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Thank you for making the clarifications to some of the written portions of the article, they are certainly more clear than what I had originally wrote. On the other hand, this article was not flawed, as the difference between a + b and a - ( - b ) is strictly a matter of convention and in fact they are completely equivalent statements. Also, merely switching signs does not change the physics, and again is a matter of convention that does not at all render the physics as flawed.
Robert A. Mitchell 21:05, 11 October 2006 (UTC)
The physics on this page is incorrect.
The relative velocity of person A (moving with velocity a) with respect to person B (moving with velocity b)
is the vector a - b
The entire article is flawed accordingly.
Tayana 16:32, 20 September 2006 (UTC)
Your original article stated that the relative velocity is the vector sum (presumably a + b) while the cited equation show this as vector difference (a - b) , which is the correct answer, but not in accord with your statement as summation of velocities [it is accepted that (a + b) and (a - b) are sumations, but getting the sign of velocity wrong fails to understand the basic physics of the situation.]. The relative velocity a - b applies always which resolves to a + b in a subset of cases
Tayana
20:29, 27 October 2006 (UTC)
If a car (A) was travelling North at 50 m/sec and another car (B) was travelling East at 50 m/sec what would car B's velocity be relative to car A? So would car B's velocity (relative to car A) be 70.7 m/sec South-East or 70.7 m/sec North-West?
-- Phat Solja 09:38, 4 June 2007 (UTC)
Hi the definition of "relative velocity" here is at odds with that as used by for example Einstein and the Physics text books that I know. According to those, "relative velocity" is defined in *one* reference frame, and is the vector subtraction of the velocities of the objects.
That there are two competing definitions - one that has been standard and another one that some people try to replce it with - has also been discussed in a paper in the Aus.J.P., and that paper was highly critical of the definition that this Wikipedia article promotes. Thus at the moment this article is WP:POV. Surprisingly, I now notice that this problem has already been addressed by Tayana, but without any reaction. Thus I'll mark this article POV so that people may notice.
References:
- Einstein's 1905 paper on SRT, paragraph 3 http://www.fourmilab.ch/etexts/einstein/specrel/www/
- Alonso&Finn, "Fundamental University Physics", volume 1
- G. Builder, "The constancy of the velocity of light", Aust.J.P. 1958 p.457-480
Harald88 22:58, 13 June 2007 (UTC)
The definitions are wrong, the derivations are wrong, the best thing is to wipe it out and start from scratch, there is no way to correct this junk. WWStone 01:06, 14 June 2007 (UTC)
Tayana 00:26, 7 September 2007 (UTC)
Reverted to an accurate description to replace a poorly expressed special case, non encyclopedic and obviously a straight lift from a text book, while passing from the page of the text book to the Wikipedia page, without passing through the brain of the writer. 22:31, 29 September 2007 (UTC)
I notice that one or two people continuously revert ot a version that is blatantly against NPOV policy; moreover, it is poorly sourced and I think that that version is of less good quality (less clear for occasional readers) than the version that was elaborated by some of us, as was discussed above. If only they added some parts of it to expand one meaning of relative velocity it probably wouldn't be too bad. I propose to ask for semi-protection of this page. Harald88 21:58, 2 October 2007 (UTC)
We overlooked that in fact there are not less than three meanings of "relative velocity": many older publications and some modern publications use the word "velocity" for "speed". Thus the relative speeds as in Doppler effect can also be described with the term "relative velocity". For example, the English translation of Einstein's 1905 relativity paper uses the term both for vectorial velocity in the first meaning of the term, as for the Doppler "velocity". What may also play a role is that in many other languages (such as German) there is only one word for both meanings. It will be good to mention that shortly as such inconsistencies can lead to quite a lot of confusion. And perhaps we should also add an example to stress how different the outcome is in some particular cases. BTW, I notice that the Doppler effect article needs some improvement on just this point! Harald88 12:54, 3 October 2007 (UTC)
Tayana 23:57, 7 October 2007 (UTC)
In the first part of the reversion, the relative velocity of one body with respect to another body is defined correctly as a vector difference, yet in a follow up paragraph relative velocity is shown as a sum of the vectors. There is no indication of why. Harald88 is confusing the topic and does not appear to understand the basic principles. The reference to NPOV is somewhat naive. The version of Tayana is correct while Harald88 is incosistent and flawed.
194.46.251.87 20:51, 11 October 2007 (UTC)
I find the following example not so useful and doubtful; moreover it contains an error, so I moved it here for discussion:
Now, let us change the example. A rocket flies at high speed to the moon. It sends a laser beam sideways. When the rocket passes the space station at a very short distance, the laser beam hits a photo cell on the space station, which causes the station to send a short burst of laser light to the moon. At the same time a photo cell in the rocket gets hit by a laser beam that the space station has been emitting side ways and the rocket also sends a short burst of laser light to the moon. As calculated (naively) by an observer on the space station, the relative velocity (a+b) of the photons in the burst of laser light emitted by the rocket is the velocity (a) of the rocket relative to the space station plus the velocity (b) of the photons relative to the rocket. Because the photons in both bursts of light travel at the speed of light, the photons emitted by the rocket should hit the moon before the photons emitted by the space station. But it turns out that the photons in both laser bursts will hit the moon at the same time.
It's (too?) complicated, has at least one error and in classical mechanics as well as in relativity light is a wave and its speed is independent of the velocity of the source; thus not even naively one would think so! Also, the example was in the wrong section. But I do think that such an example, perhaps simpler and with a bullet, could be useful for the last part of the article. Suggestions? Harald88 23:12, 11 October 2007 (UTC)
Done! This should be a better starting point for further improvements - I'm a bit tired, so don't make a fuss if something is still not quite OK but just improve more!
Cheers, Harald88 00:00, 12 October 2007 (UTC)
The paragraph:
For example, let's assume that the objects are two cars that move towards each other, and the reference frame is the road. The velocity of the one car (moving with velocity a) relative to the velocity of the other car (moving with velocity b) is the vector (a - b).
Harald88 is propagating heresy here. The relative velocity in the case of the two cars approaching each other as presented in above paragraph is (a+b), why; because the two cars are moving in opposite directions so the relative velocity is (a-(-b))
Reading through his contributions suggest a lack of basic understanding of elementary physics. A reference to a university website that explained the basic physics was removed by him.
Please Harald88 desist from expressing opinions and reverting on items that you don't properly understand.
194.46.253.155 19:52, 18 October 2007 (UTC)
I found the existing explanation of usage 2 much too complicated. I simplified it as follows :
I also added a textbook reference for it and adapted the corresponding example. Moreover, I added an example for the third usage as well as a remark about the preferred use of inertial frames. Harald88 06:55, 5 November 2007 (UTC)
Excuse me for being blunt, but this page is in terrible shape. Even if we accept the need for a separate article on "relative velocity" (which is questionable), the various definitions presented in the current version of this article (5-Nov-2007) are mostly just plain wrong. The whole section that talks about the rate of change of distance with time (ds/dt) and calls that the "scalar velocity" is flat out wrong. The scalar velocity is simply the magnitude of the velocity, which is to say, the square root of the sum of squares of the components. For example, if a particle is moving in a circle around the origin, at a particular moment when it crosses the x axis its velocity has components vx=0, vy=1. Now, it's distance from the origin isn't changing, so ds/dt = 0, but the scalar velocity of the particle with respect to the rest frame of a particle at the origin is not zero, it is sqrt(0^2 +1^2) = 1. This is just one example. The entire article needs to be re-written. Lumpy27 19:59, 5 November 2007 (UTC)
I believe we should merge this article with the velcity article. the reason is that having separate articles for velocity and relative velocity suggests that they are two distinct things while actually they are two names of exactly the same thing. all velocity is relative. all velocity is relative velocity, there exists no velocity which is not relative velocity. the word velocity always means relative velocity, and there is no such thing as absolute velocity. Mushoo 10:19, 9 November 2007 (UTC)
I tend to agree that this article could be merged with the article on "velocity", because once the word "velocity" is understood, there is not much more to understanding the phrase "relative velocity". The only reason I can see for having a separate article on "relative velocity" is to explain the way in which this phrase is used. If we keep this as a separate article, I propose that the article should read as follows:
Relative Velocity
The expression “relative velocity” signifies the difference between the velocities of two objects, with the understanding that the individual velocities are each evaluated in terms of a single system of coordinates, usually an inertial coordinate system unless specifically stated otherwise. (See velocity)
For example, if the velocities of particles A and B are vA and vB respectively in terms of a given inertial coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB. Conversely the velocity of B relative to A is vB – vA.
If one of the particles is at rest with respect to the coordinate system in terms of which the individual velocities are evaluated, then the relative velocity is simply the velocity of the other particle. If no other system of coordinates is specified, the expression “velocity of A relative to B” is usually understood as shorthand for “the velocity of A in terms of an inertial coordinates system with respect to which B is at rest”.
In Galilean kinematics (i.e., not accounting for the effects of special relativity), the relative velocity between two particles is the same with respect to any system of inertial coordinates. This is because changing from one inertial coordinate system to another (according to Galilean kinematics) simply adds a common increment vector to each velocity vector, so the difference between any pair of velocities is unaffected.
However, taking the effects of special relativity into account, the relative velocity between two particles actually depends on the inertial coordinate system in terms of which the individual velocities are evaluated. This is because the effect of changing from one system of inertial coordinates to another is more complicated than simply adding a common increment vector to each velocity vector. See special relativity.
References:
Either it should be revised as above, or else merged into the "velocity" article. Do I hear any objections? ~~
The lead was much too long, making that readers might even not reach the introduction. For completness I copy the deleted part here below for consideration if it's useful to insert somewhere - some of it actually may fit in the article on velocity:
Harald88 13:08, 11 November 2007 (UTC)
I've made an attempt to further improve the proposed new baseline for this article. I think these words would be suitable, either for this article on "relative velocity", or as a new section in the main article on "velocity".
Relative Velocity
The expression “relative velocity” signifies the difference between the velocities of two objects, with the understanding that the individual velocities are each evaluated in terms of a single system of coordinates, usually an inertial coordinate system unless specifically stated otherwise. (See velocity)
For example, if the velocities of particles A and B are vA and vB respectively in terms of a given inertial coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB. Conversely the velocity of B relative to A is vB – vA. If no other system of coordinates is specified, the expression “velocity of A relative to B” is usually understood as shorthand for “the velocity of A in terms of an inertial coordinates system with respect to which B is at rest”.
In Galilean kinematics (i.e., not accounting for the effects of special relativity), the relative velocity between two particles is the same with respect to any system of inertial coordinates. This is because changing from one inertial coordinate system to another (according to Galilean kinematics) simply adds a common increment vector to each velocity vector, so the difference between any pair of velocities is unaffected. However, taking the effects of special relativity into account, the relative velocity between two particles actually depends on the inertial coordinate system in terms of which the individual velocities are evaluated. This is because the effect of changing from one system of inertial coordinates to another is more complicated than simply adding a common increment vector to each velocity vector. See special relativity.
References:
Does anyone have any specific and rational objections to this wording? Lumpy27 17:50, 11 November 2007 (UTC)
194.46.187.17 ( talk) 01:46, 21 November 2007 (UTC)
This article is a candidate for for deletion, as it is in a mess and has had inconsistent and inaccurate edits with seeming destructive edit wars. Relative velocity is not an article of opinion but of basic fact!. A paragraph can be incorporated in Velocity. Zubenzenubi ( talk) 02:46, 21 January 2008 (UTC)
I agree with you. This was my suggestion originally too. Anyone who objects to deleting this article and including a paragraph in the velocity article please object here before 23rd Jan 2008. I will delete this article by then if no one else does so. Mushoo ( talk) 08:43, 21 January 2008 (UTC)
As at least several users (such as here above) and myself find the external links to vector addition and relative velocity useful for this article, thus reverted the deletion again. Anon motivated: Remove spurious external links. One was just a web page on vectors, and the other a web page on special relativity. Both those topics have their own wiki articles. My comment: there is nothing spurious about these pages and many readers will benefit from direct links to the most tricky aspects of relative velocity - which are vector addition and special relativistic calculations. Of course, there is nothing against finding better external links. Harald88 (talk) 18:22, 29 March 2008 (UTC)
I just noticed that the word "vectors" already is linked to the wiki article, along with "difference" and "velocities", so I really think it's covered. Those external links really are superfluous, and less relevant and less useful than the links in the article itself. So, I'll remove them. Lumpy27 ( talk) 19:47, 31 March 2008 (UTC)
I see that Lumpy27 removed the links again, eventhough no additional opinions from others were provided. At this point in time there is a majority of editors and readers in favour of keeping them. Thus I reverted again. Still, it may be useful to establish opinions more clearly (even more useful would be if more good links are provided!). Thus here an opinion poll (including those expressed earlier on this page and by the one who put them here):
Keep or delete links - opinion summary (in brackets is inferred; please add your opinion if not already mentioned):
You say the votes listed in brackets are "inferred", and then you tabulate a list of votes, all of which are inferred with the exception of your own. While this is quite amusing (and I trust you intended it as a joke), the fact remains that you are merely expressing your own opinion (the quality of which is comensurate with that of your other edits). I have clearly explained why the external links are superfluous and essentially irrelevant. This entire article has already been discussed for deletion, which shows that it is only marginally justified to even be here. We certainly don't need to pad it with superfluous and irrelevant "external links". Lumpy27 ( talk) 18:27, 12 April 2008 (UTC)
When presented correctly, relative velocity is a trivial concept, it doesn't require it's own article. —Preceding unsigned comment added by NOrbeck ( talk • contribs) 17:18, 16 July 2010 (UTC)
I respectfully disagree. As the category statement states below, this is a Start-Class article of high importance. A good grounding in Galilean notions of relative velocity is (1) difficult for students to acquire and (2) essential for grasping Special Relativity- guyvan52 ( talk) 21:41, 19 January 2014 (UTC)
In the subsection now titled In two dimensions I propose to not use the Galilean transformation, but instead the concept of vector subtraction. Referring to the same figure, I would begin with equations of motion for A and B:
represents the location of B as seen from A. (we need either a figure or a link describing vector subtraction).
-- guyvan52 ( talk) 03:53, 20 January 2014 (UTC)
Yours truly, -- guyvan52 ( talk) 22:14, 20 January 2014 (UTC)
Is it just me or is the figure at the left too cluttered? I propose one that resembles the figure to the right. I would relabel the symbols so that the two large vectors (currently A and C) would become A and B (to represent the motion of the two particles) and the short vector (currently B) would be the difference. I would include two orange balls at the at the tails, labeled Ai and Bi, that are nearly overlapping to represent the initial locations of object A and B. Then use the subscripts at Af and Bf at the heads. Somewhere (in the figure, caption, or text) it would be explained that the magnitude of A is vAt. In the final state (at the heads) the particles are |Af-Bf| apart, and they have been traveling for time t. See The River Needs a Cork
I just looked at Velocity-addition_formula#General_case_.28engineering_units.2C_replaced_V_with_v_.2F_c_.29 and now believe your equations are correct. But that does not necessarily imply that they belong in this article. I propose that we instead reference the aforementioned Wikipedia article, where the equations are fully derived and stated in two different notations. The way I see it, Velocity-addition formula is the advanced article, and this article is for beginners (i.e. most college freshmen). I hate to do it to you because you worked so hard (and so carefully as far as I can tell). But a Wikipedia article needs consistency in its level. This article started with a picture showing a person walking on a train, which in my opinion, establishes it as an elementary article.
Since your equations appear to be correct, I will remove the harsh template questioning its correctness. But we still have a problem with the level of this article that needs to be resolved.-- guyvan52 ( talk) 13:51, 5 August 2014 (UTC)
It is at present written on the page that dt=dt' is not valid at high speed (time dilation). This is so poorly written. It is not valid AT ALL since Relativity theory, but can be neglected in usual calculations, because of extremely small differences in results. Yet, there is ALWAYS a difference, even at low speed. This is a mistake that propagate everywhere the concept that Relativity is only a "high speed theory". It is not. It's a change in paradigm, whatever the speed you consider. Newton theory became just an approximation of Relativity theory. ( talk) 13:53, 5 August 2014 (UTC) please correct this.
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Thank you for making the clarifications to some of the written portions of the article, they are certainly more clear than what I had originally wrote. On the other hand, this article was not flawed, as the difference between a + b and a - ( - b ) is strictly a matter of convention and in fact they are completely equivalent statements. Also, merely switching signs does not change the physics, and again is a matter of convention that does not at all render the physics as flawed.
Robert A. Mitchell 21:05, 11 October 2006 (UTC)
The physics on this page is incorrect.
The relative velocity of person A (moving with velocity a) with respect to person B (moving with velocity b)
is the vector a - b
The entire article is flawed accordingly.
Tayana 16:32, 20 September 2006 (UTC)
Your original article stated that the relative velocity is the vector sum (presumably a + b) while the cited equation show this as vector difference (a - b) , which is the correct answer, but not in accord with your statement as summation of velocities [it is accepted that (a + b) and (a - b) are sumations, but getting the sign of velocity wrong fails to understand the basic physics of the situation.]. The relative velocity a - b applies always which resolves to a + b in a subset of cases
Tayana
20:29, 27 October 2006 (UTC)
If a car (A) was travelling North at 50 m/sec and another car (B) was travelling East at 50 m/sec what would car B's velocity be relative to car A? So would car B's velocity (relative to car A) be 70.7 m/sec South-East or 70.7 m/sec North-West?
-- Phat Solja 09:38, 4 June 2007 (UTC)
Hi the definition of "relative velocity" here is at odds with that as used by for example Einstein and the Physics text books that I know. According to those, "relative velocity" is defined in *one* reference frame, and is the vector subtraction of the velocities of the objects.
That there are two competing definitions - one that has been standard and another one that some people try to replce it with - has also been discussed in a paper in the Aus.J.P., and that paper was highly critical of the definition that this Wikipedia article promotes. Thus at the moment this article is WP:POV. Surprisingly, I now notice that this problem has already been addressed by Tayana, but without any reaction. Thus I'll mark this article POV so that people may notice.
References:
- Einstein's 1905 paper on SRT, paragraph 3 http://www.fourmilab.ch/etexts/einstein/specrel/www/
- Alonso&Finn, "Fundamental University Physics", volume 1
- G. Builder, "The constancy of the velocity of light", Aust.J.P. 1958 p.457-480
Harald88 22:58, 13 June 2007 (UTC)
The definitions are wrong, the derivations are wrong, the best thing is to wipe it out and start from scratch, there is no way to correct this junk. WWStone 01:06, 14 June 2007 (UTC)
Tayana 00:26, 7 September 2007 (UTC)
Reverted to an accurate description to replace a poorly expressed special case, non encyclopedic and obviously a straight lift from a text book, while passing from the page of the text book to the Wikipedia page, without passing through the brain of the writer. 22:31, 29 September 2007 (UTC)
I notice that one or two people continuously revert ot a version that is blatantly against NPOV policy; moreover, it is poorly sourced and I think that that version is of less good quality (less clear for occasional readers) than the version that was elaborated by some of us, as was discussed above. If only they added some parts of it to expand one meaning of relative velocity it probably wouldn't be too bad. I propose to ask for semi-protection of this page. Harald88 21:58, 2 October 2007 (UTC)
We overlooked that in fact there are not less than three meanings of "relative velocity": many older publications and some modern publications use the word "velocity" for "speed". Thus the relative speeds as in Doppler effect can also be described with the term "relative velocity". For example, the English translation of Einstein's 1905 relativity paper uses the term both for vectorial velocity in the first meaning of the term, as for the Doppler "velocity". What may also play a role is that in many other languages (such as German) there is only one word for both meanings. It will be good to mention that shortly as such inconsistencies can lead to quite a lot of confusion. And perhaps we should also add an example to stress how different the outcome is in some particular cases. BTW, I notice that the Doppler effect article needs some improvement on just this point! Harald88 12:54, 3 October 2007 (UTC)
Tayana 23:57, 7 October 2007 (UTC)
In the first part of the reversion, the relative velocity of one body with respect to another body is defined correctly as a vector difference, yet in a follow up paragraph relative velocity is shown as a sum of the vectors. There is no indication of why. Harald88 is confusing the topic and does not appear to understand the basic principles. The reference to NPOV is somewhat naive. The version of Tayana is correct while Harald88 is incosistent and flawed.
194.46.251.87 20:51, 11 October 2007 (UTC)
I find the following example not so useful and doubtful; moreover it contains an error, so I moved it here for discussion:
Now, let us change the example. A rocket flies at high speed to the moon. It sends a laser beam sideways. When the rocket passes the space station at a very short distance, the laser beam hits a photo cell on the space station, which causes the station to send a short burst of laser light to the moon. At the same time a photo cell in the rocket gets hit by a laser beam that the space station has been emitting side ways and the rocket also sends a short burst of laser light to the moon. As calculated (naively) by an observer on the space station, the relative velocity (a+b) of the photons in the burst of laser light emitted by the rocket is the velocity (a) of the rocket relative to the space station plus the velocity (b) of the photons relative to the rocket. Because the photons in both bursts of light travel at the speed of light, the photons emitted by the rocket should hit the moon before the photons emitted by the space station. But it turns out that the photons in both laser bursts will hit the moon at the same time.
It's (too?) complicated, has at least one error and in classical mechanics as well as in relativity light is a wave and its speed is independent of the velocity of the source; thus not even naively one would think so! Also, the example was in the wrong section. But I do think that such an example, perhaps simpler and with a bullet, could be useful for the last part of the article. Suggestions? Harald88 23:12, 11 October 2007 (UTC)
Done! This should be a better starting point for further improvements - I'm a bit tired, so don't make a fuss if something is still not quite OK but just improve more!
Cheers, Harald88 00:00, 12 October 2007 (UTC)
The paragraph:
For example, let's assume that the objects are two cars that move towards each other, and the reference frame is the road. The velocity of the one car (moving with velocity a) relative to the velocity of the other car (moving with velocity b) is the vector (a - b).
Harald88 is propagating heresy here. The relative velocity in the case of the two cars approaching each other as presented in above paragraph is (a+b), why; because the two cars are moving in opposite directions so the relative velocity is (a-(-b))
Reading through his contributions suggest a lack of basic understanding of elementary physics. A reference to a university website that explained the basic physics was removed by him.
Please Harald88 desist from expressing opinions and reverting on items that you don't properly understand.
194.46.253.155 19:52, 18 October 2007 (UTC)
I found the existing explanation of usage 2 much too complicated. I simplified it as follows :
I also added a textbook reference for it and adapted the corresponding example. Moreover, I added an example for the third usage as well as a remark about the preferred use of inertial frames. Harald88 06:55, 5 November 2007 (UTC)
Excuse me for being blunt, but this page is in terrible shape. Even if we accept the need for a separate article on "relative velocity" (which is questionable), the various definitions presented in the current version of this article (5-Nov-2007) are mostly just plain wrong. The whole section that talks about the rate of change of distance with time (ds/dt) and calls that the "scalar velocity" is flat out wrong. The scalar velocity is simply the magnitude of the velocity, which is to say, the square root of the sum of squares of the components. For example, if a particle is moving in a circle around the origin, at a particular moment when it crosses the x axis its velocity has components vx=0, vy=1. Now, it's distance from the origin isn't changing, so ds/dt = 0, but the scalar velocity of the particle with respect to the rest frame of a particle at the origin is not zero, it is sqrt(0^2 +1^2) = 1. This is just one example. The entire article needs to be re-written. Lumpy27 19:59, 5 November 2007 (UTC)
I believe we should merge this article with the velcity article. the reason is that having separate articles for velocity and relative velocity suggests that they are two distinct things while actually they are two names of exactly the same thing. all velocity is relative. all velocity is relative velocity, there exists no velocity which is not relative velocity. the word velocity always means relative velocity, and there is no such thing as absolute velocity. Mushoo 10:19, 9 November 2007 (UTC)
I tend to agree that this article could be merged with the article on "velocity", because once the word "velocity" is understood, there is not much more to understanding the phrase "relative velocity". The only reason I can see for having a separate article on "relative velocity" is to explain the way in which this phrase is used. If we keep this as a separate article, I propose that the article should read as follows:
Relative Velocity
The expression “relative velocity” signifies the difference between the velocities of two objects, with the understanding that the individual velocities are each evaluated in terms of a single system of coordinates, usually an inertial coordinate system unless specifically stated otherwise. (See velocity)
For example, if the velocities of particles A and B are vA and vB respectively in terms of a given inertial coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB. Conversely the velocity of B relative to A is vB – vA.
If one of the particles is at rest with respect to the coordinate system in terms of which the individual velocities are evaluated, then the relative velocity is simply the velocity of the other particle. If no other system of coordinates is specified, the expression “velocity of A relative to B” is usually understood as shorthand for “the velocity of A in terms of an inertial coordinates system with respect to which B is at rest”.
In Galilean kinematics (i.e., not accounting for the effects of special relativity), the relative velocity between two particles is the same with respect to any system of inertial coordinates. This is because changing from one inertial coordinate system to another (according to Galilean kinematics) simply adds a common increment vector to each velocity vector, so the difference between any pair of velocities is unaffected.
However, taking the effects of special relativity into account, the relative velocity between two particles actually depends on the inertial coordinate system in terms of which the individual velocities are evaluated. This is because the effect of changing from one system of inertial coordinates to another is more complicated than simply adding a common increment vector to each velocity vector. See special relativity.
References:
Either it should be revised as above, or else merged into the "velocity" article. Do I hear any objections? ~~
The lead was much too long, making that readers might even not reach the introduction. For completness I copy the deleted part here below for consideration if it's useful to insert somewhere - some of it actually may fit in the article on velocity:
Harald88 13:08, 11 November 2007 (UTC)
I've made an attempt to further improve the proposed new baseline for this article. I think these words would be suitable, either for this article on "relative velocity", or as a new section in the main article on "velocity".
Relative Velocity
The expression “relative velocity” signifies the difference between the velocities of two objects, with the understanding that the individual velocities are each evaluated in terms of a single system of coordinates, usually an inertial coordinate system unless specifically stated otherwise. (See velocity)
For example, if the velocities of particles A and B are vA and vB respectively in terms of a given inertial coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB. Conversely the velocity of B relative to A is vB – vA. If no other system of coordinates is specified, the expression “velocity of A relative to B” is usually understood as shorthand for “the velocity of A in terms of an inertial coordinates system with respect to which B is at rest”.
In Galilean kinematics (i.e., not accounting for the effects of special relativity), the relative velocity between two particles is the same with respect to any system of inertial coordinates. This is because changing from one inertial coordinate system to another (according to Galilean kinematics) simply adds a common increment vector to each velocity vector, so the difference between any pair of velocities is unaffected. However, taking the effects of special relativity into account, the relative velocity between two particles actually depends on the inertial coordinate system in terms of which the individual velocities are evaluated. This is because the effect of changing from one system of inertial coordinates to another is more complicated than simply adding a common increment vector to each velocity vector. See special relativity.
References:
Does anyone have any specific and rational objections to this wording? Lumpy27 17:50, 11 November 2007 (UTC)
194.46.187.17 ( talk) 01:46, 21 November 2007 (UTC)
This article is a candidate for for deletion, as it is in a mess and has had inconsistent and inaccurate edits with seeming destructive edit wars. Relative velocity is not an article of opinion but of basic fact!. A paragraph can be incorporated in Velocity. Zubenzenubi ( talk) 02:46, 21 January 2008 (UTC)
I agree with you. This was my suggestion originally too. Anyone who objects to deleting this article and including a paragraph in the velocity article please object here before 23rd Jan 2008. I will delete this article by then if no one else does so. Mushoo ( talk) 08:43, 21 January 2008 (UTC)
As at least several users (such as here above) and myself find the external links to vector addition and relative velocity useful for this article, thus reverted the deletion again. Anon motivated: Remove spurious external links. One was just a web page on vectors, and the other a web page on special relativity. Both those topics have their own wiki articles. My comment: there is nothing spurious about these pages and many readers will benefit from direct links to the most tricky aspects of relative velocity - which are vector addition and special relativistic calculations. Of course, there is nothing against finding better external links. Harald88 (talk) 18:22, 29 March 2008 (UTC)
I just noticed that the word "vectors" already is linked to the wiki article, along with "difference" and "velocities", so I really think it's covered. Those external links really are superfluous, and less relevant and less useful than the links in the article itself. So, I'll remove them. Lumpy27 ( talk) 19:47, 31 March 2008 (UTC)
I see that Lumpy27 removed the links again, eventhough no additional opinions from others were provided. At this point in time there is a majority of editors and readers in favour of keeping them. Thus I reverted again. Still, it may be useful to establish opinions more clearly (even more useful would be if more good links are provided!). Thus here an opinion poll (including those expressed earlier on this page and by the one who put them here):
Keep or delete links - opinion summary (in brackets is inferred; please add your opinion if not already mentioned):
You say the votes listed in brackets are "inferred", and then you tabulate a list of votes, all of which are inferred with the exception of your own. While this is quite amusing (and I trust you intended it as a joke), the fact remains that you are merely expressing your own opinion (the quality of which is comensurate with that of your other edits). I have clearly explained why the external links are superfluous and essentially irrelevant. This entire article has already been discussed for deletion, which shows that it is only marginally justified to even be here. We certainly don't need to pad it with superfluous and irrelevant "external links". Lumpy27 ( talk) 18:27, 12 April 2008 (UTC)
When presented correctly, relative velocity is a trivial concept, it doesn't require it's own article. —Preceding unsigned comment added by NOrbeck ( talk • contribs) 17:18, 16 July 2010 (UTC)
I respectfully disagree. As the category statement states below, this is a Start-Class article of high importance. A good grounding in Galilean notions of relative velocity is (1) difficult for students to acquire and (2) essential for grasping Special Relativity- guyvan52 ( talk) 21:41, 19 January 2014 (UTC)
In the subsection now titled In two dimensions I propose to not use the Galilean transformation, but instead the concept of vector subtraction. Referring to the same figure, I would begin with equations of motion for A and B:
represents the location of B as seen from A. (we need either a figure or a link describing vector subtraction).
-- guyvan52 ( talk) 03:53, 20 January 2014 (UTC)
Yours truly, -- guyvan52 ( talk) 22:14, 20 January 2014 (UTC)
Is it just me or is the figure at the left too cluttered? I propose one that resembles the figure to the right. I would relabel the symbols so that the two large vectors (currently A and C) would become A and B (to represent the motion of the two particles) and the short vector (currently B) would be the difference. I would include two orange balls at the at the tails, labeled Ai and Bi, that are nearly overlapping to represent the initial locations of object A and B. Then use the subscripts at Af and Bf at the heads. Somewhere (in the figure, caption, or text) it would be explained that the magnitude of A is vAt. In the final state (at the heads) the particles are |Af-Bf| apart, and they have been traveling for time t. See The River Needs a Cork
I just looked at Velocity-addition_formula#General_case_.28engineering_units.2C_replaced_V_with_v_.2F_c_.29 and now believe your equations are correct. But that does not necessarily imply that they belong in this article. I propose that we instead reference the aforementioned Wikipedia article, where the equations are fully derived and stated in two different notations. The way I see it, Velocity-addition formula is the advanced article, and this article is for beginners (i.e. most college freshmen). I hate to do it to you because you worked so hard (and so carefully as far as I can tell). But a Wikipedia article needs consistency in its level. This article started with a picture showing a person walking on a train, which in my opinion, establishes it as an elementary article.
Since your equations appear to be correct, I will remove the harsh template questioning its correctness. But we still have a problem with the level of this article that needs to be resolved.-- guyvan52 ( talk) 13:51, 5 August 2014 (UTC)
It is at present written on the page that dt=dt' is not valid at high speed (time dilation). This is so poorly written. It is not valid AT ALL since Relativity theory, but can be neglected in usual calculations, because of extremely small differences in results. Yet, there is ALWAYS a difference, even at low speed. This is a mistake that propagate everywhere the concept that Relativity is only a "high speed theory". It is not. It's a change in paradigm, whatever the speed you consider. Newton theory became just an approximation of Relativity theory. ( talk) 13:53, 5 August 2014 (UTC) please correct this.