confusing centrifugal force with centripetal force.

And now, how about this for an introductory sentence?

"When an object is constrained to move in circular motion, an outward radial force will be observed to act on that object"

Would you agree that that is a correct statement of fact? There is certainly no need to distinguish between the reactive kind and the other kind because they are exactly the same effect.

Beyond that, I can't think that much more is needed in the introduction other than to state that a controversy exists regarding whether or not it is real or fictitious. David Tombe ( talk) 02:13, 22 April 2008 (UTC)

Your proposal is not a correct statement of fact. It is simply false. An outward centrifugal force appears to act on an object only when it is described in a rotating coordinate system - and then not just for objects moving in circles, but for all object that are observed in that coordinate system. The outwards force that appears in an inertial system when an object moves in a circle does not act on the object that moves circularly, but on the constraints that make it move in a circle. This is clearly described in the article (at least when you have not recently vandalised it), and there are several descriptions of it to be found on this talk page.

Your continued assertions that these two forces are the same force are simply wrong. The two forces do not even apply to the same body. There is no controversy whatsoever about whether any of these forces are real or fictitious. Everybody agrees that the reactive force is (usually) real; and everybody agrees that the fictitious force is fictitious. Nothing of this will change because you continue to claim that it is false. – Henning Makholm 04:11, 22 April 2008 (UTC)

Henning, you are making it more complicated that it is. When an object is constrained to move in a circle, then an outward centrifugal force will act on it.

And there is a controversy about whether centrifugal force is real or fictitious. And there is only one centrifugal force. It is sheer double talk to split centrifugal force into two in order to cater for both beliefs. David Tombe ( talk) 04:44, 22 April 2008 (UTC)

David, read what Henning wrote again. Your proposal is not a correct statement of fact. It is simply false. -- PeR ( talk) 07:04, 22 April 2008 (UTC)

PeR, OK, let's go through Henning Makholm's reply stage by stage. He says,

An outward centrifugal force appears to act on an object only when it is described in a rotating coordinate system

The very fact that we state the word 'outward' describes the effect perfectly without having to mention anything about rotating coordinate systems. Henning Makholm is making it more complicated than it is.

He then states,

- and then not just for objects moving in circles, but for all object that are observed in that coordinate system.

This statement was totally unnecessary because all objects that are observed in that coordinate system will be partaking in the circular motion in question. This was just a clouding statement.

Utter nonsense. Our choice to describe things from a rotating coordinate system cannot possibly make things move circularly. There is an infinitude of possible kinds of movements that are circular in neither an inertial coordinate system nor in a rotating one. – Henning Makholm 19:50, 22 April 2008 (UTC)

Henning, my apologies. I should have clarified that all objects that experience centrifugal force in that coordinate system will be partaking in the circular motion in question. We don't need to mention rotating frames. It is only necessary that an object be constrained to follow a curved path. David Tombe ( talk) 05:38, 23 April 2008 (UTC)

He then states,

The outwards force that appears in an inertial system when an object moves in a circle does not act on the object that moves circularly, but on the constraints that make it move in a circle.

What happens in a centrifuge regarding the large particles before they reach the edge? Is the centrifugal force not acting on them?

When viewed from an inertial coordinate system, there is no centrifugal force acting on particles. Before they reach the edge, they drift with constant velocity within the centrifuge. When viewed from a co-rotating system, a centrifugal force acts on particles as they drift towards the edge, and keeps acting to pin them to the wall. In both cases the particles will start pushing the wall outwards once they stick to the wall (this is the reactive meaning of the centrifugal force). – Henning Makholm 19:50, 22 April 2008 (UTC)

Henning, Yes there is. These particles have been constrained to partake in the circular motion, and a centrifugal force acts radially outwards on them and causes them to accelerate towards the edge. If they were not constrained to move circularly with the centrifuge, then no centrifugal force would act on them. The centrifugal force is an absolute radial effect. David Tombe ( talk) 06:03, 23 April 2008 (UTC)

He then says,

Your continued assertions that these two forces are the same force are simply wrong. The two forces do not even apply to the same body.

It's only in Henning Makholm's imagination that there are two centrifugal forces. No textbook ever states such a notion.

Perhaps not. But there are sufficient citations for either of the two different notions, and they are clearly two different notions, sharing essentially nothing but the name. – Henning Makholm 19:50, 22 April 2008 (UTC)

As for Henning Makholm's claim that the two forces don't even apply to the same body, he is only making the matter worse. In the example in the introduction to the main article, the bit that you call the fictitious centrifugal force acts to throw the man towards the car door. The bit which you call the reactive centrifugal force occurs by virtue of the man pushing against the car door as a result of that very same centrifugal force.

In this example, the fictitious centrifugal force applies to the passenger. The reactive centrifugal force applies to the car door. That is two different forces, and arguments about one causing the other does not make them into the same force. – Henning Makholm 19:50, 22 April 2008 (UTC)

Henning, it's a transmission of the same effect. It is splitting hairs to divide it into two different forces. That can all be discussed in the main article. There is no need to mention the reactive effect in the introduction. David Tombe ( talk) 06:03, 23 April 2008 (UTC)

And he is saying that these two centrifugal forces do not act on the same body. It's like saying that the force with which a man hits the ground is not the same force as the gravity which caused him to fall over the cliff.

Of course they are not. The gravity applies to the man and causes him to accelerate downwards. Later, contact forces apply to the dirt where the man hits and cause the dirt to be rearranged. They are not the same force -- not only do they act on different bodies, they act at different times. Gravity acts continuously during the fall; the contact forces act only during the collision. – Henning Makholm 19:50, 22 April 2008 (UTC)

Henning, No. Even when the object is lying at rest on the Earth, gravity is still pushing it against the Earth. David Tombe ( talk) 06:03, 23 April 2008 (UTC)

The man pushes against the car door because of the one and only centrifugal force.

From an inertial viewpoint, the man pushes against the car door because the car door pushes against the man, trying to make him turn a corner. In any case the reason why the man pushes is not the same as the force against the door that the pushing constitutes. – Henning Makholm 19:50, 22 April 2008 (UTC)

I need to have a citation which specifically states that centrifugal force applies to two different forces. David Tombe ( talk) 08:04, 22 April 2008 (UTC)

I agree with your last statement. We need to cite a science-history book that states that Newton and others used the word "centrifugal force" with a different meaning than that which is used today. (The current references only show the usage of the term, which is not the same thing.) The rest of your analysis is just plain wrong. Sorry. My best advice is that you try reading the fictitious force article, some elementary mechanics textbooks, and then try reading Hennings text again. -- PeR ( talk) 10:00, 22 April 2008 (UTC)

What we seem to need is citations for the ordinary, fictitious, meaning of "centrifugal force". Once both meanings are properly cited to be (have been) in use, there will be no need to cite separately the obvious fact that the two meanings are different. – Henning Makholm 19:50, 22 April 2008 (UTC)~

Henning, That is not good enough. We know that there is centrifugal force. And we know that there are references that apply it to the reaction against the force that constrains the object to the curved path. But that is not sufficient to justify an unconventional claim that centrifugal force is a term which applies to two different forces. Such a claim is a grossly misleading exaggeration of the truth. David Tombe ( talk) 06:03, 23 April 2008 (UTC)

PeR, so far your entire contribution to this debate has been to state that I am wrong and that I should read more of what Henning Makholm has to say, as if by reading his nonsense over and over again, then I might actually believe it eventually.

I'd like to hear your own analysis of the situation.

Let's go back to the very beginning. Tell me at what point this basic sentence goes wrong,

The centrifugal force is an outward radial force that acts on any object that is constrained to move in circular motion. David Tombe ( talk) 13:32, 22 April 2008 (UTC)

Your statement doesn't properly describe the fictitious force (modern use of the term "centrifugal force"), because it fails to mention the rotating reference frame. It doesn't describe the reaction force (Newton's use of the term), because it says that it acts on the object itself, not the thing which is constraining it to move in a circle. -- PeR ( talk) 13:53, 22 April 2008 (UTC)

PeR, the fact that the object is constrained to move in circular motion caters for the rotating frame of reference aspect. As for the reaction bit, that can be dealt with in the main body of the article. That is an extension of the concept. A body which is being acted upon by a centrifugal force naturally transmits this force on when it comes into contact with another body. —Preceding unsigned comment added by David Tombe ( talk • contribs) 14:38, 22 April 2008 (UTC)

This is utterly wrong. The choice of which reference frame to use (and hence whether or not one must consider a fictitious centrifugal force) can be made independently of how things move. Some choices may be more or less convenient according to whether they simply the movements, but the actual movements cannot make any choice of reference frame more or less correct. – Henning Makholm 19:50, 22 April 2008 (UTC)

The wikified version is teaching the false doctrine that centrifugal force is a term which applies to two different forces.

This doctrine is based on the idea that the centrifugal force which throws the passenger towards the door of the swerving car is a different force from the force which the passenger eventually causes on the door when contact is made.

The argument goes that a fictitious force throws the passenger to the car door and when contact is made, this is then transmitted into a real force which pushes against the door.

Such an argument is the same as saying that the force which an object causes on the Earth's surface due to its weight is a different force from the gravitional force that pushes the person against the surface of the Earth.

There is one force of gravity, and there is one centrifugal force.

The introduction to the article must describe in as simple terms as possible what that one centrifugal force is. David Tombe ( talk) 13:47, 22 April 2008 (UTC)

I don't know whether what you say is true or not, but please IF you are going to rewrite the article, rewrite it in such a way that the article is wikified! Stephenb (Talk) 15:01, 22 April 2008 (UTC)

Looking at both versions of the text, I have to say it looks as though reverting was correct, but I'm no physicist. Have you guys thought of trying Wikipedia:Third opinion and getting another opinion? Stephenb (Talk) 15:29, 22 April 2008 (UTC)~

Stephen, thanks for replying. But I can assure you that the onus of wikification is on them. They need to provide a citation which clearly states that centrifugal force is a term which applies to two different forces. There is no textbook or encyclopaedia which will state that. David Tombe ( talk) 05:41, 23 April 2008 (UTC)

You misunderstand. Wikification is the process of turning the text into an article, using proper grammar, formatting, references and citations. Whether or not your version or the other version contains faulty information is not why I reverted. The "consensus" version was wikified; yours was not, and looked like someone had edited it in bad faith resulting in a poor article, which is bordering on vandalism (since it appeared to remove information too). Stephenb (Talk) 09:10, 23 April 2008 (UTC)

In the old days, before about 1950, physics books called centrifugal force an inertial force. In those days inertial force was the term used for what today are labeled fictious forces. What this means is that the force is frame dependent. The force can be made to go away by simply switching from a noninertial frame to an inertial frame and the force disapears. The older terminology is certainly less of a problem, since students now wonder what is this fictious force? in my view the entire discussion of this is confusing and of questionable value as part of the article. There are no fictious forces, since they dont exist by definition of the word. So saying centrifugal force is fictious is the same as saying it doesnt exist. But since it does exist, that is bound to create confusion. I propose using the term frame dependent force since that captures the essential meaning of what is happening and we get rid of this textbook stupidity of fictious forces. Electrodynamicist ( talk) 16:07, 22 April 2008 (UTC)

It is definitely worth mentioning that "fictitious force" is synonymous to the older "inertial force". Indeed it is a poorly chosen term, but this is an encyclopedia, not a place for redefining terminology. If it were, there certainly wouldn't be an article entitled imaginary number. -- PeR ( talk) 18:21, 22 April 2008 (UTC)

Update: Looking at some different uses of the term "inertial force" (including the Wikipedia disambig page inertial force) it seems the term has to meanings, in the same way as "centrifugal force" does. Thus, the sentence The centrifugal force is an inertial force. is correct in two ways (out of four :-). -- PeR ( talk) 09:50, 25 April 2008 (UTC)

Henning, a rotating reference frame is irrelevant. The object in question has to actually be rotating with that reference frame before the centrifugal force will be induced. In other words, the object has to be constrained to move in circular motion.

There is no need to mention reference frames. In the swerving car scenario, the passenger is being constrained to follow the circular path by virtue of the back of his seat pushing him. A radially outward centrifugal force then occurs at right angles to this.

We must not lose track of the fact that this centrifugal effect is not something that is confined to circular motion. It occurs in any curved path motion. It occurs in elliptical and hyperbolic motion.

Therefore , mention of a rotating frame of reference merely confuses the issue because there could be an object which is stationary in the inertial frame. In the rotating frame, this object would trace out a circle, but it would experince no centrifugal force.

Regarding the 'reactive' centrifugal force, this is not a different force. It is an extension, or a transmission of the same effect. David Tombe ( talk) 05:28, 23 April 2008 (UTC)

PeR, You have just reverted a perfectly good introduction to a shambles version. Did you even read what I said about elliptical motion? Anyway, a citation will be needed for the version which you have put in place.

We haven't even heard any evidence yet that you understand the issues in question. You seem to always just defer to what Henning Makholm says. The version which I put in was easier to read and it covered the key points. Nobody is disputing any fact which I wrote in that introduction. David Tombe ( talk) 06:11, 23 April 2008 (UTC)

David, you might want to read through this. Notice how everybody else (including me) is politely trying to explain why you're wrong? Notice how nobody agrees with you? Maybe you should consider the possibility that the others may be right? -- PeR ( talk) 08:24, 23 April 2008 (UTC)

PeR, You obviously haven't been paying the slightest bit of attention to anything that has been going on. Your mind is totally locked into last year's argument.

We are not arguing about whether the centrifugal force is real or fictitious. That was last year's argument and I still have my own opinion on that matter.

At the moment, we are trying to clean up the existing introduction in certain key respects. These are notably,

(1) To avoid any specific statement, especially in the first line of the introduction, to the extent that centrifugal force is a term which is applied to two different forces.

The reality is that one of those effects is a transmitted effect of the other. That can be dealt with in the main body of the article. There is no need to deal with that in the introduction.

(ii) We need to generalize the wording to cater for all kinds of curved path motion. In the so-called consensus version, one might get the impression that centrifugal force only occurs with circular motion.

So far, your only contribution to this debate has been to continually repeat that I am wrong without even being specific as to which particular point you are talking about. And you seem to have a habbit of referring what other people have said.

Can we soon maybe hear some of your own views, just so that we can be sure that you actually understand the issues in question. David Tombe ( talk) 08:52, 23 April 2008 (UTC)

Rracecarr, The edits that you undid were designed to generalize the situation to cater for curved motion generally, which it seems that you began to realize after you had made the reversion.

They were also designed to treat reactive centrifugal force as a knock effect rather than as a distinct force in its own right.

The version which you reverted to contains some errors. Notably it doesn't specify that an object has to be co-rotating in a rotating frame in order to experience centrifugal force.

Surely you must know that already. Centrifugal force is treated in modern applied maths courses as one of two inertial effects which supplement the true acceleration when we do a rotating coordinate frame transformation. In order for the centrifugal force to be non-zero the object must have a tangential speed of zero relative to the rotating frame.

Ideally, I would like to see the introduction very much simplified and all matters to do with reactive centrifugal force dealt with in a section in the main article. David Tombe ( talk) 15:30, 23 April 2008 (UTC)

There are at least 2 errors in the version being pushed by DT. 1) Centrifugal force is present in a rotating frame whether or not the object rotates with the frame; 2) the centrifugal force does not act away from the focus--this is sloppy terminology. For example, the centripetal force experienced by a particle moving along a parabolic path does not in general point toward the focus of the parabola. Rracecarr ( talk) 15:30, 23 April 2008 (UTC)

Rracecarr, Regarding point number (1), if an object is not co-rotating with a rotating frame, then it experiences no centrifugal force.

Imagine you are standing on the ground. Above you is a large rotating disc. Somebody sitting on that rotating disc will consider that you are tracing out a circular path. Neither he nor you will observe any centrifugal force.

You are getting confused with Coriolis force. Coriolis force is different because it is a tangential effect and a fictitious Coriolis effect can indeed be induced on an object which is moving, but not necessarily co-rotating with the frame. Centrifugal force is a radial force and it cannot be introduced as an artifact of rotation. But if somebody is constrained to co-rotate, then they will experience an outward radial centrifugal force.

On point number (2), yes it was sloppy terminology but I wanted to get the point started that we are not confined to circular motion.

What you should have done was improved the terminology. There was no need for a wholesale reversion. David Tombe ( talk) 15:42, 23 April 2008 (UTC)

You are flat wrong that there is no centrifugal force if the object does not rotate with the frame. The centrifugal force in a rotating frame of reference is totally independent of the velocity of the object. It depends only on the position, and is only zero if the object is collocated with the axis of rotation. I'm not going to revert right now because I'm already past 3RR (as are you--I think you're at 5). Rracecarr ( talk) 16:18, 23 April 2008 (UTC)

No Rracecarr, it is you that is totally wrong. If an object is not rotating with the frame, it will be tracing out a circle in that frame. There will be no centrifugal force acting on it in any shape or form.

To get centrifugal force, we need to have a tangential speed measured relative to the true inertial frame. Co-rotation with a rotating frame is a perfect scenario.

That might seem logical to do it that way. Unfortunately, that's not the way that the centrifugal force is defined. The centrifugal force is defined based solely on the rotation speed of the reference frame, and distance from the axis and the coriolis force compensates for any difference due to the motion of the particle. The advantage of this definition is that corotation isn't needed, and it can deal with particles moving in arbitrary ways, not just ones that happen to be rotating about a center.- ( User) WolfKeeper ( Talk) 16:29, 3 May 2008 (UTC)

When the car swerves around the corner, the seat of the car is constraining the passenger to co-rotate in the circle we the car is following. Hence a radial centrifugal force is induced which throws the passenger to the side door.

I can see that your confusion comes due to your special interest in Coriolis force. Fictitious Coriolis force has got important differences to centrifugal force.

Circular motion can induce tangential motion as an artifact. But it cannot induce radial motion as an artifact. Coriolis force is a tangential effect and centrifugal force is a radial effect.

In classical mecahnics, I'm sure you have done the equations. We end up with the two 'inertial terms'. One is Coriolis force. If we do a radial motion in the rotating frame, we will get an apparent tangential deflection as viewed from the rotating frame.

However, the centrifugal force term only becomes active if there is a tangential velocity as measured relative to the true frame. David Tombe ( talk) 16:32, 23 April 2008 (UTC)

This edit misses the point. Centrifugal force is a useful concept in rotating reference frames, and it acts on all objects, whether they're moving in a curved path, a straight path, or not moving at all. In my view you have removed the most important and useful definition. I'm not going to waste time arguing with you, because it is obvious that you won't listen. Fortunately, someone else who understands physics will likely be along soon to correct your mistakes. Otherwise I will revert tomorrow. Rracecarr ( talk) 16:36, 23 April 2008 (UTC)

Rracecarr, the centrifugal force that I am talking about is the one that occurs in a centrifuge. As the heavy particles in the solution are constrained to co-rotate, they experience an outward radial force which moves them to the edge.

The centrifugal force that you are talking about is a mathematical game. It doesn't exist. There is a circular motion artifact. That is all.

But thanks to PeR's message on my talk page, I can now finally see where you are coming from. Somehow, you can see in this circular motion, a resultant between a Coriolis force and a centrifugal force.

If that is official teaching, then so be it. But in that case, we really need to be introducing three centrifugal forces into the main article.

(1) The real centrifugal force such as occurs in the centrifuge when particles get thrown to the edge, or when passengers get thrown to the side door when a car swerves around a corner.

(2) Then there is the knock on effect of this which some people describe as the reactive centrifugal force. When the object in (1) presses against something, due to the centrifugal force, it transmits the effect on to that something, just as a book on a table transmits the force of gravity unto the table in the form of its weight.

(3) And finally we have this ultra mathematical nicety which contributes towards an artificial circular path as viewed from a rotating frame of reference.

Finally I know what you are talking about. But quite frankly, when a reader wants to read about centrifugal force, they will only be interested in (1), and I think that it is (1) which the article should be concentrating on.

It seems that you, PeR, and Henning Makholm have been subtely pushing (3) and are determined to keep it that way. David Tombe ( talk) 17:14, 23 April 2008 (UTC)

Your (1) and (3) are the same thing. They are forces which appear when you view the world through a rotating frame of reference. It seems you would like to draw a distinction between the intuitive force (1) and the mathematical description of it (3). Rracecarr ( talk) 17:46, 23 April 2008 (UTC)

Rracecarr, The only thing that viewing something from a rotating reference frame does is to introduce a circular motion artifact on top of the alreay existing motion. It does absolutely nothing else.

The centrifuge on the other hand produces a very real radial effect which is absolute, and can be viewed from any frame of reference.

So the fictitious effect which you are interested in is not the same thing as the centrifugal force as is commonly understood by the man in the street.

The man in the street sees centrifugal force as the outward radial force which occurs when an object is constrained to follow a curved path.

You are just playing out cheap mathematical games and confusing this whole article.

There is a big difference between an object that is co-rotating in a rotating reference frame and an object that is at rest in the inertial frame and viewed from the rotating frame. In the former, an actual centrifugal force accelerates the object radially outwards. In the latter, nothing happens.

If you can't see the difference between the two situations, then you are not living in the real world.

You, and PeR, and Henning Makholm are totally messing this article up to satisfy your own curiosity about irrelevent manipulations of maths.

You seem to think that there is something very interesting about the fact that the artificial circle can mathematically equate to the summation of the expression for Centrifugal force and the expression for Coriolis force.

At best, that is hardly interesting, and it's certainly not what a reader has in mind when he wants to read about centrifugal force.

But at any rate, the whole basis of this idea is faulty. Take a look at the mathematical expressions for the two fictitious forces. They both involve the angular velocity quantity ω. This angular velocity equates to v/r where v is the speed relative to the true frame.

In other words, these expressions only have any significance for objects moving at v relative to the true frame (ie. co-rotating with the rotating frame).

This can be easily demonstrated simply by looking at the centrifuge. If there is no co-rotation then the centrifuge will not operate.

This theory of yours, that a fictitious centrifugal force combines with a fictitious Coriolis force to yield a fictitious centripetal force is totally bogus.

And you are sacrificing this whole article in the name of this pet theory of yours. David Tombe ( talk) 05:43, 24 April 2008 (UTC)

I am going to try not to be snippety or condescending, in the hopes that you will listen rather than simply defend. Heavy things move toward the outside of a spinning centrifuge. This effect can be understood in 2 different ways: by analyzing in an inertial reference frame (the lab) or by analyzing in a frame which rotates with the centrifuge.

In the lab frame, the stuff in the centrifuge spins in circles: it accelerates inward toward the middle of the centrifuge. A centripetal force is required to maintain this centripetal acceleration, and the heavier particles require more force, due to Newton's second law. Because it is "harder" to bend the paths of the heavier particles, they go "straighter" and move toward the outside. Intuitively, it seems there is a centrifugal force flinging them outward, but in the lab frame there really is no such force. If you write out the equations of motion, there is no term for centrifugal force--it exists only in people's imaginations.

The second way of understanding the effect is by moving to the frame with rotates with the centrifuge. In that case, the stuff inside doesn't spin around at all--it basically sits still, but again, the heavier particles move toward the outside. In this frame, the movement is caused by a centrifugal force, which arises because of the rotating frame of reference. The centrifugal force exists in this frame, in the sense that there is a term for it in the equation of motion, but it is fictitious in the sense that it only exists because we've chosen a rotating frame of reference--there is still no actual physical source of outward force. Rracecarr ( talk) 18:48, 24 April 2008 (UTC)

Rracecarr, Thank you for your response. I can understand why you think like that, but you are overlooking some points.

First, I should point out that I understand that wikipedia is about presenting the official viewpoint, and if my viewpoint differs from the official viewpoint, then I will not be attempting to impose my viewpoint on the main page.

The official viewpoint regarding the centrifugal force in the centrifuge is that it is an 'inertial' force, and as such, I will not be arguing with that fact on the main page.

At the moment, I am trying to get you to see that whether the centrifugal force in the centrifuge is 'inertial' or 'fictitious' or whatever, that it is quite different from the purely fictitious effect which is an artifact of a rotating frame of reference. In the latter case, a particle that is stationary in the true frame is not being subjected to any kinds of force whatsoever.

Now even if you wish to write off the centrifuge effect as being fictitious too, you must at least admit that it is nevertheless real enough to invoke Archimedes' principle.

That alone is sufficient grounds upon which to distinguish between the two scenarios.

Regarding my own opinions on what you said, I should state that in the laboratory Cartesian frame that centrifugal force is disguised as 'Inertia'. It is the straight line motion that is the extreme hyperbola asociated with a central force orbit in which the inward gravity force is zero.

The reality of the situation is that there is a radially outward force in circular motion, no matter from what frame of reference we view it.

But that is only my opinion and I will not enforce that on the main page. Nevertheless, I believe that if you stand back and take the broader view, you will realize that there is a point here.

What I am trying to correct on the main page is the presentation, coherence and emphasis.

I want the reactive centrifugal force to be discussed as a knock on effect in the main article. There are some good citations there, but it shouldn't be clouding the introduction.

I want the introduction to focus on the 'inertial' effect that occurs in a centrifuge or when a passenger gets flung to the side door of a swerving car. I want it to refer to the general case of curved path motion and not exclusively to circular motion.

I am opposed to the emphasis that is placed on the issue of rotating frames of reference as these are not needed to observe the effect.

I am opposed to the emphasis that is placed on the artificial circular motion. That is not centrifugal force. The theory that makes out that a fictitious centripetal force results from a fictitious centrifugal force and a fictitious Coriolis force is false on a number of counts.

(1)You cannot have a centripetal force in isolation. In the radial direction, it must be balanced by centrifugal force otherwise there would be radial motion.

Yes, but radial motion can occur in general.- ( User) WolfKeeper ( Talk) 05:21, 25 April 2008 (UTC)

(2)Despite what some people say, the Coriolis force does not act radially. The entire derivation is based on the principle that it is a tangential force and so it cannot act along the same line as the centrifugal force. The two forces are always mutually perpendicular.

Sorry, this is quite wrong. The Coriolis acceleration is: ${\displaystyle -2\mathbf {\omega \times v} }$. As you can see, since it is a cross-product, if v is perpendicular to r then it acts completely radially.- ( User) WolfKeeper ( Talk) 05:21, 25 April 2008 (UTC)

(3)Those 'inertial' force equations are only designed to apply to objects that co-rotate. The angular velocity ω terms refer to the tangential velocity of the co-rotating object. For an object that is stationary in the true frame, those terms do not exist. David Tombe ( talk) 04:31, 25 April 2008 (UTC)

Sorry, but that is wrong also. Coriolis and Centrifugal acceleration/forces apply to all objects when considered from the rotating frame of reference. They do not have to be rotating in 'reality' (i.e. as seen from an inertial frame).- ( User) WolfKeeper ( Talk) 05:21, 25 April 2008 (UTC)

Actually, if you consider the *lab* from Racecarr's above example with the centrifuge, the fictitious acceleration also acts on it! So how come it doesn't fly off? It's because the coriolis force holds the lab in a circular motion around the centrifuge, because the coriolis acceleration/force is purely radial in that case!- ( User) WolfKeeper ( Talk) 05:21, 25 April 2008 (UTC)

Wolfkeeper, I was fully aware of the fact that the Coriolis acceleration is ${\displaystyle -2\mathbf {\omega \times v} }$. But if you ever studied the derivation of this term, you would see that it is only the tangential component that we are interested in.

No. The equation means what it says. omega is a vector aligned with the rotation axis which is of length proportional to the angular velocity, v is a vector that is aligned with the instantaneous velocity of a particle. 'x' is the cross product. There is no other valid interpretation of that equation; and it most definitely may point radially.- ( User) WolfKeeper ( Talk) 17:34, 25 April 2008 (UTC)

Once again, you have become fixated on this ultra fictitious scenario regarding why the background stars don't fly off due to the Earth's diurnal rotation.

No, not at all.- ( User) WolfKeeper ( Talk) 17:34, 25 April 2008 (UTC)

The question I am trying to address is,

can you see the difference between these two case scenarios?

(a) A stationary object as viewed from a rotating frame of reference.

(b) An object co-rotating with a rotating frame of reference hence inducing a radial centrifugal force which is real enough to invoke Archimedes' principle.

Can you see the difference between those two scenarios? David Tombe ( talk) 07:02, 25 April 2008 (UTC)

You didn't answer my question (below). Explain your own theory properly, before you ask others why they think it's wrong. -- PeR ( talk) 07:51, 25 April 2008 (UTC)

PeR, you missed the point. This has got nothing to do with any theories of mine. I'm trying to focus your attention on the fact that swinging buckets of water over your head the not the same as the background stars describing circles across the sky.

Your team are fixated on the latter and all the mathematical games that you can play to try and argue that a stationary object has got a net summation of fictitious forces acting on it.

This article is supposed to be about the 'inertial' centrifugal force of the centrifuge. David Tombe ( talk) 15:02, 25 April 2008 (UTC)

PeR, Regarding your private message to me, I should reply that you are not in a position to tell other people not to edit this page. Wikipedia is an ongoing thing. Since you didn't like my alternative version (although somebody else obviously did), I decided to fix up the existing version instead.

And you can discuss these matters on the talk page. You don't need to go private behind the scenes.

I now understand exactly where you, Henning Makholm and RRacecarr are going wrong. You can't see the difference between the situation which occurs when an object is co-rotating with a rotating reference frame, and when the object is not co-rotating.

It is only when the object is co-rotating that we get any actual effect. The situation that you like to highlight regarding the artificial circle, really is fictitious in the true sense of the word, and it is of no interest to anybody.

The situation which I am interested in is the inertial effect which occurs in a centrifuge.

In the introduction, we need to state the very basic and simple sentence that when an object is constrained to move in a curved path, it experiences a radially outward force.

The introduction cannot be allowed to focus on that obscure fictitious scenario that you seem to be so interested in, and indeed there is precious reason to even bother mentioning it in the main article.

You cannot dominate the topic with all that nonsense about a fictitious Coriolis force twice as strong as a fictitious centrifugal force causing a fictitious centripetal force. That is not what the readers are interested in.

Secondly, the reactive aspect shouldn't be in the introduction. It should be in a section in the main article.

The readers want the outward radial effect which comes from constrained curved motion. They want swinging buckets of water over the head. They want masses being swung around on the end of a string and discussions about whether they fly off radially tangentially or both, when released.

There is no need to mention rotating frames of reference because a centrifuge can be seen to have worked irrespective of which reference frame we view it from.

You are trying to cloud up this article with what you believe to be some clever realization about fictitious forces summing together to give other fictitious forces and you don't want to face up to what centrifugal force is really about. David Tombe ( talk) 11:19, 24 April 2008 (UTC)

Your talk page is not behind the scenes. Anyone can read it.

Here's a part of what you wrote in the introduction:

An inertial or " fictitious" centrifugal force appears when a rotating reference frame is used for analysis, providing that the object in question co-rotates with the frame. The true acceleration on objects that are co-rotating with the frame is supplemented by a radially outward (fictitious) centrifugal force.

This effect can be extended generally to all curved path motions.

Now tell me, with your "definition" of centrifugal force, when is an object considered to be co-rotating with the frame? When it is stationary in the frame, sure. But what if it has a very small, but nonzero velocity relative to the frame? What if this speed becomes slightly larger? What if the speed in the rotating frame is so large that the object is stationary in the inertial frame? In that case you say there is no centrifugal force. Where do you draw the limit? Does your centrifugal force end abruptly, or does it phase out as the velocity relative to the rotating frame increases? Mechanics is an exact science, so please give equations explaining your theory. Also, please give a reference to the textbook where you found that equation. -- PeR ( talk) 18:45, 24 April 2008 (UTC)

PeR, centrifugal force exists to the extent that the motion co-rotates. Ultimately the effect can be traced to the tangential velocity with respect to the rotation axis in the laboratory frame. David Tombe ( talk) 04:34, 25 April 2008 (UTC)

"to the extent that the motion co-rotates" is rather vague. Mechanics is an exact science, so please give equations with a refrence. -- PeR ( talk) 06:56, 25 April 2008 (UTC)

PeR, you are just pretending that you don't understand. If it doesn't co-rotate, there is no centrifugal force. The object sits still unaffected.

If it fully co-rotates, the radial centrifugal force is given by v^2/r, where v is the tangential speed.

If it partially co-rotates, the centrifugal force is given by the same equation but with the speed changed to the tangential speed of the object in question, with respect to the same rotation axis.

At the moment, you are just in denial of reality. For too long, you have had your mind focused on some irrelevant fictitious form of centrifugal force and there is a group of you closing ranks to defend that erroneous way of thinking.

I'm sorry, but you don't understand. This article is completely about that 'erroneous' way of thinking as you put it. The problem you have is a) it's self consistent b) it models reality correctly (it must do, since it's derived from an inertial frame using correct logic).- ( User) WolfKeeper ( Talk) 17:22, 25 April 2008 (UTC)

So far, there is you, Henning Makholm, RRacecarr, Wolfkeeper, and now FiziksFighter. I am expecting more to arrive to back you all up before this is over.

I have no doubt that you will all attempt to confound the issue with a hail of bogus mathematics. But this issue doesn't depend on maths. It depends on basic common sense.

Only a fool thinks that the background stars are being subjected to a combination of fictitious forces that result in a final inward fictitious radial centripetal force. David Tombe ( talk) 16:22, 25 April 2008 (UTC)

The thing is, maths is a model of reality, not reality. In the rotating non inertial frame model that is the subject of the article, yes, yes they are. You're just going to have to live with that.- ( User) WolfKeeper ( Talk) 17:22, 25 April 2008 (UTC)

The two sorts of centrifugal force are distinct topics. Distinct topics should have their own articles- that's one of the differences between a dictionary and an encyclopedia. Just because they are called the same doesn't meant they get to go in the same article. In fact, it's wrong to have them in the same article in the wikipedia.- ( User) WolfKeeper ( Talk) 05:42, 25 April 2008 (UTC)

Agreed. I think there should be an article entitled Fictitious forces in a rotating reference frame, that would be a subarticle of both this one, Fictitious force, and Coriolis force. It is much easier to discuss centrifugal and Coriolis forces together than one at a time, since you rarely have one without the other. A significant portion of the current article is devoted to explaining the difference between the two meanings of the term. Perhaps it should be moved to Centrifugal force (disambiguation). Then we create a new article entitled Centrifugal force (reaction force), and leave Centrifugal force as a redirect to the disambig. For good measure we should also create a page Centrifugal force (fictitious) that redirects to Fictitious forces in a rotating reference frame. -- PeR ( talk) 06:47, 25 April 2008 (UTC)

Or maybe we could move this article to centrifugal force (fictitious) with a redirect from centrifugal force and split off the real force to centrifugal force (reaction force) and put a cross-reference 'for' at the top. I'm leaning against a disamb at this time, there's only two meanings and I'm pretty sure that the real force isn't being referenced very much.- ( User) WolfKeeper ( Talk) 17:55, 25 April 2008 (UTC)

Or possibly instead of centrifugal force (fictitious) we could move it to centrifugal effect which would talk about the acceleration, and then include the force equation as well. There just doesn't seem to be quite the same degree of garbage going on over at coriolis effect and there's more symmetry in the wiki better reflecting the physics.- ( User) WolfKeeper ( Talk) 18:03, 25 April 2008 (UTC)

I like Wolf 1 a lot. Not so big on Wolf 2 ( centrifugal effect). It is not in such common usage as Coriolis effect, and the same discussion of acceleration can be included at both the centrifugal force articles. Rracecarr ( talk) 18:13, 25 April 2008 (UTC)

Yes, I agree. I did a google on 'centrifugal effect' and it's not common enough to be an article title.- ( User) WolfKeeper ( Talk) 19:13, 25 April 2008 (UTC)

I also thought that the classical use of the term was uncommon these days, but I'm starting to change my mind. It seems to be used applied mechanics. And I have heard materials science people use the term correctly in the classical sense when discussing rotating parts in machinery. I think, because the term is not introduced at high-school level, people from different fields will have learned the term with different meanings, and people who learned about the fictitious kind from a theoretical physics class might never realize that people who studied statics use the same term with a different meaning. -- PeR ( talk) 21:50, 25 April 2008 (UTC)

Sure, if it wasn't in use, we wouldn't have it in an article. It's in the article because we found references to it, less than to the d'Alembert force version, but it's definitely in use.- ( User) WolfKeeper ( Talk) 22:08, 25 April 2008 (UTC)

OK, I've created Reactive centrifugal force, on reflection it seemed a better name than Centrifugal force (reactive), but we can always move it, or add redirects if necessary.- ( User) WolfKeeper ( Talk) 02:37, 27 April 2008 (UTC)

Good, I think. That leaves us with the question of where to explain the differences between the two meanings. They are confused often enough (and the confusion can be difficult enough to dispel) that I think it falls within our encyclopedic mandate to set the difference straight explicitly. – Henning Makholm 02:55, 27 April 2008 (UTC)

Ok, I've hacked the article a bit, I'm not totally happy with it, but it's about 60% there. I think we need to prune back the reactive force more, and probably explain more about the reactive force in its own article.- ( User) WolfKeeper ( Talk) 03:02, 27 April 2008 (UTC)

Agreed, though I think we may have more than 40% to go yet. The previous consensus state of the article was not quite a model of brilliance and clarity in its explanation of the fictitious force, and we should be able to do better if we don't have to do it in the context of an (apparent!) controversy between two meanings of the word. In particular, I think the "Rotating reference frames" and "Fictitious forces" sections overlap each other without good reason; they should be combined into a single section which tells it all in a logical sequence.

As for references to the reactive force, I think there should be the hatnote, plus a more verbose discussion late in the article, probably including the table of differences. I suggest that the "confusion and misconception" section might be coopted for this, and possibly be given a more encyclopedic-sounding title along the way. – Henning Makholm 03:15, 27 April 2008 (UTC)

It would seem now that the article should be split into three.

(a) The ultra fictitious centrifugal force associated with the mathematical games surrounding the articial circle produced by a rotating frame of refeence.

(b) The 'inertial' centrifugal force which invokes Archimedes' principle in a centrifuge and causes real differential effects on the particles in a solution observable from all frames of reference.

(c) The knock on effect that a body being acted upon by (2) has on any object obstructing its path. David Tombe ( talk) 07:11, 25 April 2008 (UTC)

No. -- PeR ( talk) 07:48, 25 April 2008 (UTC)

Well PeR, since you have been so disagreeable up until now, I would hardly have expected any other response from you.

I will however take this matter to the wiki physics project.

The question will be put. Are these two effects the same thing?

(a) An object in the rest frame that is not co-rotating with a rotating frame appears to trace out a circle in the rotating frame. An example of this is the stars as they cross the sky at night time.

(b) When objects co-rotate with a rotating frame, a radial centrifugal force is induced which is real enough to invoke Archimedes' principle. An example is the centrifuge.

Are these two effects the same? David Tombe ( talk) 08:50, 25 April 2008 (UTC)

Just make sure you include a link to this page, so that people can catch up on what has already been said. -- PeR ( talk) 09:24, 25 April 2008 (UTC)

Electrodynamicist, while I appreciate you reverting to that concise introduction, my own belief now is that we should be dealing with the so-called consensus version on one point at a time.

The issue ultimately comes down to the fact that some of the editors here want to focus attention exclusively on the ultra fictitious centrifugal force which they create around stationary particles just by playing around with maths, and wrongly too. David Tombe ( talk) 14:48, 25 April 2008 (UTC)

Maybe we can write the article in such a way that everyone is happy. As I understand it, David Tombe is unhappy that the consensus version does not discuss in the intro, in a straightforward, plain English way, things like buckets swinging over heads. I think he may be right that such a "common sense" description is in order. However, the rest of us are not happy with phrases like outward radial force which acts on objects moving in a circular path, since such a force does not actually exist. Surely there is a wording that will satisfy everyone.

Working in that direction, I have a couple of questions for David Tombe:

1) When an elevator starts to move upward, you feel heavier. What do you call that "force"?

2) Do you acknowledge that what you call "ultra mathematical games" are, fundamentally, exactly the same centrifugal force you want the article to focus on, just expressed in a different language? Would you agree to an article that talked about water in a bucket and moved smoothly on to discuss that situation from the reference frame of the bucket, and so to fictitious forces? Rracecarr ( talk) 17:52, 25 April 2008 (UTC)

Rracecarr, regarding the man being accelerated upwards in an elevator, I don't have a special name for that force. The force acts against gravity and there is a resultant upward force. It's the same as any contact force. It causes acceleration.

On the maths, I am well versed in the equations for a rotating frame of reference. But I believe that these equations can be used to cloud the underlying realities of the situation.

When a man is stationary in an inertial frame, then there is nothing happening. It is irrelevant that somebody in a rotating frame views him as travelling in a circle.

But when a centrifuge causes particles to move outwards to the edge, we have a very real effect that has caused relative motion between different particles in the solution. We have invoked Archimedes' principle.

One should be able to see that these two situations are not the same, without having to go into any maths.

At least I know now that it is because of the maths that you think that the situations are the same.

Regarding that maths, one key point is that Wolfkeeper seems to think that the cross product expression for Coriolis force proves that the Coriolis force acts in any direction. He is overlooking the fact that the cross product was introduced to be in the tangential direction with the magnitude being the product of the angular speed and a radially aligned magnitude.

Another point is that in order for circular motion to occur, we need to have a net zero radial force. In the circular artifact scenario, the forces aren't balanced

And a third point is that when you study the derivation of those equations, you will see that the angular velocity is intricately linked to the linear velocity. There has to be a physical connection between the v term and the ω term. In your artificial circle example, the stationary object has got no physical connection with the motion.

So nothing happens. It is neither centrifugal force nor Coriolis force. It is merely a circular motion artifact.

But we shouldn't need to go into this maths to have to see that. It should be obvious from a common sense premises that centrifugal force only occurs on an object which is being constrained to move in a curved path.

On your second question, I would adopt the policy that all articles should began with a simple and basic introduction but maybe brightened up with one or two obscure points of interest.

As the article progresses, I would never object to more and more complicated and specialized aspects being introduced. The issue of rotating frames of reference could be introduced as a specialized section.

The current introduction could be re-worded by giving a basic description of centrifugal force as per the kind that is experienced in everyday situations. A clarification clause should be introduced to make sure that readers don't confuse it with centripetal force.

The swerving car example could then be given. Or indeed the artificially induced gravity scenario of a rotating cylinder. But I don't believe that the knock on effect needs to be emphasized as a separate centrifugal force. It is merely what weight is to gravity.

Finally, Wolfkeeper asked why is there never a similar dispute going on at the Coriolis force page? The reason is that the discussion surrounding where Coriolis force is real and where it is fictitious, and where it doesn't exist at all is to too complicated, too controversial and too likely to break wikipedia's rules agains original research and opinion. Furthermore, even at best, the man in the street is not familiar with what Coriolis force really means, and there is no easy way to explain it without involving alot of arguments. So its best to leave that article for the time being.

Centrifugal force has a clean cut off between what is actually centrifugal force and what has been confused for centrifugal force. That is because it is a radial effect. But Coriolis force is a tangential effect and so circular motion can create an artifact which gets confused with what genuinely is a fictitious Coriolis force. Then there is the controversy surrounding where Coriolis force becomes real. So we have three stages of analysis in Coriolis force. the Foucault pendulum at the poles is only an artifact. The missile flying through the air from Miami to New York is Coriolis force but purely fictitious. Finally the atmosphere involves a v that is physically connected with an entrained ω and so the effects can be real and viewable from outer space. The latter scenario corresponds by analogy to the reality of the centrifuge where the v and the ω are physically connected. David Tombe ( talk) 19:05, 25 April 2008 (UTC)

All I know is, coriolis and centrifugal force fall out of a completely valid mathematical manipulation of a general equation of motion with respect to an inertial reference frame, and in that sense at least, they are very, very real.- ( User) WolfKeeper ( Talk) 19:30, 25 April 2008 (UTC)

Let's stick with the elevator for a minute. The force experienced by the person in the elevator is fundamentally the same as the centrifugal force experience by particles in a centrifuge, right? Both are the result of acceleration--the only difference is that in the elevator it is linear acceleration, whereas in the centrifuge it is centripetal acceleration. Agree? Rracecarr ( talk) 20:20, 25 April 2008 (UTC)

Bucket swinging over head

I agree with David Tombe, that the introduction needs to be more accessible, and that swinging a bucket over one's head is a good example. Here's a draft text:

The term "Centrifugal force" has two different meanings. The classical meaning of the term, as used by Isaac Newton and others, is to denote the reaction force to a centripetal force. In modern usage the term can also be used to denote a fictitious force that occurs in a rotating reference frame.

An example of the classical use of the term is the statement.

When swinging a bucket over your head, the bucket pulls on your hand with a centrifugal force.

The hand exerts a centripetal force (action) on the bucket, and the bucket in turn exerts a centrifugal force (reaction) on the hand.

In contrast, an example of the modern usage would be:

When swinging a bucket of water over your head, the water stays in place due to the centrifugal force.

This sentence considers a reference frame that rotates with the bucket. (In an inertial reference the water could not be said to "stay in place", since it is moving in a circle along with the bucket.) The force referred to here is a fictitious, or pseudo force that is not caused by physical interaction, and therefore has no corresponding reaction force in the rotating frame. It is simply a mathematical construction that makes a it possible to describe the system as seen from the bucket's perspective.

I'll work it into the introduction once the edit war there has ceased.

-- PeR ( talk) 21:28, 25 April 2008 (UTC)

This looks good, PeR. How about removing the hand from the example:

The term "Centrifugal force" has two different meanings. The classical meaning of the term, as used by Isaac Newton and others, is to denote the reaction force to a centripetal force. In modern usage the term can also be used to denote a fictitious force that occurs in a rotating reference frame.

An example of the classical use of the term is the statement.

When swinging a bucket of water over your head, the water pushes on the bucket with a centrifugal force.

The bucket exerts a centripetal force (action) on the water, and the water in turn exerts a centrifugal force (reaction) on the bucket.

In contrast, an example of the modern usage would be:

When swinging a bucket of water over your head, the centrifugal force acting on the water causes it to stay in place.

This sentence considers a reference frame that rotates with the bucket. (In an inertial reference the water could not be said to "stay in place", since it is moving in a circle along with the bucket.) The force referred to here is a fictitious, or pseudo force that is not caused by physical interaction, and therefore has no corresponding reaction force in the rotating frame. It is simply a mathematical construction that makes a it possible to describe the system as seen from the bucket's perspective.

Rracecarr ( talk) 21:44, 25 April 2008 (UTC)

Better with the removed hand, but I like my version better for the second quote. (Shorter, less complex). -- PeR ( talk) 22:10, 25 April 2008 (UTC)

I thought it was important to emphasize a difference between the two quotes: in the first the force acts on the bucket, in the second, it acts on the water. Rracecarr ( talk) 22:22, 25 April 2008 (UTC)

Yep. On second thought, I like your version better for both quotes. -- PeR ( talk) 22:24, 25 April 2008 (UTC)

You guys need to actually read Newton's book since what you say here is wrong. From reading what is written here, I see what you dont know what you are doing and dont understand the arguments involved at all. Obviously this means the article does need major changes to correct the misconceptions of the editors who wrote the so called consensus version. I also suggest you actually educate yourselves before writing any more articles for wikipedia. 72.64.46.3 ( talk) 23:13, 25 April 2008 (UTC)

Maybe it is you, David Tombe, who needs education. That would seem the more likely possibility, since you are the only one who thinks the above is wrong. Rracecarr ( talk) 02:57, 26 April 2008 (UTC)

Rracecarr, I think we need to be quite clear about this. I am not the anonymous writing from 72.64.46.3 David Tombe ( talk) 07:16, 26 April 2008 (UTC)

Silly of me. Why would I assume that about 4 anon IPs, all in the Hampton, VA, USA area, doing your reverting for you and answering questions aimed at you, none of which has ever contributed to any other articles? Rracecarr ( talk) 16:04, 26 April 2008 (UTC)

Actually, I think the rude anon in Hampton, VA, might be someone else. (Possibly a friend of David's.) The recent edits by User:58.10.103.101, is from a different country, and David has signed contributions from that country in his own name before. -- PeR ( talk) 16:24, 26 April 2008 (UTC)

Yes, I knew 58.10.103.101 was David, but that does not mean the VA anon isn't. Still, I have struck the sarcastic comment, and I will keep my other suspicions to myself. Rracecarr ( talk) 16:31, 26 April 2008 (UTC)

Interesting to note that the VA anon is now prefixing a "Mr" to usernames. That is something that David Tombe used to do last year... -- PeR ( talk) 17:41, 1 May 2008 (UTC)

VA anon = User:Electrodynamicist, beyond a shadow. Rracecarr ( talk) 23:28, 2 May 2008 (UTC)

Rracecarr, the upward force that the elevator floor is applying to the person inside the elevator is definitely not the same kind of force as the centrifugal force which causes the heavier particles to move outwards in a centrifuge.

It is exactly, precisely the same kind of force. In the elevator, the acceleration producing the "force" is linear. In a centrifuge, it is centripetal. That is the only difference. If you had an elevator that would continue to accelerate hard for a long while, it would work just as well as a centrifuge for separating particles, and for just the same reason. If you can understand that, I think a lot of the problems we're having will go away. Rracecarr ( talk) 16:20, 26 April 2008 (UTC)

I looked at your new edits. I noticed that you emphasized the fact that the inward centripetal force is being caused by an object. That immediately tells me that you are leading towards a point, with that point being almost certainly related to the issue of action and reaction.

I think that one of the big mistakes that people are making here is in actually trying to decide which force is the action and which force is the reaction. We don't need to bother doing that. When an object moves in a circle, the outward centrifugal force and the inward centripetal force will always be balanced.

I actually agree with you here. There is technically no way of defining which is the action and which the reaction. The thing that is important to remember is that the centripetal force acts on the object moving in a circle, but the centrifugal force does not. It acts on the thing exerts the centripetal force on the object moving in a circle. Rracecarr ( talk) 16:20, 26 April 2008 (UTC)

You must also remember that the centripetal force does not have to be caused by an object. It could be caused by gravity, electrostatics, or indeed the Lorentz force.

On a macroscopic scale, it is ALWAYS caused by the forces you mention--gravitational or electromagnetic. The other kinds of force only act over microscopic distances. But gravitational and electromagnetic fields do not occur in isolation. They are the result of masses and charges. So yes, the centripetal force is always exerted by an object, and that object is always subject to a reactive centrifugal force. Rracecarr ( talk) 16:20, 26 April 2008 (UTC)

Therefore, always remember to make your point in the most general way.

The most general way of describing a centrifugal force is that it is an outward force which occurs when any object is constrained to move in a curved path.

On what does this force act? You need to be clear. Rracecarr ( talk) 16:20, 26 April 2008 (UTC)

I hope that you can now understand why we don't need to differentiate between a centrifugal force and a reactive centrifugal force, especially in the introduction. I tried to make that simple statement, I then added the fact that we shouldn't confuse it with centripetal force, and I finally stated that whereas in former times, centrifugal force was considered to be real, the modern day view is that it is fictitious. David Tombe ( talk) 06:52, 26 April 2008 (UTC)

Wolfkeeper, I know exactly the derivation that you are talking about. I am very familiar with it. But never lose track of the physical reality to which it applies. There are two key aspects of this maths which you are overlooking,

(1) The Coriolis term is specifically derived to be in the tangential direction. It is a tangential effect arising from a radial motion, whereas the centrifugal force is a radial effect arising from a tangential motion.

(2) The maths only has physical meaning when v and ω are physically connected. For centrifugal force this means co-rotation. For Coriolis force, this means that v has a physical connection with the source of the rotation, such as is the case with the hydrodynamics of cyclones, or with a Foucault pendulum at mid-latitudes.

In the case of there being no physical connection, such as with a missile or a bird flying over a children's roundabaout, then there will be a fictitious Coriolis force, but only acting on radial motion. The artificial effect which acts on tangential motion in the unconnected state is not even Coriolis force.

It's all very well coming up with this maths, and the maths is indeed correct. But never lose sight of the physical meaning of the maths. David Tombe ( talk) 07:03, 26 April 2008 (UTC)

PeR, Unlike with Coriolis force, centrifugal force is something that the public are more aware of. The swerving car will almost certainly be the first situatation in which a child will become subconsciously aware of it, whereas the bucket of water being swung over the head will be the first situation that will draw attention to it. The centrifuge as an engineering tool will follow on at high.

So either the bucket of water or the swerving car make good examples in the introduction. But we must first state the general description of the centrifugal force.

Take note of what I said above to Wolfkeeper. Neither centrifugal force nor Coriolis force are the artificial tangential effects which are viewed from a rotating frame of reference. You clouded your point up when you started introducing this dimension.

You began good and gave an example of centrifugal force showing that the water in the bucket was defying gravity. Then you contradicted yourself by trying to argue that in the rotating frame there was no such force. Of course there is. David Tombe ( talk) 07:14, 26 April 2008 (UTC)

PeR, I just looked at your last paragraph again. You are very badly confused. You are equating the water in the swinging bucket with the ultra fictitious artificial circle produced when a stationary object is viewed from a rotating frame of reference. The latter inolves no forces at all. In the water in the bucket, centrifugal force causes pressure.

People can be hurt by centrifugal force, but nobody has ever been hurt as a direct result of being viewed from a rotating frame of reference. David Tombe ( talk) 07:23, 26 April 2008 (UTC)

FyzixFighter, You have endorsed Rracecarr's latest edits. Let's look at it,

"A mass undergoing circular motion constantly accelerates toward the center of the circle. This centripetal acceleration is caused by a centripetal force, which is applied to the mass by some other object. In accordance with Newton's Third Law of Motion, the mass exerts an equal and opposite force on the object. This is the real or "reactive" centrifugal force: it is directed away from the center of rotation, and is exerted by the rotating mass on the object which imposes the centripetal acceleration. Although this sense was used by Isaac Newton,[1] it is only occasionally used in modern discussions.[2][3][4][5]"

Would you agree that centripetal force can by cuased other than by contact action from an object? For example gravity, electrostatics, or the Lorentz force.

Would you agree that this passage could be simply stated as,

"When an object moves in circular motion, the centripetal force and the centrifugal force are balanced" ?

Why not actually think about the issues before joining up with a team for an edit war? Let's see you here in the debate. David Tombe ( talk) 07:37, 26 April 2008 (UTC)

I just woke up and wow... I don't want to derail the already existing conversation so I'll just answer up here. No, I would not say that the centripetal force and centrifugal force are balanced because in order for two forces to "balance", they must be acting on the same object. The two forces in this case are not acting on the same object so saying they are balanced makes no sense. They are equal and opposite, but that does not mean they are balanced. We do not say that the force of the earth on the apple is balanced by the force of the apple on the earth as the earth falls. Now frankly, it's not up to us to explain classical mechanics to you. You cry foul when we don't have a reference, yet you have never provided a reliable source that says there are three types of "centrifugal force" - you invoke common sense, but in my experience common sense is not a reliable source. By the way, here's a few references for the two types of centrifugal force - "A Dictionary of Physics", pg 57, Oxford ; New York : Oxford University Press, 1996 and "McGraw-Hill Dictionary of Physics", pg 77, New York : McGraw-Hill, 1984. -- FyzixFighter ( talk) 16:29, 26 April 2008 (UTC)

You say that an object moves in a circle when forces are balanced. I think I read somewhere that it would move in a straight line. Is that a statement you found in a book, or one that you made up yourself? -- PeR ( talk) 07:39, 26 April 2008 (UTC)

No PeR. I said that when something moves in a circle, the radial forces are balanced. You completely twisted what I said because you are now realizing that you have been totally wrong all along. David Tombe ( talk) 07:42, 26 April 2008 (UTC)

No, I honestly don't understand what you mean. In your mind, what forces are acting upon the object that moves in a circle? Could you list them all, and say what they sum up to? -- PeR ( talk) 07:52, 26 April 2008 (UTC)

PeR, when an object is moving in a circle, there is a centripetal force acting inwards radially and a centrifugal force acting outwards radially. The inward centripetal force could be supplied by anything from tension in a string, to pressure from the floor of a rotating cylinder, or to gravity, electrostatics, or the Lorentz force.

At any rate, if the motion is circular, the centrifugal force exactly cancels with the centripetal force because there is zero radial acceleration.

If however the two forces are not balanced, the resulting motion will be more complicated. The most well known case is in planetary orbits. In a Keplerian ellipse, parabola or hyperbola, the outward centrifugal force does not balance with the inward gravitational force. David Tombe ( talk) 09:45, 26 April 2008 (UTC)

(Let's just talk about circular motion for the time being.) You say there is "zero radial acceleration". Do you mean that the circular motion is due to acceleration in some other direction? (If so: Which direction? What causes that acceleration?) Or are you saying that an object can deviate from a straight line without acceleration? -- PeR ( talk) 10:45, 26 April 2008 (UTC)

PeR, We have not addressed the issue of how the object came to be moving in circular motion. We are merely focusing on the fact that when an object is already moving in circular motion that there can be no net radial acceleration, otherwise it wouldn't be circular motion. Hence the centrifugal force and the centripetal forces will be balanced.

You will never understand this issue if you continue to focus your attention on the special case of circular motion. I suggest that you study the general case of motion that results when an inward radial gravity force acts in tandem with an outward radial centrifugal force.

There are many possible results in terms of size, direction etc. all dependent on the initial conditions. But all solutions will come down to either an ellipse, a parabola, or a hyperbola, The circle is just a special case.

And so yes, it is possible to have an obect moving in a curved path with no net acceleration if that curved path forms part of a circle. David Tombe ( talk) 11:20, 26 April 2008 (UTC)

You say:

...it is possible to have an obect moving in a curved path with no net acceleration if that curved path forms part of a circle.

Now, most textbooks define acceleration as "rate of change in velocity". Do you use a different definition? Or do you propose that an object moving in a circle never changes its velocity? -- PeR ( talk) 12:06, 26 April 2008 (UTC)

Again I say you need to learn some physics. The velocity does not change only the direction changes. Your understanding is limited. You need to recuse yourself from editing, along with the rest of the fools here, because you obviously dont know physics. 71.251.185.86 ( talk) 13:29, 26 April 2008 (UTC)

PeR, A centripetal force alone cannot cause a circular motion. It can do so only in conjunction with a centrifugal force. The two of them act together in tandem and maintain the object in the tangential direction while maintaining the tangential speed. The net radial acceleration is zero.

Consider a weight being swung around in a circle on the end of the string. The tension which supplies the inward centripetal force only comes into existence as a reaction to the outward centrifugal force.

That is in total contrast to all the assertions that had been made on the main page falsely saying that centrifugal force is a reaction to a centripetal force. In the case of the weight on the end of the string, it is the other way around. David Tombe ( talk) 13:50, 26 April 2008 (UTC)

David, I'd really like to hear your answer to my question above. Feel free to answer here, or on your talk page. -- PeR ( talk) 14:41, 26 April 2008 (UTC)

PeR, I go along with the official definition of acceleration. Now using the very same maths that you use to promote your theories about the rotating frame of reference, we consider a position vector in the radial direction. Differentiate it. It is a product because it involves the unit vector which has to be dealt with separately to account for direction change.

The final result is an expression for acceleration in the radial direction and acceleration in the tangential direction. The tangential direction contains the Coriolis force but we are not interested in that right now.

When the centrifugal force, which is always radially outwards, is balanced by another inward radial force, then we will have zero radial acceleration and hence circular motion.

If there is no tangential acceleration and hence no angular acceleration, then we will have a net zero acceleration for an object moving in a circle. David Tombe ( talk) 14:49, 26 April 2008 (UTC)

You say we have zero net acceleration, so by the textbook definition, zero change in velocity. Velocity includes direction of movement, so you are saying that an object can move in a circle without changing its direction of movement? Or do you use a different definition of velocity? -- PeR ( talk) 15:28, 26 April 2008 (UTC)

Look at the old talk archive -- it appears that David still insists on taking unadjusted coordinate accelerations in a polar coordinate system. That's how he thinks uniform circular movement has no net acceleration. – Henning Makholm 01:08, 27 April 2008 (UTC)

If I can also jump in, David take that same analysis that you just put above to looking at what kind of acceleration is required for circular motion. But let's not start out at the position vector, let's go right to the velocity vector. The velocity vector in constant circular motion is v*theta_hat, where v is a constant. Differentiating this with respect to time gives 0*omega_hat+v*d(omega_hat)/dt. Now when you go through the math for the unit vectors, you will find that d(omega_hat)/dt is -d(omega)/dt*r_hat (honestly this is a lot easier to see when done in cartesian unit vectors, and will yield the same results - most calculus-based, freshman physics textbooks go this route). So even though the motion is circular, the acceleration is radial. I'm guessing though that you're going to disagree with me on the d(omega_hat)/dt = -d(omega)/dt*r_hat bit. -- FyzixFighter ( talk) 16:52, 26 April 2008 (UTC)

FyzixFigher, Sorry for the late reply. Yes, in the Cartesian frame there will be inward radial acceleration in circular motion in conjunction with inertia, which is essentially outward centrifugal force under another name. David Tombe ( talk) 15:22, 28 April 2008 (UTC)

Whether you use cartesian unit vectors (x_hat and y_hat) or cylinderical unit vectors (r_hat, theta_hat), the net acceleration in the inertial frame of reference is always radially inward. It is only when you go to a non-inertial frame that fictitious forces, such as the Coriolis and centrifugal force, appear for F_net=m*a to be true for those rotating coordinates. Inertia is not a force - if this is the crux of your argument (as it would appear to me), then provide a reliable source that says as much. The same applies for everything else, provide a reliable source that describes the centrifugal force as a real, physical, non-fictitious source or your edits will continue to be reverted. The talk page is not here to debate whose view of physics is correct, nor to try to teach correct physics. -- FyzixFighter ( talk) 15:40, 28 April 2008 (UTC)

You wish to look at the picture from an inertial Cartesian reference frame thinking that the centrifugal force will disappear.

In an inertial Cartesian reference frame, a particle in circular motion will indeed have an acceleration. The direction of the particle's velocity is constantly changing. It will have an acceleration always pointing in towards the centre of the circle.

That inward acceleration will be in the radial direction in relation to the circle itself. The outward centrifugal force will still be there too in the radial direction. It doesn't go away. Both of these forces exist in the radial direction.

The reality of the centrifugal force as an absolute fact can be proved because the effects of a centrifuge are observed by both somebody riding on the centrifuge and by a person sitting in the corner of the room.

From the tangential/radial perspective, there is no acceleration. The centripetal and centrifugal forces exactly cancel.

From the inertial Cartesian perspective, these same two forces work in tandem to cause the acceleration that changes the direction of the particle, but not its speed.

There is no question of having the centripetal force acting alone. In some cases, such as the weight being spun on the end of a string, the centripetal force is only activated by the centrifugal force.

If the string were to be replaced by a spring, we could have an elliptical motion in which the two forces alternate their magnitudes.

You cannot make the very real centrifugal force vanish simply by viewing the picture from the laboratory frame. David Tombe ( talk) 05:37, 27 April 2008 (UTC)

Rracecarr, regarding the elevator, the correct analogy that you are looking for is,

(i) Centrifugal force is to gravity,

whereas,

(ii) Centripetal force is to 'Normal Reaction'.

You will have to learn to generalize your approach and not confine the study to circular motion, and contact forces in which the centrifugal force is causing a pressure. David Tombe ( talk) 05:43, 27 April 2008 (UTC)

This split has been motivated as a knee-jerk reaction to save face on realizing that the so called consensus version contained many errors. It has effectively moved the one and only centrifugal force off to a new page.

The remaining page deals with a pure artifact that arises from a misinterpretaion of mathematics, and it describes neither centrifugal force nor Coriolis force.

The real centrifugal force has now been labelled as 'Reactive centrifugal force' in a separate article, when in fact there are many scenarios when it is clearly not a reaction.

Take planetary orbital theory as an example. The centrifugal force is not acting as a reaction to gravity. It acts in tandem with gravity to yield elliptical orbits.

An object being swung around on the end of a string induces the tension in the string to provide the centripetal force. Clearly in this scenario, the centrifugal force is the pro-active force.

The situation is now a worse mess than ever. David Tombe ( talk) 06:10, 27 April 2008 (UTC)

David, in our previous discussion, you started with the hypothesis

When an object moves in circular motion, the centripetal force and the centrifugal force are balanced

and that lead you to the conclusion

...it is possible to have an object moving in a curved path with no net acceleration if that curved path forms part of a circle.

Now you are saying

In an inertial Cartesian reference frame, a particle in circular motion will indeed have an acceleration. The direction of the particle's velocity is constantly changing. It will have an acceleration always pointing in towards the centre of the circle

which means that your previous conclusion was false. My question to you is then: Was your initial hypothesis also false? Or was there an error in one of the steps from the hypothesis to the conclusion? In that case: Which step?

-- PeR ( talk) 06:34, 27 April 2008 (UTC)

PeR, using radial and tangential coordinates, there is no net acceleration in circular motion. Using Cartesian coordinates there is.

But the underlying reality that you are denying is that in either case, the motion in question is the result of a centripetal force acting in tandem with a centrifugal force.

You are desperately trying to make centrifugal force go away. Your colleagues have now even moved it to a separate page.

You need to study planetary orbital theory. Two forces combine together to yield an ellipse, a parabola, or a hyperbola. The circle is a special case of the ellipse. You cannot make the centrifugal force go away by focusing attention on circular motion in a Cartesian reference frame. David Tombe ( talk) 08:07, 27 April 2008 (UTC)

You didn't answer my question. -- PeR ( talk) 08:16, 27 April 2008 (UTC)

PeR, your question was based on the supposition that my previous assertion had been false. My previous assertion that it is possible to have circular motion with no acceleration is a correct assertion. It occurs when we view circular motion in terms of radial and tangential coordinates.

Changing to different coordinate systems can change accelerations. But it can never change the reality of absolute effects such as Archimedes' principle occuring in a centrifuge. David Tombe ( talk) 08:47, 27 April 2008 (UTC)

I'm still not sure what you mean. Are you saying that your previous statement

the centripetal force and the centrifugal force are balanced

only is true when viewed in "radial and tangential coordinates", but not in stationary Cartesian coordinates?

-- PeR ( talk) 09:00, 27 April 2008 (UTC)

PeR, in Cartesian coordinates, in the special case of circular motion, the combined effect of the centrifugal force and the centripetal force is to cause that circular motion. The combination changes the direction of the object without effecting its radial speed. It's up to you whether or not you want to call that 'balanced'. But at the end of the day, it has got no bearing on the main issue. Centrifugal force has to be present in circular motion. You are trying to argue to the contrary. You are trying to tell me that we can have circular motion with a centripetal force alone.

Consider the special case of a circular gravity orbit as viewed from a Cartesian frame. If the centrifugal force ceased, then the gravity force that had been acting as the centripetal force would bring the object straight to the center. A circular motion cannot contain only a centripetal force. It has to have both a centripetal force and a centrifugal force. David Tombe ( talk) 09:16, 27 April 2008 (UTC)

According to the article on force, there are only 4 types of fundamental forces. In the example you just provided, the centripetal force is gravitational. Which type is the centrifugal force? Rracecarr ( talk) 15:42, 27 April 2008 (UTC)

By "balanced" it thought you meant "the sum of the centrifugal force and the centripetal force is zero". If that is not what you meant, then please clarify. What, according to you, is the sum of the forces acting on an object that moves in a circle in a stationary Cartesian coordinate system? -- PeR ( talk) 09:27, 27 April 2008 (UTC)

PeR, for the purposes of this discussion, the only thing that matters is that the two forces are balanced in radial and tangential coordinates. Your entire argument about the artificial circle is explained in radial and tangential coordinates, and in that case, the two forces are definitely not balanced.

We are not going to cloud the issue by discussing it all in Cartesian coordinates. Have you ever seen the expression for centripetal force written in Cartesian coordinates? —Preceding unsigned comment added by David Tombe ( talk • contribs) 07:42, 28 April 2008 (UTC)

Of course I have seen an expression for the centripetal force in Cartesian coordinates. You can find one in almost any physics textbook. So now you are saying that your statement

the centripetal force and the centrifugal force are balanced

only is true when viewed in "radial and tangential coordinates", but not in stationary Cartesian coordinates?

Or do you prefer to say that you don't understand what's going on in Cartesian coordinates, and we keep the discussion in "radial and tangential coordinates"?

-- PeR ( talk) 09:17, 28 April 2008 (UTC)

fx = -cos(wt) m r w^2, fy = -sin(wt) m r w^2; trivially obtained by differentiating twice with respect to time: x=r cos(wt) + cx, y=r sin(wt) + cy, where r = radius, w is the angular speed of the mass about its center, t is the time, (cx,cy) is the rotation center. I didn't even need to look it up.- ( User) WolfKeeper ( Talk) 09:27, 28 April 2008 (UTC)

Yes Wolfkeeper, I didn't even need to look it up either. I was only asking had you ever actually seen it been used. PeR is trying to cloud this issue by introducing Cartesian coordinates which are seldom used in this topic. A coordinate system cannot chnage the reality of a situation. The centrifuge works whether you describe it Cartesianly or polarly. It works whether you call it inertia or centrifugal force. But one thing is sure. Centrifugal force only arises when we have real rotation of the object in question. David Tombe ( talk) 10:37, 28 April 2008 (UTC)

So, David, now that you have seen an expression for the centripetal force in Cartesian coordinates, will you finally answer my question: What, according to you, is the sum of all forces acting on an object that moves in a circle in a stationary Cartesian coordinate system? -- PeR ( talk) 13:15, 28 April 2008 (UTC)

PeR, in the Cartesian inertial frame, an object describing a circle experiences centripetal force and inertia. Inertia is another word for centrifugal force. David Tombe ( talk) 14:01, 28 April 2008 (UTC)

That wasn't an answer to my question. -- PeR ( talk) 15:09, 28 April 2008 (UTC)

PeR, the sum of all forces in a circular motion in the Cartesian frame is a change in direction without a change in speed. There was absolutely no point to your question. It was just an attempt at verbal witchcraft to deflect the issue from the reality of centrifugal force. David Tombe ( talk) 15:26, 28 April 2008 (UTC)

What I meant by the word "sum" is the mathematical vector sum of the two forces that you mention. The vector sum of two forces will be another force that can be measured in Newtons. The change in velocity that you give as an answer would be measured in meters per second.

Perhaps it would be clearer if we put numbers on everything:

Consider an object, with the mass of one kilogram, that is swung on a rope in a gravity-free and frictionless environment, so that it moves in a circle with a radius of one meter, with an angular velocity of one radian per second, as seen from an inertial (stationary, non-rotating) reference frame. What are the centripetal/centrifugal/other forces (magnitude and direction) acting on that object as seen from that reference frame? What is their vector sum? What is the acceleration of the object?

Rest assured that there is no "witchcraft" going on here. I simply want to pinpoint exactly where our views differ. I'll give you my answer to the questions first:

Answer according to User:PeR

* Centripetal force acting on the object = 1 N, directed towards the center of rotation. (This force is provided by the rope.)

* Centrifugal force acting on the object = 0. (There is no centrifugal force acting on the object.)

* Other forces acting on the object = 0. (There are no other forces in this example.)

* Vector sum of the above forces = 1 N, directed towards the center of rotation.

* Acceleration of the object = 1 m/s^2, directed towards the center of rotation. (Because F = ma).

Now, just so there's no misunderstanding, I'd like you to replace the question-marks in the table below with magnitude/direction pairs.

Answer according to User:David Tombe

* Centripetal force on the object = -1 N

* Centrifugal force on the object = 0

* Other forces acting on the object = 0

* Vector sum of the above forces = 1 N

* Acceleration of the object = 1 m/s^2, directed towards the center of rotation.

Note that my answer will be the same regardless of whether Cartesian coordinates or polar coordinates are used. If your answer will be different depending on coordinate system, then please make one copy of the answer table for each coordinate system.

I've tried to make the example as simple as it could be while still highlighting our different views. Your input will be appreciated.

-- PeR ( talk) 09:12, 1 May 2008 (UTC)

PeR, My answers are inserted above. There will be no net acceleration as viewed in tangential/polar coordinates, but in the inertial frame, there will be exactly as you say, an acceleration of 1m/s^2 directed into the centre of the circle.

But we don't actually need to be arguing about this. Let's just say for the sake of argument that a stationary object as viewed from a rotating reference frame traces out a circle and that you are correct that fictitious forces combine to create a fictitious centripetal force. I don't actually agree with that at all, but let's accept it anyway for the sake of argument.

I have accepted that applied maths courses teach the doctrine that those rotating reference frame equations apply to all particles, irrespective of co-rotation. I did the course myself many years ago.

I decided to compromise and accept the wording of the first sentence in the existing introduction which sates the above fact. Personally, I see no need to cloud the issue with rotating frames, but I have decided to accept that line since it is in the modern maths books.

I then decided to draw attention to the fact that when co-rotation does actually occur, that we will get an actual radial acceleration or an actual hydrostatic pressure. That is the centrifugal force that the man in the street is looking for.

But Wolfkeeper instantly reverted it on the false premises that I was suggesting that centrifugal force only occurs in co-rotation.

When his error was pointed out, he dug in and stuck to his position.

He is now trying to deny hydrostatic pressure in a rotating bucket.

That is what the argument is about now.

I have offered up a perfectly good compromise introduction that covers all the key points accurately, but Wolfkeeper is behaving totally irrationally.

So I have a question for you. Is the hydrostatic pressure in a rotating bucket an absolute reality, or is it only something which we view from a particular frame of reference?

Also, do have a look at my new introduction because I'd be interested to hear exactly what aspects of it you disapprove of. It would have neatly tidied up the whole reactive centrifugal force thing. David Tombe ( talk) 09:37, 1 May 2008 (UTC)

I'm still confused. The question was regarding an intertial frame, and you filled in "Acceleration of the object = 0". But then you immediately state: "in the inertial frame, there will be exactly as you say, an acceleration of 1m/s^2 directed into the centre of the circle." Which is it?

-- PeR ( talk) 09:50, 1 May 2008 (UTC)

Regarding your new introduction: I have read it. It is getting better compared to your initial attempts, but it still misses a few key points, for example you keep removing the link to fictitious force, which is a term that is vital to the subject. I think you'd be much more productive if you worked on it here on the talk page. In article space, it'll just keep getting reverted because of the inaccuracies.

By the way, the title of this section, reductio ad absurdum, essentially means if your initial hypothesis leads you to state that "one equals zero", then your initial hypothesis was false.

-- PeR ( talk) 10:12, 1 May 2008 (UTC)

PeR, I realize now that it was the inertial frame that your box was for. Sorry, I answered as if it was for radial/tangential. I will correct it now. My answers for 'inertial frame' are the same as yours.

On the other issue, you mentioned inaccuracies. Can you please point out those inaccuracies. I don't actually believe that you are genuine. You have given yourself away by having stated that the term 'fictitious' is essential. Why should the term fictitious be so essential for the situations concerning actual radial acceleration and hydrostatic pressure?

I think you are in the same boat as Wolfkeeper. You are living in a fictitious world of denial. You will do anything to make sure that there is nothing in the introduction to this article that might lead anybody to suspect that centrifugal force might be real.

You are in a conspiracy with Henning Makholm, FyzixFighter, and Wolfkeeper to impose a false view of reality through the wikipedia pages.

There are no inaccurate facts in my new introduction, and for you to say so is a downright lie. The truth is that you are offended by references to the co-rotation scenario where actual hydrostatic pressure is induced. That is a real absolute effect. It is frame independent, and it doesn't fit in nicely with you fictitious view of the world where everything is relative and there are no absolutes.

So you are trying to suppress this fact. That's what it all comes down to. You are platooning in superior numbers with a group who know alot more about how to manipulate the wikipedia rules and regaulations than they know about physics.

All this rubbish above about 'what is the acceleration in the inertial frame' is an irrelevant decoy to enable you to obfuscate the whole issue. David Tombe ( talk) 10:29, 1 May 2008 (UTC)

So now you do agree that there is no centrifugal force when using an inertial frame of reference. That is very good. We are half-way to agreement. Now, when you say "radial/tangential", do you mean a set of coordinate axes that rotates so that the radial coordinate axis always points to the object? Is it OK by you if we refer to that as a "rotating coordinate system"? If we were to color-code the forces, so that forces that are the same in any reference frame are called "blue" forces, and forces that are zero in an inertial frame, but exist in a rotating frame are called "red" forces, would you then agree with the statement: the force from the rope is a "blue" force, and the centrifugal force is a "red" force? -- PeR ( talk)

P.S. Please stop writing insults to your fellow editors. We might think you're trolling. -- PeR ( talk)

PeR, I hope we're going to get to the point of this soon. My ultimate argument will be that centrifugal force is absolute and doesn't depend on frame of reference. It is an outward radial effect. It doesn't matter how we view it.

What you are doing is trying to fudge the issue by looking at it in Cartesian coordinates. In Cartesian coordinates, centrifugal force becomes inertia. Now I know that you will immediately say that inertia is not a force. But that then drags us into a conversation on original research and we don't need to go down that road.

In the Cartesian frame, which incidentally I don't believe exists in real life, centrifugal force in the presence of a negligible central force of attraction such as gravity, will result in a highly eccentric hyperbolic motion. This approximates to the straight line.

We call straight line motion inertia. It is the tendency to move in a straight line at constant speed unless some other force acts.

Hence if we analyze circular motion in a Cartesian frame the centripetal force will act in addition to inertia(centrifugal force) and cause a radially inward acceleration which changes the dircetion but not the speed of the particle. Basically the centripetal force causes the particle to deviate from its straight line path, as per inertia.

But we are way behind now with the main argument. First can you tell me where the 'point of view' material is in my proposed introduction. I guarantee that you can't do that. It is a false inuendo. you are basically referring to the clauses that illustrate true facts that are not convenient for the term 'fictitious force'.

On your specific question, both those forces are radial so they both have to be the same colour. I say that they are both blue. They both always exist at any time in the radial direction. Even in the Cartesian frame, they both exist in the radial dircetion. David Tombe ( talk) 13:19, 1 May 2008 (UTC)

Previously you said:

I answered as if it was for radial/tangential. I will correct it now. My answers for 'inertial frame' are the same as yours.

and changed the "centrfiugal force" from one Newton to zero.

Now, if it is true that "centrifugal force is absolute and doesn't depend on frame of reference" then why did you change your answer?

Also, if the centrifugal force doesn't depend on frame of reference, then what is it, one Newton or zero? (The answer you have filled in now, above, is zero. To me that's the same thing as saying it doesn't exist in that frame of reference.)

-- PeR ( talk) 13:56, 1 May 2008 (UTC)

PeR, Can you get to the point please. In radial coordinates the centrifugal force and the centripetal force balance in circular motion. That's all we need to know. In Cartesian coordinates, the physics doesn't change but the way we describe it all changes. In Cartesian coordinates, there is no radial direction. It doesn't actually matter about Cartesian coordinates. The reason why you keep concentrating on Cartesian coordinates is because you know it is more complicated and you can see an opportunity to cloud the whole issue.

Basically you are hoping to be able to conclude that in Cartesian coordinates in circular motion, we have centripetal force only and no centrifugal force. You are then going to go to your artificial circle scenario and try and reason that we could therefore have centripetal force only in that case too. But you can't do that. There was inertia in the Cartesian scenario for the real circular motion. In your artificial circular motion there is no inertia, and anyway, in radial coordinates the forces in your artificial scenario are not balanced.

Your theory is wrong. It is wrong because the equations only apply to co-rotation, and to radial velocity for Coriolis purposes, and when misapplied as in the artificial circle scenario, the forces don't even balance.

I am not going to look any more at Cartesian coordinates simply for you to confuse the issue and make false conclusions because that's exactly what you are trying to do.

And you don't need to look at the maths at all to know that your theory is wrong. The fact that hydrostatic pressure can be generated in a rotating bucket is sufficient to show that a real effect occurs in co-rotation which does not occur when something stationary is viewed from a rortating frame. David Tombe ( talk) 15:08, 1 May 2008 (UTC)

Rracecarr, in the centrifuge, heavier particles actually move past lighter particles. This is a real effect which is observed from every frame of reference. For this effect to occur, a force must be acting and it cannot be centripetal force because the particles have not yet contacted the reaction surface, notwithstanding the fact that centripetal force is in the wrong direction anyway.

The fictitious circle that you are emphasizing is not the same situation at all. It is merely an artifact.

The maths which you believe unites the two situations is only applicable when the v and the ω are physically connected. That follows from the derivation. And if you study the derivation, you will see that when the velocity formula is expanded into the acceleration formula, the v in the v times ω term gets replaced with another v which is only radial.

In other words, that maths does not apply to the artificial circle. You have unanchored the maths from the physical reality to which it applies. David Tombe ( talk) 06:20, 28 April 2008 (UTC)

Since you didn't answer me above, I copy and paste:

[David Tombe said] Consider the special case of a circular gravity orbit as viewed from a Cartesian frame. If the centrifugal force ceased, then the gravity force that had been acting as the centripetal force would bring the object straight to the center. A circular motion cannot contain only a centripetal force. It has to have both a centripetal force and a centrifugal force. David Tombe ( talk) 09:16, 27 April 2008 (UTC)

[I said] According to the article on force, there are only 4 types of fundamental forces. In the example you just provided, the centripetal force is gravitational. Which type is the centrifugal force? Rracecarr ( talk) 13:43, 28 April 2008 (UTC)

RRacecarr, centrifugal force is real whether it is listed in that list of four fundamental forces or not. We are not going to deny the reality of what goes on in a centrifuge because the force in question is not listed on somebody's list of four fundamental forces.

Might you by any chance consider an elliptical orbit as viewed from a cartesian inertial frame. At some stage of the orbit, the gravitational centripetal force is pulling the object closer to the origin. Then there comes a point when the object starts to move radially outwards. Is the force that makes that object move radially outwards on the list of four fundamental forces as per the reference above? David Tombe ( talk) 13:58, 28 April 2008 (UTC)

Allow me to insert a few comments here about this entire debate from the viewpoint of Physics as it is used today.

First, viewing things in the cartesian coordinates or radial/tangential components makes no difference - both will have no force acting outward on the mass at the end of a spring (for example). In both frames of reference the centripetal force is supplied by the tension in the string, and the tension is due to the inertia (which is not a force - it is the resistance a body has to change in motion). The more mass the object has, the greater its resistance to a change in motion and the more force will have to be applied toward the center to change that motion.

Viewing the object from a rotating frame of reference will make it appear that there is an outward force acting on the object. This is because the frame of reference itself is accelerating. Accelerations only appear and disappear under coordinate transformations if you are transforming between inertial and non-inertial reference frames. Generally in physics we avoid using non-inertial reference frames for normal motion, like a mass swung at the end of a string or a planet in orbit around a star.

The centrifuge problem is not mysterious. Heavier particles have greater inertia and therefore require a greater force to follow a curved path. The force exerted on lighter particles by the material around it is enough to cause it to follow a curved path. The force exerted by surrounding medium is not great enough to cause the heavier particles to follow a curved path, so they push their way through the medium until the encounter the end of the tube. In either case, the net force acting on the particles is directed inward. Some choose to view this from an accelerating (rotating) frame of reference in which they observe an outward force - and this viewpoint can be useful - but don't confuse the appearance of a force in this frame as a true force, the force arises from the fact that the frame of reference is accelerating.

Which leads me to my last comment - according to how centripetal force is presently taught - it is the net force acting in the radial direction. It is the sum of both inward and outward forces that might be acting on the particle and it is directed inward. For example, if I am sitting in a seat of a car with someone seated next to me, and the car quickly goes through a curve such that I am pushed up against the door of the car, and the other person is pushed up against me, there are two radial forces acting on me. The normal force from the car door is acting toward the center, the contact force between me and the other person is directed out of the circle. The sum of those two forces is the centripetal force. It is just a restatement of Newton's 2nd Law - which in this case the acceleration is centripetal acceleration.

Hope this helps clear things up. PhySusie ( talk) 14:45, 28 April 2008 (UTC)

Susie, Thanks for your comments. There are a number of points that you have raised that I would like to go over. You say that in circular motion, there is no outward force even in radial/tangential coordinates?

I would say that there is no net force in the radial direction due to the fact that the centripetal and centrifugal forces cancel out.

In the centrifuge, you say that the net force is inward? Not while the heavy particles are accelerating radially outwards towards the edge.

If heavy particles push past the lighter particles, then we have an effect which is observable from all reference frames. In fact we have a distinct force acting radially outwards.

How can you equate this to the situation in which a stationary object is observed to move in a circle by somebody in a rotating frame of reference? In the latter scenario, there are absolutely no forces acting at all.

Finally, you say that in the Cartesian system, that the centrifugal force does not exist. Inertia is centrifugal force. Centrifugal force acting alone causes straight line motion. If we have a circular motion as viewed in the Cartesian frame, then we have a radially inward centripetal force acting in tandem with inertia.

I do however agree with your assertion that it doesn't matter which kind of coordinate system we use. centrifugal force is either real or it is not real. We therefore may as well use the radial/tangential system for analysis as this is the most convenient.

Anyway, thank you for your comments. David Tombe ( talk) 15:05, 28 April 2008 (UTC)

Hi David! It seems like you've retained an intuitive understanding of the term "force" which everyone starts out with, but which is not the same as the physics definition, and which generations of physics teachers have struggled to iron out of people's heads. For example, inertia is not a "force", in the sense that physicists use the term. For example, when a plane travels through the air at constant velocity, Newton's second law says that the net force on it is zero. Have you tried reading about centripetal and centrifugal forces in an intro physics textbook? (Any readable textbook will do.) I think that might help you better understand where PeR, PhySusie, and others are coming from.

Here's an example of your intuitive understanding coming into conflict with the physicists' one. If "there is no net force in the radial direction", then Newton's second law demands that there is no net acceleration in the radial direction (acceleration in the mathematical, not colloquial, sense). And circular motion is impossible without acceleration in the radial direction. See the article uniform circular motion for the relevent formula, for example. :-) -- Steve ( talk) 17:37, 28 April 2008 (UTC)

Steve, it all comes down to a single question. Are these two situations the same?

(a)An object that is stationary in the inertial frame is seen to move in a circle from a rotating frame. This effect is entirely an artifact.

(b)An object which moves in a circle experiences an outward radial acceleration. The centrifuge is an example of this, and it is a real effect because heavy particles actually partake in relative motion to the lighter particles. As such, there is a real effect which can be observed from all reference frames.

At the moment, the fictitious force page deals with a set of equations which are believed to unite these two effects into one. However, if you look at the derivation of these equations, you will see that the ω for the rotating frame is actually the tangential component of the particle velocity. In other words, the particle velocity is routed through ω.

This physical connection only occurs in scenario (b). In other words, those equations only work when an object is co-rotating.

As it stands now, sceanrio (b) has been removed to another page and explained very badly. It has been explained purely within the context of circular motion in which the centripetal force is being supplied by contact pressure. It ignores elliptical motion and cases that might be caused by tension as in a string, or gravity, electrostatics or electromagnetism.

And the centrifugal force does not alwaays react to the centripetal force. In the case of a tense string, the centripetal force is reacting to the centrifugal force.

I believe that the two articles should be joined together again and that centrifugal force should be introduced as case (b). David Tombe ( talk) 07:45, 29 April 2008 (UTC)

David, I know you're interested in arguing whether (a) and (b) are or aren't the same, and are or aren't illusory, but you're destroying your credibility by not using the terms "force" and "acceleration" to mean what they mean in physics. For example, every physics textbook explains why an object which moves in a circle must experience an inward radial acceleration, just the opposite of what you said. It would be worth your while to invest the thirty minutes to read an intro physics textbook on this, so that you can understand what other people are saying and vice-versa. Once you understand what other people mean by "force" and "acceleration", and understand the textbook derivation of centrifugal and coriolis force, and also read up on uniform circular motion, then you'll be in a great position to discuss what is or isn't an illusion or whatever else, without everyone getting hung up and distracted by the technical and terminological errors that you are making. Have you tried this? Do you not have access to an intro physics textbook? -- Steve ( talk) 16:16, 29 April 2008 (UTC)

Steve, I'm not sure if you have caught on yet to what the argument is about or who is arguing for what. As far as this article is concerned it matters not whether I use the term force or acceleration because we are talking about an inertial force. If I by chance should ever say the word acceleration and you are not happy about it, then just multiply it by mass.

None of this impinges on the issue of what is or isn't an illusion. When heavy particles move past lighter particles in a centrifuge, that is a vision which can be viewed from any frame of reference. Now it's my own opinion that centrifugal force is real and I don't care whether you want to call it centrifugal force or inertia. But that is not what this argument is about. It was last year however. Last year I had a long argument with PeR on whether or not centrifugal force was real, which accounts for his childish behaviour at the moment.

At the moment the issue is quite simply about wording the introduction in the most basic way to describe centrifugal force for what it is. When I looked at the introduction recently, it was in a total mess with some other kind of centrifugal force called 'reactive centrifugal force' being described and described wrongly.

What are the key elements of centrifugal force? It occurs when something moves in a curved path. It doesn't matter whether it is a contact push or a contact pull that causes the direction change. It doesn't matter whether it is gravity, electrostatics, or the Lorentz force. It doesn't matter whether the curve is a circle, an ellipse, a parabola, or a hyperbola. The only point of interest is that there is an outward radial motion in conjunction with tangential motion.

So I have been trying to delete all references to circles, to objects, to reactions, to Netwon's third law etc. because they are all irreleavnt and merely act to cloud the issue.

That is all I have been doing.

The point which seemed to make PeR scream when I first edited the article last week was the reference to the fact that in the days of Newton, Bernoulli, and Maxwell, centrifugal force was considered to be real, but that nowadays the official position is that centrifugal force is fictitious.

PeR being an ardent fictitiousist obviously took great offence at even the mention of the fact that such wasn't always the belief of the ruling physics party.

It's not of course of paramount importance to draw attention to what people believed in the past although there already was a reference to the fact that Newton believed that centrifugal force was real.

The important thing is to give a simple first line description, and mine was modelled on an average of on-line articles on centrifugal force.

I can't think why all this should have caused such a major edit war but it has become quite clear to me that PeR, Henning Makholm, and RRacecarr are determined to promote centrifugal force as a purely fictitious concept and to avoid mention of all such matters as Newton's bucket and the centrifuge etc.

Do the general readers want to see an article beginning with irrelevant stuff about rotating reference frames? You know as well as I do that centrifugal force is frame independent and can easily be described in layman's terms.

Just one after thought. I have read your comments again. PeR may have given you the impression that I hold some kind of unorthodox view on acceleration in circular motion. But my position is quite orthodox. In Cartesian coordinates, a particle has an inward acceleration (the centripetal acceleration) that causes the direction of the particle to continually change but not the speed. PeR was making mischief and engaging in verbal witchcraft because in radial/tangential coordinates, the radial acceleration is zero. (The radial direction itself is of course accelerating). The reason for this was that in the example of the stationary object as observed from the rotating frame, PeR thought that a combined Coriolis force and centrifugal force would yield an inward centripetal force. I pointed out that for circular motion, we need to have the forces in the radial direction balanced. PeR then began to undermine this idea by referring to the Cartesian situation and meanwhle trying to expose an inconsistency in what I had been saying. In fact if you read the dialogue you will notice his style. He often asked questions based on a misrepresentation of what I had said before.

So forget about all that about centripetal force and meanings of acceleration or force. The main issue is about getting a simple description of centrifugal force into the introduction. David Tombe ( talk) 18:44, 29 April 2008 (UTC)

Again, David, every post you write has physical and mathematical errors (or at best, "unconventional terminologies") that are distracting from what you're trying to say and harm your credibility. For example, there's a well-defined, coordinate-independent thing called acceleration. The acceleration of a circularly-rotating object points radially inward in any system of coordinates, not just cartesian. The way everyone else understands the term "radial acceleration" is the component of acceleration in the radial direction. You, apparently, sometimes mean that, and sometimes mean "second derivative of the radial coordinate in polar coordinates". So if that's what you mean, say "second derivative of the radial coordinate in polar coordinates". Then everyone will understand what your saying. Likewise, force is equal to mass times acceleration, but "radial force" (meaning the radial component of force) is not equal to "mass times the second derivative of the radial coordinate in polar coordinates". If you want to discuss "mass times the second derivative of the radial coordinate in polar coordinates", that's fine, just call it by that name, not by the term "radial force" or "force in the radial direction", since no one else would call it by that name.

Have you found and read a textbook on this yet? I imagine you could have done so many times over in the time it took you to compose that response. :-) -- Steve ( talk) 18:07, 30 April 2008 (UTC)

Steve, This is nothing to do with unconventional terminologies. But just for the record, I have always been referring to the total acceleration in the radial direction. I have not been restricting my meaning to the r double dot term. In circular motion the sum of r double dot and r theta dot squared is zero.

But anyhow, shall we get to the main point. My proposed introduction today was erased because it contained an unacceptable truth. It contained references to true situations which might cause a reader to question whether or not 'fictitious' was the best term to use to describe centrifugal force.

In the wake of the reversion, a new character arrived on the scenes by the name of Anome. He immediately started to pile on references to back up the fact that there are sources which say that centrifugal force is fictitious.

We all know that.

But that doesn't mean that we have to hide away other true facts that might cause people to question the term. Those true facts are (i)In cases of co-rotation, a particle experiences an actual acceleration in the outward radial direction, and (ii) that in a rotating bucket of water, a hydrostatic pressure is induced.

There is no original research there. There is no point of view being expressed. And there is no need for references for such basic facts.

But these facts are not being tolerated and they are being hastily erased.

Just to prove that what I am saying is right, can you answer me one question. Would you support an introduction that highlighted the term 'fictitious' with loads of citations, but then went on to mention things which might pour some doubt on the suitability of the term? And by those things, I'm talking for example about the centrifuge and the hydrostatic pressure in the rotating bucket.

And I don't really believe at all that you can't see through all this, and what exactly is going on. You are pretty smart. You are smarter than most, but sometimes you get blinkered by terminologies and lose sight of the higher picture.

This is not about terminologies. This is about denial. This is about refusal to see a mechanical equivalent to the Faraday paradox.

By the way, I'm always amused about these beginners physics books that you want me to look at. What level do you have in mind? David Tombe ( talk) 12:59, 1 May 2008 (UTC)

I have no idea what your education, background, or position is. But whatever it is, your statement: "in circular motion...there is no net force in the radial direction" is false. In circular motion, there is a net force, and it's radially inward, as is clearly explained in every introductory college-level physics textbook. If you're a professional physicist, then you are a professional physicist who would benefit greatly from carefully re-reading the appropriate section of an introductory college-level physics textbook. If you've never read an introductory college-level physics textbook, you really should, and in fact you probably should have done that before accusing everyone else of being confused and reverting their edits. You keep trying to change the subject, but I'm going to keep telling you that until you stop repeatedly making elementary factual errors such as this one, no one will believe that you understand what you're talking about. -- Steve ( talk) 16:06, 1 May 2008 (UTC)

Steve, there can be no reason to ever justify dealing with circular or elliptical motion problems in Cartesian coordinates. It is like trying to fit a square peg into a round hole. We always end up talking about the radial direction no matter how hard we try not to. The only people who want to introduce Cartesian coordinates into circular motion are those who want to confuse the issue in order to detract attention away from the failure of their own theories in polar coordinates.

All these matters and arguments can be dealt with satisfactorily entirely within the language of polar coordinates. And in polar coordinates, when a body is moving in a circle, the net radial acceleration is zero. David Tombe ( talk) 10:25, 2 May 2008 (UTC)

David, when you say polar coordinates, do you mean polar coordinates for an inertial, stationary frame or polar coordinates for a rotating frame? Or do you not distinguish between the two? -- FyzixFighter ( talk) 15:52, 2 May 2008 (UTC)

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)

David: You might look at circular motion example. In that example the mere fact that a particle moves in a circle is shown to imply an inward acceleration radially toward the center of the circle. Newton's second law then says there is a force ( m × a ) at work to keep the motion in a circle. Maybe it is apocryphal, but story is that Newton asked why the moon did not fall to the earth, since it is attracted by gravity. His answer: the moon does fall toward the earth, but it also is moving tangentially so rapidly that the little progress it makes in dropping toward the earth is made up for by the tangential movement that carries it further away. Gravity provides the centripetal force needed to keep circular motion. Brews ohare ( talk) 17:52, 2 May 2008 (UTC)

Brews, Exactly. From a Cartesian perspective. But as soon as you start to talk the language of 'radial', then a centripetal force is balanced by a centrifugal force. This conversation is continued in a special section at the bottom of the page. David Tombe ( talk) 17:57, 2 May 2008 (UTC)

Come on, David. You aren't really going to argue that the physical prediction of the need for a centripetal force will be different if I change variables? What kind of physical theory depends upon the coordinate system? It's just a mathematical convenience! If you need convincing, circular motion example is almost in circular coordinates already: just do it. Brews ohare ( talk) 18:17, 2 May 2008 (UTC)

Brews, Correct. The physics doesn't change simply by changing coordinate frames. But we use polar coordinates for these issues because they give us a radial direction. There is no other way to conceive of the direction of centripetal force. And as soon as we start thinking 'radial' for centripetal force, then there will be a radial centrifugal force too.

In the Cartesian frame we are dealing with exactly the same physics. But it is much more complicated to express. It involves the angular rotation of that radial vector (which is where your actual acceleration comes into it) in conjunction with 'inertia'. David Tombe ( talk) 18:47, 2 May 2008 (UTC)

Hi David: I posted a coordinate system free, entirely vector derivation at Vector derivation. I obtain the same answers. There is only the centripetal force. Does that settle things? Brews ohare ( talk) 21:28, 2 May 2008 (UTC)

What appears to have happened now is that the ultra fictitious case of centrifugal force, which is based on a faulty interpretation of maths, has been moved to a position of primacy in an article all of its own, as being the flagship carrier for centrifugal force. It seems that the editors think that this is what the public are looking for when they go to look up centrifugal force.

Centrifugal force is no loner the real effect that occurs in the centrifuge. It is now a fictitious circular motion that we observe from a rotating frame of reference.

Well as far as that is current textbook theory, then the introduction is basically correct now since I have removed the bit about the object having to be moving. If we're going to have a wrong article, better that it is correctly wrong.

Unfortunately though, real centrifugal force has been moved away to a page of its own where people are less likely to look. And it has been totally confused by giving it the misnomer 'Reactive centrifugal Force'. Yet we can see clearly in the case of a weight being swung around on the end of the string that centrifugal force is anything but reactive. And more so in the centrifuge where the heavier particles push their way through the lighter particles to make their way to the outer edge. What is that supposed to be in reaction to? Certainly not the centripetal force as is claimed in the article.

Then to make matters worse, the article gives the impression that centrifugal force is only something that occurs with circular motion, and not elliptical or hyperbolic motion. It would seem that the latter two concepts were too advanced for whoever wrote the article.

And finally, whoever wrote the article considers contact pressure with an object to be the only legitimate means of bringing about centrifugal force. Gravity, electrostatics, and the Lorentz force have been excluded.

All attempts to generalize it to curved motion caused by any force have been fiercely resisted particularly by PeR and FyzixFighter.

Clearly there is team vandalism going on at present on this article. It is now in a worse state than when the edit war began. David Tombe ( talk) 07:57, 28 April 2008 (UTC)

PeR, there is no need to leave formal warnings for me in my tray. You have accused me of wikistalking. That is very rich coming from you. It's a case of the pot calling the kettle black.

You and FyzixFighter have been actively making a point of deleteing every single edit that I make. I am trying to improve this article. I tried to generalize the definition of centrifugal force but both of you reverted it to a high school version that shies away from anything more complicated than a circle.

That is wikistalking if ever there was a case. You are simply making that statement that you will let Wolfkeeper and Rracecarr edit these pages but under no account are you going to alow me to have the slightest input. That is wikistalking.

So do you want to call a truce, or do you want the administration to be brought in? David Tombe ( talk) 08:04, 28 April 2008 (UTC)

The vandalism warning concerned your edit to Rollerblade. It has nothing to do with this article. If you want to discuss the edit, then do so on Talk:Rollerblade. If you want to discuss the warning, then do so on your talk page. -- PeR ( talk) 08:27, 28 April 2008 (UTC)

And likewise, do you want to discuss why you removed my edits yesterday? I generalized circular to curved. I generalized contact pressure forces to all forces. And I pointed out that centrifugal force is not reactive, but rather centripetal force is reactive. But you and FyzixFighgher swiftly reverted those edits as a matter of duty to your team. That is foul play. You can't have it both ways. If you are going to delete all my edits, then you are going to see all your edits deleted too. And if the administration come in then its all your fault. David Tombe ( talk) 10:30, 28 April 2008 (UTC)

OK, here's a reasonably good example of centrifugal force. In the rotating frame of reference that is rotating with the Earth- centrifugal force holds up the space elevator. While in the inertial frame of reference it's (ironically) inertia, in the Earth-synchronous rotating frame of reference- it isn't moving. The force that holds it up is the centrifugal force.- ( User) WolfKeeper ( Talk) 08:25, 28 April 2008 (UTC)

Wolfkeeper, I can simplify that for you.

In the Inertial frame of reference, it is inertia that holds the space station up.

In the frame that is co-rotating with the space station, you can use those equations for the rotating reference frame BECAUSE the object in question is co-rotating. And so, yes, it is centrifugal force that holds the space station up in the rotating frame.

Ah hah! Doing that, that is what this article is about.- ( User) WolfKeeper ( Talk) 10:43, 28 April 2008 (UTC)

Except these equations in the article deal with the general case, where the elevator is wobbling around, and not totally stationary, and there are elevator cars generating coriolis forces on the cable as they climb it, and with the moon pulling this way and that way, and with the Earth attachment point being moved around by ship- all this can be done in the rotating frame of reference.- ( User) WolfKeeper ( Talk) 10:45, 28 April 2008 (UTC)

Either way, the effect is observed from both reference frames whether you call it centrifugal force or inertia.

But this is not the same as the artificial circle scenario in which the object is at rest in the inertial frame. In that case, you cannot apply those equations. There is no co-rotation and there is neither inertia nor centrifugal force.

In my books, inertia is merely centrifugal force as observed in an inertial frame of reference.

Let's not lose track of the main point of the argument. The centrifuge effect is viewable from all frames of reference. It causes heavy particles to have relative motion to lighter particles. But that effect only occurs when the object co-rotates with the rotating frame. It doesn't matter whether we chose to call it inertia or centrifugal force.

So why not simplify the article and leave rotating reference frames out of it. Why not describe centrifugal force in its simplest manner ie. the outward radial force that occurs on all objects that are constrained to follow a curved path. David Tombe ( talk) 10:26, 28 April 2008 (UTC)

Because it would totally piss-off (among others) weathermen, who spend all their working life working in a rotating reference frame, without ever wishing to do all their work in a non rotating reference frame?- ( User) WolfKeeper ( Talk) 10:39, 28 April 2008 (UTC)

Wolfkeeper, the equations are fine so long as the object in question co-rotates. When the object co-rotates, we have centrifugal force. When the object doesn't co-rotate, we have nothing.

Are you incapable of seeing the difference between an illusion of circular motion and a very real radial force that can cause hydrostatic pressure? David Tombe ( talk) 14:03, 28 April 2008 (UTC)

Sorry, David but your assertion is wrong. Any object in rotating reference frame will experience a centrifugal force (and a coriolis force). It is just that when it is co-rotating with the frame (i.e. it is stationary in the rotating frame) it feels only the centrifugal force and no coriolis forces, because those happen to be zero. For a noninteracting object, the coriolis and centrifugal forces will conspire tot let the object follow the straight path it would follow in the inertial frame. Very simple. ( TimothyRias ( talk) 11:35, 29 April 2008 (UTC))

Timothy, you are overlooking quite a number of factors. In one scenario, there is a very real effect. It can cause hydrostatic pressure in a liquid. It can cause heavy particles to push past light particles in a way that can be viewed from all reference frames.

In the other sceanrio, nothing happens. All we get is the illusion of a circular path as viewed from the rotating frame.

You seem to think that these two effects are exactly the same and that they are united under the maths for rotating reference frames. In fact, that maths only applies to the former scenario. If you see the derivation of that maths you will notice that the ω term which is ostensibly the angular velocity of the rotating frame, is actually physically related to the tangential component of the moving particle.

If the particle does not co-rotate, then you can't apply those equations.

The derivation, for the same resons also tells us that the v term for the rotating frame has to be radial. Centrifugal force is a radial effect arising from a tangential motion, and the Coriolis force is a tangential effect arising from a radial motion. In fact from the velocity formula you can actually see that they are two mutually perpendicular aspects of the same thing.

Hence, there will be no Coriolis force ever acting in the radial direction.

So your argument about the stationary particle experiencing a centripetal force composed of an outward centrifugal force added to an inward Coriolis force that is twice as strong, is wrong.

And it is further wrong on the grounds that it would lead to a net inward radial acceleration. In circular motion, we need a net zero radial acceleration. David Tombe ( talk) 12:16, 29 April 2008 (UTC)

First of all the effect is real in both cases. In the sense that a particle that is stationary in an inertial frame, really moves in a circle in the rotating frame. This is not an illusion. The physics in the rotating frame is just as good as in the inertial frame. It depends on the physical situation which happens to be easier to use.

Your statement If you see the derivation of that maths you will notice that the ω term which is ostensibly the angular velocity of the rotating frame, is actually physically related to the tangential component of the moving particle. is false. In the formula:

${\displaystyle \mathbf {a} _{\mathrm {rot} }=\mathbf {a} -2\mathbf {\omega \times v} -\mathbf {\omega \times (\omega \times r)} }$

ω is the angular velocity of the frame and nothing else. Only the variable r and v (the later being the time derivative of the first) have any relation to the particle. If a particle is stationary in an inertial frame, then ofcourse v is related to ω through ${\displaystyle v=-\omega \times r)}$. In that case the coriolis acceleration is ${\displaystyle -2\mathbf {\omega \times v} =2\mathbf {\omega \times \omega \times r} }$ which is twice the centrifugal acceleration but pointed inward. Thus refutes your statement that Hence, there will be no Coriolis force ever acting in the radial direction.

Finally we have your statement In circular motion, we need a net zero radial acceleration. which is just plain wrong. Circular motion just as any other nonstraight motion implies a netto acceleration, because obviously the velocity is not constant. (it changes direction). This is basic high school physics. ( TimothyRias ( talk) 12:57, 29 April 2008 (UTC))

Timothy, I have already considered all your points many times. If you look at the derivation of the formula above, you will see that v is routed through ω. They are not independent of each other. In the limit for calculus purposes v reduces to exactly the radial velocity, and ω will always implicitly contain the tangential velocity. There is no point in reading the final result out to me. I studied it all years ago.

The application of this formula which you are making is detached from the physical reality upon which the formula was derived.

And on your other points, there will indeed be an inward acceleration in a circle when we look at it in Cartesian coordinates. This inward acceleration changes the direction of the particle but not its speed. However, if we move over to radial/tangential coordinates, then the radial force will be zero. In your example, which is done in radial/tangential coordinates, the net radial acceleration is not zero and so it doesn't describe a circle. David Tombe ( talk) 18:09, 29 April 2008 (UTC)

Do you have a reference for that bizarre claim? You keep saying that, but it isn't true. If it was true, merely changing from cartesian coordinates to polar coordinates would make something go around in a circle all by itself!!!!!- ( User) WolfKeeper ( Talk) 19:39, 29 April 2008 (UTC)

Wolfkeeper, now you are starting to talk nonsense. How do you infer that the inapllicability of a set of equations means that changing between two coordinate systems would make something go around in a circle all by itself!!!!!? You have now ceased to engage in rational argument. You are at that stage where you misrepresent and twist what others have said and then ridicule your own misrepresentations. David Tombe ( talk) 20:11, 29 April 2008 (UTC)

I'm sorry if you think that that is the case, I would never do that intentionally. However, I'm hoping that you will be able to cite this claim of yours, because I don't see how this could ever be, but since it's true, you'll be able to give us a good reference?- ( User) WolfKeeper ( Talk) 22:12, 29 April 2008 (UTC)

You have been over extending the application of a formula which was derived exclusively to cater for particles in co-rotation, or to put it more simply, to cater for particles which are actually moving in a circle.

On your other point, I'm not going to get into an argument about whether or not both situations are real. I would just hope that you would realize that the two situations are quite different. In one situation, an object sits still and nothing happens to it. In the other situation, there is an actual tangential motion which leads to a radially outward motion which can cause pressure and diffusion that is visible from all frames of reference. check out the Bucket argument. David Tombe ( talk) 18:09, 29 April 2008 (UTC)

David, would you mind explaining why you keep claiming that ω has anything to do with the velocity of the particle. There are plenty of ways to derive the above result that clearly show that this is not the case. ω is nothing more than a parameter in coordinate change ${\displaystyle \mathbf {x} \rightarrow R(\mathbf {\omega } t)\mathbf {x} }$ where R(ω) is a rotation matrix. If ${\displaystyle \mathbf {r} (t)}$ is a path then ${\displaystyle \mathbf {r} (t)\rightarrow r_{rot}(t)=R(\mathbf {\omega } t)\mathbf {r} (t)}$ and for the second time derivative ${\displaystyle {\ddot {\mathbf {r} }}_{rot}(t)\rightarrow {\ddot {\mathbf {r} }}(t)-2\mathbf {\omega \times {\dot {r}}_{rot}(t)} -\mathbf {\omega \times (\omega \times r_{rot}(t))} }$. Which is the result above. Omega in no way depends on r. ( TimothyRias ( talk) 07:50, 30 April 2008 (UTC))