Talk:Centrifugal force (rotating reference frame)/Archive 13

"crank rant"
The following was commented out:
 * The whirling table is a lab experiment, and standing there watching the table you have a detached viewpoint. It seems pretty much arbitrary whether to deal with centripetal force or centrifugal force. But if you were the bead, not the lab observer, and if you wanted to stay at a particular position on the rod, the centrifugal force would be how you looked at things. Centrifugal force would be pushing you around. Maybe the centripetal interpretation would come to you later, but not while you were coping with matters. Centrifugal force is not just mathematics.

The purpose of this observation was to be clear that in some situations (e.g. for the bead) centrifugal force is a real phenomena, and not something easily dismissed as a question of mathematical convenience.

I'd like to re-insert it, or some rewording of the comment. Brews ohare (talk) 19:00, 28 December 2008 (UTC)


 * If you could rewrite it to sound encyclopedic, and base it on a source, it might turn into something useful. As it stands, it really gives no help in interpreting what is meant by how the force relates to "fictional", which is what the force really is in this situation.  And literal, centripal force is what's pushing you "around", and centrigual force is what you feel trying to prevent you from going "around".  And it's unclear what the "not just mathematics" in meant to mean; is it just "mathematical physics" then?  Dicklyon (talk) 19:53, 28 December 2008 (UTC)

Proposal for a shortened section on planetary orbits
This very short paragraph should take the place of the existing section.

Centrifugal force arises in planetary orbits. The radial planetary orbital equation,


 * $$ \ddot r = -G(M + m)/r^{2} + l^{2}/r^{3}$$

can be solved to show that planetary orbits are either ellipses, parabolae, or hyperbolae. See Kepler Problem. The inverse cube law term on the right hand side of the equation is the centrifugal acceleration.

If there are no objections, I'll go ahead and replace the old section with this shortened section. David Tombe (talk) 20:38, 14 April 2009 (UTC)


 * This is wrong, as you have been told many times. $$\ddot r$$ is not an acceleration, and the corrections for taking differentials in the non-linear cylindrical coordinate system have nothing to do with centrifugal forces. –Henning Makholm (talk) 21:27, 14 April 2009 (UTC)

Henning, It's equation 3-12 in Goldstein. It's absolutely correct. I've used it many times. In fact, for you to boldly state that this equation is wrong shows just how little you know about this topic. Let me remind you of what you said this time last year. You said,


 * 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)

By denying the planetary orbital equation, you have clearly exposed the fact that it is you that doesn't understand the first thing about this article's subject. And it was largely your lack of understanding of the subject, and the fact that everybody decided to support you, that led to this prolonged argument.

Now the other editors here are not agreeing with you on what you have said. Their argument with me is not over the substance of planetary orbital theory, but rather over terminologies. It will now be interesting to watch and see whether or not they will change sides. Will they try and pretend that they are in agreement with you? It will be interesting to watch. David Tombe (talk) 16:35, 15 April 2009 (UTC)


 * I don't think he's denying the equation; just your interpretation. In particular, the second derivative of r is not an acceleration, since r is not a position in an inertial frame. Dicklyon (talk) 19:00, 15 April 2009 (UTC)

Dick, Well I'll look forward to hearing his interpretation of the equation. I interpret it as the radial planetary orbital equation. And it's quite ridiculous to say that the second derivative of r is not an acceleration. Of course it's an acceleration. Gravity is an acceleration so how could we have that equation at all if the left hand side was not also an acceleration? And it's also ridiculous to say that r is not a position in an inertial frame when it is the position variable in the gravitational term. The equation is on the table. Are you now trying to deny the reality of all the terms in it? David Tombe (talk) 19:49, 15 April 2009 (UTC)


 * "it's quite ridiculous to say that the second derivative of r is not an acceleration"


 * That has always been the crux of our differences (that is, between you and everyone else). The position variable r is a coordinate in an accelerating frame; therefore its second derivative is not itself an acceleration.  Gravity can be considered an acceleration, or a force; nobody is going to argue there, I expect.  As I've said many times, the equation is fine; the terms can be interpreted as pseudo-accelerations or pseudo-forces.  Centrifugal force in a pseudo force that exists only because of the accelerating frame that you're in; in an inertial frame, the only force on the planet is from gravity.  It's just a matter of what words you put on things.   Dicklyon (talk) 23:58, 15 April 2009 (UTC)

Dick, nowhere in the analysis of planetary orbits are rotating frames of reference involved. Planetary orbital theory does not need to use rotating frames of reference. Goldstein neither mentions rotating frames nor fictitious forces. And how can you have an equation in which some of the terms are accelerations and others not? The variable r is the radial distance. And the argument between myself and others has been different depending on who those others are. In your case, we are agreed in substance but you don't seem to be able to accept that the terms are real. In the case of Henning Makholm, he doesn't even agree with the planetary orbital equation and he wants to replace that section with a simple circular motion example. Simple circular motion examples have been the cause of alot of the trouble because the equality masks the fact that centripetal force and centrifugal force are two different quantities. David Tombe (talk) 00:11, 16 April 2009 (UTC)


 * The position r is measured along a direction that rotates with the planet. That is, it's a coordinate in an accelerating (rotating) frame.  If you cant to think of it as just radial distance in an inertial frame, that's fine, too, but then where do you get the idea that the second-derivative of a radial coordinate can be considered to be an acceleration?  Dicklyon (talk) 00:15, 16 April 2009 (UTC)

Dick, when the second derivative of the radial distance arises due to gravity you seem to have no qualms at all about calling it radial acceleration. But when it is induced by transverse motion as is the case with centrifugal force, you immediately deny that it could possibly be an acceleration. You have an outward radial force yielded by the expression mrω^2 and you are happy enough to call it centrifugal force, yet you insist that it is only a pseudo-force. Why? What puts these kinds of notions into your head? You certainly didn't read it in Goldstein's.

What I'll do is, I'll put the proposed shortened section in and I'll call the inverse cube law term 'centrifugal force'. I will then watch to see what extras that you add to qualify the name.David Tombe (talk) 00:21, 16 April 2009 (UTC)


 * Please don't make up mischaracterizations of my position. I never consider the second derivative of r measured in a rotating frame to be an acceleration.  In particular, in circular orbit, r is constant, yet the acceleration of gravity, which is real, is nonzero; there's no contradiction here; an acceleration orthogonal to the direction of r bends the path, but leaves r unchanged; r is not the acceleration.  Dicklyon (talk) 00:38, 16 April 2009 (UTC)

Dick, the term on the left hand side is either an acceleration or it isn't. If it is an acceleration in relation to the gravitational term on the left hand side, then it must also be an acceleration in relation to the centrifugal term. David Tombe (talk) 09:00, 16 April 2009 (UTC)

Attempt at shortening
As well intentioned as the edits were that inflated that section, I have to agree with the others that it does seem to delve too deeply into details better covered elsewhere. Might I suggest the following for the section, including renaming the section Central forces


 * Centrifugal force can often arise in the analysis of orbital motion and, more generally, of motion in a central-force field. The symmetry of a central force lends itself to a description in polar coordinates. Thus, the dynamics of a mass, m, in a central-force field, expressed using Newton's second law of motion, becomes:
 * $$F(r)\hat r=m((\ddot r-r\dot\theta^2)\hat r+(r\ddot\theta+2\dot r\dot\theta)\hat\theta)$$
 * where F(r) is the central force.
 * Because of the conservation of angular momentum and the absence of a net force in the azimuthal direction, the angular momentum, L, remains constant. This allows the radial component of this equation to be expressed solely with respect of the radial coordinate, r, and the angular momentum, yielding the radial equation:
 * $$m\ddot r-\frac{L^2}{mr^3}=F(r)$$.
 * The $$-L^2/mr^3$$ term in the radial acceleration is often called the centripetal acceleration.(Taylor,pp.29 & 359)


 * The equations of motion for r that result from this are the same that would arise from a particle in a fictitious one-dimensional scenario under the influence of a force:(Goldstein, Ch 3)
 * $$F'(r)=F(r)+\frac{L^2}{mr^3}$$
 * where the additional term added to the central force is called the centrifugal force. For the one-dimensional scenario, the radial equation then becomes:
 * $$m\ddot r=F'(r)=\frac{L^2}{mr^3}+F(r)$$.
 * Expressing the radial equation in this way physically corresponds to describing the dynamics within a non-inertial frame that co-rotates with the particle.(Tatum)(Whiting) Thus, the centrifugal force is unnecessary when describing the motion in the inertial frame; the influence ascribed to this fictitious force in the rotating frame is expressed by the centripetal acceleration term within the radial acceleration in the inertial frame.(Taylor,pp.358-359)(Goldstein(2002),pp.176) When the angular velocity of the co-rotating frame is not constant, such as for elliptical and unbound orbits in orbital mechanics, other fictitious forces - the Coriolis force and the Euler force - will arise but can be ignored since they will cancel each other.(Whiting)

I apologize for short-handing the references, but I wanted people to be able to see them rather then hiding them in the ref-tags. Taylor, Tatum, and Goldstein are already in the article. The Whiting article is the one I mentioned above. Certainly this needs refinement, but I think that it covers in a more succinct and focused fashion the basic points that the current section is trying to convey. --FyzixFighter (talk) 05:23, 16 April 2009 (UTC)


 * I think that looks great; well explained and not too long. Dicklyon (talk) 06:36, 16 April 2009 (UTC)

An underlying problem here is that terminology is not uniform in all areas of mechanics. A very basic part of mechanics deals with inertial frames of reference and the central role of fictitious forces which appear in noninertial frames but not in inertial frames. If the words centrifugal and centripetal are thrown around too loosely, this point is obscured. Another important part of mechanics is Lagrangian mechanics where generalized forces appear, and inertial frames fall into the background. The Lagrangian approach talks of generalized forces and in this framework $$\ddot r $$ is called often an acceleration (where "generalized" acceleration is really meant). That causes problems when, like David, the notion is used as though it applied to Newtonian accelerations that relate to real forces. Brews ohare (talk) 06:51, 16 April 2009 (UTC)


 * Brews, I would prefer the euphemisms which you used to describe the centrifugal term, than any attempts to call it the centripetal force. I can see that we are heading from bad to worse. David Tombe (talk) 09:12, 16 April 2009 (UTC)


 * FyzixFighter, That had all the potential of being a very good proposal. But how on Earth did you conclude that the inverse cube law term is a centripetal force? The centripetal force is already in the equation. The inverse cube law term acts outwards. You have then acknowledged that it is the centrifugal force but only in the fictitious one-dimensional equivalent problem. There is something seriously wrong here. How can a centripetal force in one equation suddenly become a centrifugal force in another equation which looks exactly the same? David Tombe (talk) 09:08, 16 April 2009 (UTC)

Next revision
Okay - here's a another revision taking into account some of Brews' comments. Particularly I've removed use of "centripetal".

Central forces


 * Centrifugal force can often arise in the analysis of orbital motion and, more generally, in the description of motion in a central-force field. The dynamics of a mass, m, in a central-force field, expressed using Newton's second law of motion, becomes (using polar coordinates):
 * $$F(r)\hat r=m((\ddot r-r\dot\theta^2)\hat r+(r\ddot\theta+2\dot r\dot\theta)\hat\theta)$$
 * where F(r) is the central force.
 * Looking at just the radial component of this vector equation gives us
 * $$m(\ddot r-r\dot\theta^2)=F(r)$$.
 * Moving the $$r\dot\theta^2$$ term in the radial acceleration to the other side of the equation allows the radial equation to be rewritten in the form:
 * $$m\ddot r=F(r)+mr\dot\theta^2$$.
 * From this it is easy to see that the equation of motion for r is the same as that for a mass in a fictitious one-dimensional scenario under the influence of the central force and an additional radially outward force of magnitude $$mr\dot\theta^2$$.(Goldstein) It is also customary when writing the radial equation to use the conservation of angular momentum such that the radial equation becomes
 * $$m\ddot r=F(r)+\frac{L^2}{mr^3}$$
 * where L is the angular momentum. This eliminates $$\dot\theta$$ from the radial equation and gives a differential equation containing only a single time-dependent variable.
 * Expressing the radial equation in this way for the fictitious 1D case physically corresponds to describing the dynamics of the 2D system within a non-inertial frame that co-rotates with the particle.(Tatum)(Whiting) In this frame $$\Omega=\dot\theta$$, and the magnitude of the additional force in the 1D case can be expressed as $$mr\Omega^2$$, the centrifugal force for the rotating frame. However, the centrifugal force is unnecessary when describing the motion in the inertial frame; the influence ascribed to this fictitious force in the rotating frame is expressed by the $$-r\dot\theta^2$$ term within the radial acceleration in the inertial frame.(Taylor,pp.358-359)(Goldstein(2002),pp.176) When the angular velocity of the co-rotating frame is not constant, such as for elliptical and unbound orbits in orbital mechanics, other fictitious forces - the Coriolis force and the Euler force - will arise but can be ignored since they will cancel each other.(Whiting)

Version 2 comments
Thoughts? --FyzixFighter (talk) 20:16, 17 April 2009 (UTC)


 * Why not also include the equation with the L in it? Dicklyon (talk) 23:40, 17 April 2009 (UTC)
 * Done. --FyzixFighter (talk) 02:33, 18 April 2009 (UTC)


 * It might be useful to mention that the conservation of L follows from solving the theta part of the first equation. This might help readers who get confused trying to figure out what happened to this term. Also, I would postpone talking about a 1D fictitious equation, until you have eliminated thetadot in favour of L, since as long as the equation depends on theta is is not really 1D.


 * Generally, I think this proposal is much of an improvement over the current section, which (no offence to Brews) drifts way of the focus of the article. (TimothyRias (talk) 12:48, 22 April 2009 (UTC))

Balls and strings
Hi David: It seems the example under discussion is now two balls whirling about their centroid, held by a string, gravity not in the picture. You say the tension in the string is due to a real outward force, which the tension in the string resists, resulting in the balls' continuing in circular motion.

That view is that of an observer in the co-rotating frame. In that frame, which rotates with the balls, of course the balls don't appear to move at all. However, the observer can see that the string is under tension. If he applies Newton's law, this tension would draw the balls together. However, they are not moving toward each other. Hence, there must be another force, the centrifugal force, driving them apart.

Would you see it that way? Brews ohare (talk) 19:24, 20 April 2009 (UTC)


 * Brews, I could combine every single issue here into one case scenario. Consider two balls in mutual transverse motion. Their gravitational attraction is very small. Hence the centrifugal force dominates and we will have a hyperbolic orbit.


 * Now attach a string between the two balls. The centrifugal force acting on the balls will cause the string to be pulled taut.The tension that will now be induced in the string will supply a reactive inward centripetal force on top of the already existing, but very weak gravitational force. The result will now be mutual circular motion about a common centre of mass.


 * There is no need to involve rotating frames of reference. In this example we can see the centrifugal force acting on the balls as per the planetary orbital equation. It is indeed the very same centrifugal force that would be acting if we inserted a rotating frame of reference around it, but we don't need to do that. The balls then transmit this effect to the string. This is the 'knock on' effect that the editors here have been calling 'reactive centrifugal force'. But as you can see, it is not reactive. It is pro-active.


 * Dick above acknowledges the reality of the 'knock on' effect, but he calls it 'reactive centrifugal force' and thinks that it should be dealt with in a separate article. Dick also acknowledges the centrifugal force that acts directly on the balls, but he thinks that it is only fictitious.


 * Can you not now see that what is essentially one single and straightforward topic, has been fragmented due to a number of common misunderstandings? It's like as if because they learned the modern topic of rotating frames of reference and the concept of 'fictitious forces' that they cannot accept any evidence that the concept of centrifugal force might be real and that it doesn't need to involve rotating frames of reference. David Tombe (talk) 23:43, 20 April 2009 (UTC)


 * What do you mean by "only fictitious"? "Fictitious" is not a perjorative.  But I'm getting tired to trying to deal with your misinterpretations and misrepresentations of what I've said, so I'll leave alone, like I said a few times that I would. Dicklyon (talk) 23:53, 20 April 2009 (UTC)

Dick, Then you could perhaps explain what you do mean by 'fictitious'. This so-called fictitious centrifugal force causes the so-called reactive centrifugal. And in your books, the former can only be viewed in a rotating frame of reference, whereas the latter can be felt in all frames of reference. Something is clearly wrong. Can we not tidy the whole matter up and have it simply that the "outward centrifugal force on the balls pulls on the string"? Why all the extra semantics and the need to insert a frame of reference around the balls? David Tombe (talk) 10:26, 21 April 2009 (UTC)


 * "Fictitious" simply means induced by the rotating frame of reference, and not present in an inertial frame. Nothing is wrong.  There is not outward centrifugal force on the ball.  The only force on the ball is the inward force that accelerates the ball into a circular motion.  The centrifugal force is on the string, since the string is pulled outward in reaction to the force it is putting on the ball.  There's no other outward force, except in a co-rotating or fictitious 1D system where the ball appears to be standing still with a fictitious centrifugal force balancing the string's centripetal force.  Dicklyon (talk) 16:52, 21 April 2009 (UTC)

Dick, So what causes the outward pull on the string in the inertial frame? The centripetal force only exists when the string goes taut. What causes the string to go taut in the inertial frame?

Check out the problem number 8.23 at the end of chapter 8 in Taylor. It cites the equation,


 * $$ f(r)= -k/r^{2} + l^{2}/r^{3} $$

It states that the solution is a conic section. What is the outward inverse cube law force in this equation? Is it any less real that in the inward inverse square law force of gravity? David Tombe (talk) 17:41, 21 April 2009 (UTC)


 * Let's stop playing this game. Your questions have all been answered multiple times. Dicklyon (talk) 21:36, 21 April 2009 (UTC)

Dick, the key questions have never been answered.

(1) The gravity force is an inward inverse square law force, and the centrifugal force is an outward inverse cube law force. The two different power laws allow for a stability node, and the equation which I have just written above, copied out of Taylor, solves to the Keplerian conic solution. In a Keplerian orbit, both of these two forces are acting in the radial direction, and that radial direction rotates equally for both of the two forces. You haven't told me what it is about the centrifugal force that makes it fictitious, whereas the gravity force is real. You have failed to explain what the difference is between the two forces. You have claimed that centrifugal force is fictitious because the radial vector is rotating, but so is it also for the gravity force. So what is the difference?


 * No, fictitious applies only to the one that is not present in an inertial frame. That's what it means.

(2) You have also failed to explain how a so-called fictitious force acting on an object can only be viewed in a rotating frame of reference, yet when that object is attached to a string, it can pull the string taut and give rise to a centrifugal force which is real, and which can be viewed in any frame of reference.


 * It's explained above; if you don't understand the idea of which forces act in which direction on which object, say so.

(3)You have also tried to claim that the real (so-called reactive) centrifugal force is a reaction to the inward centripetal force, but you must be fully aware that the tension in the string which causes the centripetal force, only exists in the first place because of the outward centrifugal force, which you are claiming to be fictitious. So clearly it is you that has got the topic all mixed up in your mind. The centrifugal force comes first in the stretched string scenario. You have managed to get cause and effect totally reversed. You have ignored the role of the so-called fictitious centrifugal force and then claimed that a real so-called reactive centrifugal force exists as a reaction to the inward centripetal force.


 * Cause and effect is slippery stuff (does the tension in the string cause the ball to move in a curved path? or does swinging the ball around cause the tension in the string?), but it's OK with me if you want to say that the tension in the string is caused by the outward centrifugal force.  That's a force on the string; the force on the ball is only inward, which is why it moves in a curved path; except in the co-rotating frame, where there's an outward force, the fictitious centrifugal force, which when balanced keeps the radius constant.

You have created two different centrifugal forces out of one, and you having been switching them on and off as needs be. You are not motivated by a desire to understand the topic. You are only motivated by the desire to protect your original prejudice which is based on the superficial teachings in modern textbooks regarding rotating frames of reference. You have put that teaching above natural reasoning and so you won't even entertain other sources or references that contradict it. David Tombe (talk) 23:16, 21 April 2009 (UTC)


 * You have to switch when you switch from the force on the ball in the rotating frame to the real tension in the string. You can call them the same thing, as long as you understand what each actually is.  They're equal when the ball moves in a circle, and as your equations show, not otherwise.


 * So you see, it really has all been answered, many times. Just like Goldstein, where eq. 3-22 is surrounded by text that explains "the familiar centrifugal force" in terms of a "fictitious one-dimensional problem" and a "fictitious potential energy."  And your favorite, eq. 3-12, "the Lagrange equation, for the coordinate r", is perfectly valid, but nothing around it supports your strange interpretations.  Give it up.


 * Dicklyon (talk) 05:40, 22 April 2009 (UTC)

Timothy Dick, we had already established that a centrifugal force acts on the ball. The argument was merely about whether or not it was fictitious. We had also established that the ball then exerts a force on the string. My point was "How can the former force be fictitious and only observed in a rotating frame when the effect which it causes on the string is real and can be observed in any frame?" My argument is twofold,

(1) Both of the effects described above, ie. the force on the ball, and the effect which it transmits to the string are real and can be observed in any frame.

(2) The latter effect, which causes the tension in the string, is not a reacting to the centripetal force. It actually causes the centripetal force. The centripetal force is a reaction. David Tombe (talk) 13:04, 22 April 2009 (UTC)


 * David, I think the only thing we've already estabished is that you persist in misrepresenting what we've already established. Dicklyon (talk) 18:13, 22 April 2009 (UTC)


 * David, I don't know why you think you are responding to me, but I'm not getting back in discussion about physics with you. I'll just concentrate on actually making this a better article. (TimothyRias (talk) 13:15, 22 April 2009 (UTC))

Timothy, that's good that you are going to concentrate on improving the article. If you had read all the stuff above, you would have seen that that's exactly what I had set out to do. I was the one who first stated that while Brews's planetary orbital section was technically correct, that it needed drastically reduced in size in order to focus on the centrifugal force term. FyzixFighter then tried to sabotage my efforts by suggesting something similar to what I had suggested, but he included a very serious distortion whereby he tried to tell us all that the centrifugal force was actually the centripetal force. Dick immediately praised FyzixFighter's suggestion despite the fact that it contained that enormous error.

There might be some hope of improving this article when certain editors start to think for themselves instead of constantly shifting their position so as to be on the same side as the crowd. You obviously didn't notice FyzixFighter's error, which he has since tried to wriggle out of. If you had noticed it, you wouldn't have made those comments above. FyzixFighter's suggestion was not an improvement. David Tombe (talk) 18:06, 22 April 2009 (UTC)

Section break
Dick, we have established that there is an outward centrifugal force acting on the ball. It is the inverse cube law force as per equation 3-12. You are telling me that it is fictitious, yet nowhere in Goldstein does it say that it is fictitious in relation to the real radial equation at 3-11/3-12. We have also established that this force can pull on a string. What we have not established is (1) why these two aspects of the same phenomenon have to be in two completely separate wikipedia articles, (2) why the former aspect is fictitious, whereas the latter aspect is real, and (3) why the former can only be viewed in a rotating frame of reference, whereas the latter can be viewed in all frames, and (4) why you are suggesting that the latter effect is a reaction to the centripetal force when it clearly isn't. I am not misrepresenting anything. You are ducking these crucial points. David Tombe (talk) 19:37, 22 April 2009 (UTC)


 * David, there is no outward force acting on the ball; stop saying we have established things contrary to fact. The force on the ball is inward, which is why it moves in a circle.  If you make a co-rotating system where the ball appears to stand still, then there appears to be an outward force balancing the pull of the string.  That's all. Dicklyon (talk) 02:36, 23 April 2009 (UTC)

Dick, so what then happened to the centrifugal term of the planetary orbital equation? The two balls are the same as two planets for that purpose. The attached string gives an additional centripetal force on top of the already existing gravity. But that centrifugal force from equation 3-11 will still be present. It's the force which pulls the string taut. How can you think that the centrifugal force of equation 3-11 has disappeared and been replaced by a new and real centrifugal force, which you wrongly see as being a reaction to the centripetal force?

Can you not see that there is simply one centrifugal force, and that it is real? David Tombe (talk) 09:11, 23 April 2009 (UTC)


 * Hi David: I seem to recall the underlying difficulty in our discussions is that you do not accept the concept that a curved path in an inertial frame requires a force, which is in accord with Newton's law that with no force applied, a particle moves in a straight line at constant velocity. The hooker in this, as Einstein pointed out, and as you undoubtedly are aware, is that the argument is circular: one can see straight line paths in any reference frame, and one cannot establish absence of a force without invoking the straight line path. (you don't know you are seeing a force-free behavior unless you see a straight-line motion, and vice versa).
 * The modern escape from all this is to focus upon transformation properties between frames: some frames obtain straight line paths with simpler force laws than do others: the class of all frames where simple laws obtain become privileged. I am not sure that you are aware of this conventional viewpoint.
 * As an example, we can mull over how one decides whether the universe rotates. The approach is basically like this: assume it rotates. Formulate your observations using the rotation rate as a parameter. Then vary the parameter to get the best fit to observations. If it results that non-zero rotation fits better - then the universe rotates. We don't make the assumption that the simple view is a stationary universe, but make the assumption that the simple view leads to the simplest physical laws.
 * As a mind-blowing example, look at how matter rotates in a galaxy. It doesn't satisfy known physical law. So we have two choices (at least): postulate new laws (Modified Newtonian Dynamics) or postulate dark matter, a form of matter totally unrelated to any known matter and not made up of gluons or leptons or quarks etc. Whew!
 * Let's look at circular motion: in some frames the motion requires a centrifugal force and a second force (e.g. a string under tension); in others it doesn't. So the privileged frame is the one where centrifugal force never comes up, and string tension alone is all that is needed.
 * So here is where matters stand, I'd say: orthodoxy says a curved path requires centripetal force, and that is it. It is a one-force viewpoint, and kinematics (that is, the shape of the orbit and the rate of its transversal) defines what forces are needed. Having discovered that Jupiter wobbles, go look for Neptune. Of course, you have to be in a privileged frame; otherwise you get "extra" forces: Jupiter has a wobble, but there is no Neptune, so call in the "extra forces".
 * It may evolve that this view is very fundamentally wrong. There are evidences of cracks in the theoretical structure. But we aren't there yet. From a Wiki viewpoint, only a sidebar on these reservations is appropriate and it has to labeled speculative and it has to be supported by references to published iconoclasm. Brews ohare (talk) 00:05, 24 April 2009 (UTC)

Brews, It does seem that most modern textbooks are pushing the idea that centrifugal force is something which can only be observed in a rotating frame of reference. Yet if you look at problem 8-23 at the end of chapter 8 in Taylor, you will see the entire dilemma exposed in a nutshell. Problem 8-23 is in a section entitled Kepler's laws. Problem 8-23 begins by citing the key equation in this entire controversy,


 * $$ f(r)= -k/r^{2} + l^{2}/r^{3} $$

This equation is the radial planetary orbital equation and it solves to give a conic section. As you can see, it contains an inward inverse square law term and an outward inverse cube law term. The two different power laws are the basis of the orbital stability. Nowhere are rotating frames of reference or fictitious forces mentioned. We know that the radial direction will be rotating, but that applies equally to the gravitational term and the centrifugal term since they rotate equally. It is wrong therefore to suggest that the centrifugal term can only be observed in a rotating frame of reference, whereas gravity can be observed in any frame.

The key difference between the gravity term and the centrifugal term is the fact that the centrifugal term is induced by actual transverse motion. That is not the same thing as only being observable in a rotating frame of reference. And it is this subtle point which lies at the core of the entire dispute. That outward inverse cube law term is real and it can pull a string taut. What we have been witnessing on these pages is an attempt to mask this reality. There have been a number of methods involved,

(1) To manufacture a brand new centrifugal force to account for the real effect which the outward inverse cube law term causes, and then to make a special page for it on wikipedia.

(2) To further confuse this new centrifugal force by giving it the misnomer 'reactive centrifugal force'. Anybody looking closely at the situation can see that it is the centripetal force which is the reaction and not the centrifugal force. The centripetal force doesn't come about until the string is taut. We need the centrifugal force first, in order to make the string go taut.

(3) To deny the planetary orbital equation altogether. That one was tried very recently by an editor who boldly stated that the planetary orbital equation was wrong, and then went on to suggest replacing the planetary orbital section with an example involving simple circular motion.

(4) If the planetary orbital equation is accepted, another method is to hide the centrifugal force term inside a general radial vector box. That one has been tried recently by two different editors.

(5) To twist the contents of reliable sources so as to apply the term 'fictitious' as is stated in some sections, to other sections which don't use the term in the context in question. 'Fictitious force' is seldom used in connection with planetary orbits, although I have no doubt that there will be some modern exceptions, written by authors who are drunk on the concept of frames of reference.

(6) To flee into Cartesian coordinates for centrifugal force and then deny its existence, while quite happily continuing to use polar coordinates for gravity and other centripetal forces. David Tombe (talk) 10:57, 24 April 2009 (UTC)


 * Hi David: It appears that you do not think your viewpoint radical. You can prevail; it's just a question of convincing Wiki editors that they have misinterpreted Newton's methods. That is not my opinion: you might consider some examples other than Kepler's laws.
 * In fact, in a general curved path, even within the Kepler problem, the centrifugal force experienced by a comet (say) is v2/ρ, with ρ = instantaneous center of curvature, and v the instantaneous tangential velocity. That is not the polar coordinate term $$r {\dot \theta}^2$$ because $$r {\dot \theta}$$ is not the velocity tangential to the path and r is not ρ. (Coordinate r points from the origin to the path, which is not in the direction instantaneously perpendicular to the path.) Brews ohare (talk) 12:52, 24 April 2009 (UTC)

An outline for the article
Brews, I had always been using the term 'tangential' in the astronomical and trigonometrical sense, which means perpendicular to the radial vector. On reflection, the term 'transverse' might be less ambiguous, because there is another meaning for tangential which is 'along the direction of the motion'.

Ultimately what I was suggesting was that the introduction to this article simply states that centrifugal force is an outward force that arises in connection with rotation. That could then be followed by a section which states that nowadays centrifugal force is introduced as a fictitious force which arises in connection with rotating frames of reference. Finally we could have a short section on planetary orbits which merely points out the centrifugal term in the radial equation. In your existing planetary orbital section I can't find any errors as such, but the focal point is very obscured. You have played down the centrifugal term and described it in terms of what you believe it not to be. In actual fact, I'm sure that you will eventually realize that centrifugal force does have a physical cause, even if that cause can't be written in wikipedia. Meanwhile, I think it should just be described as 'the familiar centrifugal force' as per Goldstein. Dick keeps trying to say that Goldstein is only using that name in connection with the fictitious 1-D problem, but that is not true. Goldstein refers to it as the familiar centrifugal force in relation to the $$r {\dot \theta}^2$$ format of equation 3-11. That format cannot possibly be a one dimensional format because it contains the angular velocity term. It's only when the equation is written with centrifugal force in the inverse cube law format that the equation is the same as in the case of the one dimensional problem, because we have then reduced the equation to one variable. David Tombe (talk) 19:38, 24 April 2009 (UTC)


 * The article does state your initial sentence already.
 * The point about the views of nowadays also is present.
 * The role of centrifugal force in the planetary motions is tougher to do. For the case of two bodies, the standard evolution is to reduce the problem to a one-body problem, as discussed here and in two-body problem. That process does not involve centrifugal force: it is just an introduction of Jacobi coordinates. Next the single-particle solutions are found. That involves primarily the use of conservation of angular momentum. If angular momentum is invoked to reduce the problem to a one-dimensional equation, we're already in the situation you want to avoid. How would you proceed? Brews ohare (talk) 21:52, 24 April 2009 (UTC)
 * I am further confused by your remark that you wish to call $$r\dot{\theta}^2$$ the centrifugal force, and not invoke v2/ρ. To me that means that the term "centrifugal force" becomes stripped of physical content and becomes instead only a designator of a particular variable combination in polar coordinates: hardly something to lose sleep over. Might as well call it the θ-dot term. Brews ohare (talk) 23:33, 24 April 2009 (UTC)

Brews, at the end of the day, the $$r\dot{\theta}^2$$ term, the v2/ρ term, and the inverse cube law term are all different ways of expressing the outward pressure effect which is induced by absolute rotation. That effect is 'centrifugal force' and it is real. It can pull a string taut. That's all I have been trying to say. There is clearly no consensus to view the matter in such simple terms and to condense this topic into one simplified article because there is a generation who are totally averse to any recognition of the reality of centrifugal force.

The radial equation and the transverse equation contain alot of information between them. They contain the centrifugal force and the Coriolis force, both of which are real. We can observe the Coriolis force in non-circular planetary orbits and in all vortex phenomena. It is the transverse deflection of any radial motion. That is why this discussion spills over into the Coriolis force page and the Kepler's law page. Unfortuntely the Coriolis force page is beyond repair because there are too many sources which are propagating the error that the Coriolis force lies in the inertial effect. The Coriolis force in truth lies in the conservation of angular momentum. It lies in the transverse planetary orbital equation. The inertial effect of the Earth's rotation is something different and it sets the initial direction of the angular momentum.

I can direct you as to how to simplify the planetary orbital section, but I can't get involved in any of the sections about rotating frames of reference, because I only agree with those analyses in situations that involve co-rotation. As regards the planatery orbital equation, we don't even need to deal with the reduced one body equation. We can simply sate the radial equation as per 3-11 in Goldstein and say that the outward term is the familiar centrifugal force. David Tombe (talk) 12:00, 25 April 2009 (UTC)

Diatribe
I don't understand the justification for the self-admitted "diatribe" by Brews here:. If there's no source that says this interpretation is "less obvious", we shouldn't be saying so either.

I recommend we get back to the short version proposed by FyzixFighter. The long stuff by Brews is way too complex, off-topic, and interpretative. I think we can get to a short version that is accepable to everyone to who understands the meanings of the words used in sources, while keeping it simple.

After we get there, we can get back to never-ending discussions about what "fictitious" means and whether a ball on a string has an outward force on it. Any objections? Dicklyon (talk) 15:12, 25 April 2009 (UTC)


 * Dick, I object on the grounds that FyzixFighter's suggestion contained a gross inaccuracy. FyzixFighter's suggestion was a warped version of my suggestion. He changed the centrifugal force into a centripetal force.


 * At any rate, there is not much hope for this article while people like Wolfkeeper continue to mindlessly revert good faith edits. I am all for shortening the article. I have just removed alot of unnecessary chaf from the introduction, but Wolfkeeper in his normal tradition reverted it without discussing the matter. And the situation which we have here is that if I have an edit war, I will be blocked and Wolfkeeper will not be blocked. That was proved many times last summer. David Tombe (talk) 15:37, 25 April 2009 (UTC)


 * The "unnecessary chaff" you removed was the standard introductory phrase and the refernences; and you added an unsourced "conclusion". All without discussion.  What do you expect?  How is your edit distinguishable from run-of-the-mill vandalism?  Dicklyon (talk) 15:52, 25 April 2009 (UTC)

Dick, what was my unsourced conclusion? And have you got any sources which try to explain fictitious forces in terms of lack of interactions with other materials? Any source that I have ever seen simply states that fictitious forces are so-called because they don't exist in the inertial frame of reference. And why bother mentioning other fictitious forces in the introduction?

I don't intend to revert. I've made my point. I've shown you how the introduction needs to be simplified. My wording was carefully chosen to allow for the planetary orbital section which does not involve rotating frames of reference. I weighted the wording on the balance of most modern sources. I said that the modern tendency is to treat centrifugal force as a fictitious force which is observable from rotating frames of reference. I removed the row of sources because nobody is arguing with that point and it looks too much as if somebody is protesting too much.

Do you want to simplify the planetary orbital section or not? You can use FyzixFighter's model providing that you correct the gross error where he has turned the centrifugal force into a centripetal force. That will make it essentially the same as my original suggestion. David Tombe (talk) 17:23, 25 April 2009 (UTC)


 * Yes of course. Dicklyon (talk) 19:26, 25 April 2009 (UTC)

Diatribe again
Dick says: "I don't understand the justification for the self-admitted "diatribe" by Brews here: . If there's no source that says this interpretation is "less obvious", we shouldn't be saying so either."

I don't understand these observations. By justification, is the question as to what purpose the diatribe serves? Or is the question whether the diatribe provides only a personal opinion?

In the first interpretation, I'd say the entire planetary motion section should be deleted in its entirety: it serves no purpose in explaining what centrifugal force is or its role. This section is there to placate David Tombe, and as it is not serving that purpose it has no function.

In the second interpretation, the notion that v2/ρ is centrifugal force is perfectly documentable. For example: Olmsted says "centrifugal force is measured by the square of the velocity divided by the radius of the osculation circle". Check these out.

Given the v2/ρ form for centrifugal force,  the rω2 term in polar coordinates has absolutely no meaning outside of circular motion, where it just happens fortuitously that r=ρ and v = rω, and the whole discussion of this term and the usage of the name "centrifugal force" for this term has absolutely no standing in any other context than circular motion.

Circular motion examples already abound in the article, we don't need a more complicated example that drags in no new insight. Brews ohare (talk) 19:18, 25 April 2009 (UTC)


 * Placating David Tombe is neither an acceptable goal nor something that the section makes progress on. Let's replace it by a short section on planetary orbits based on Goldstein and Taylor and others; there's no reason not to mention the term that Goldstein calls "the familiar centrifugal force", and say that he calls it that, in the context of orbits that are not necessarily circular.  If you have sources that object to that usage or interpretation, we can mention those objections; but we can't mention your objection just because others do it differently. Dicklyon (talk) 19:33, 25 April 2009 (UTC)


 * I just checked your "osculating circle" references; that seems to be an obsolete concept, where "the centrifugal force of a particle" is determined by the particle's trajectory, rather than by a reference frame; like the current concept but with a reference frame rotating about the center of the osculating circle. That's not related to what Goldstein is talking about, which is simply a measurement of distance along the line between the bodies.  You can't refute Goldstein's concept by invoking a different concept.  I think we should consider making a unified article that neatly ties these various different interpretations of centrifugal force together, including the reaction force.  It seems very odd to have them in different articles as we do now, when they're just different conceptualizations of very related effects. Dicklyon (talk) 19:41, 25 April 2009 (UTC)

Dick: The terminology "osculating circle" is a bit dated, with the possible exception of differential geometry. However, the notions of "radius of curvature" and that centrifugal force is v2/ρ is anything but obsolete. Even within the limited purview of the planetary problem as formulated in the specific set-up of polar coordinates, ω2r has almost no relation to centrifugal force. Outside of polar coordinates, even within the planetary problem, ω2r has no bearing whatsoever upon centrifugal force, with the exception of circular motion.

Right, it is not what Goldstein is talking about. In his discussion of the ω2r term, Goldstein is not talking about a "concept" in the sense of some grand insight into centrifugal force. Rather, he is describing some math in words within a consciously narrow context. Even bringing up this minutiae in this article is opening the door to the entire mess we now are in, which is at bottom a lexicographer's debate over some peripheral usages of terminology, of no consequence to intuition about centrifugal force, and certainly no help to this article.

So, I am not engaged in refuting Goldstein's concept, but in placing it in perspective as an idea devoid of generality and of limited intuitive value. Brews ohare (talk) 20:33, 25 April 2009 (UTC)


 * I'm not following you at all. My impression was that you view centrifugal force as something that results from the frame of reference; that's what Goldstein does, too, though less explicitly.  Now you're saying it's dependent on the radius of curvature of a path.  How does that relate?  Is the problem with Goldstein's approach just that the co-rotating frame's rate of rotation is not uniform, and that therefore there may be complications in using the usual formula for centrifugal force in a rotating frame?  Are you saying that Goldstein is in a minority of 1 in calling omega squared times r times m the centrifugal force on a planet in a fictitious 1D formulation? Dicklyon (talk) 20:59, 25 April 2009 (UTC)


 * I don't think he's a minority of one. The context is very narrow however. If the 1-D problem is solved in a general case, the radius r becomes a function of time, for example, periodically moving back and forth through some line segment. If this motion is translated back into the 2-D single particle picture, the orbit might be elliptical, say, and the particle does not move at a constant rate, because at closer approach it has to go faster to keep up the same angular momentum, which is a constant of the motion. In such an elliptical path, what frame of reference will you pick to talk about centrifugal force?


 * I suppose one can pick the origin of coordinates where r = 0 and the particle then will exhibit a radial velocity and also an angular velocity. Then the problem is a bit more complex because Coriolis force as well as centrifugal force comes into play. The centrifugal force is then the ω2r term, as suggested, but what about the Coriolis term?


 * Alternatively, one can pick an origin at the instantaneous center of curvature rotating at the instantaneous rate. Then there is zero radial motion and there is no Coriolis force, but the centrifugal force is v2/ρ. That is the view if you live on the planet, so nature looks after finding your instantaneous frame for you. Translating this moving frame into the (r, θ) world is an act of masochism.


 * Question: does calling ω2r the "centrifugal force" convey any of this complexity, or add in any way to our understanding? Is there anything to be gained by entering into this morass? Brews ohare (talk) 21:20, 25 April 2009 (UTC)


 * That's kind of the point, that r doesn't have to be constant but can change under the given acceleration (difference of gravitatinal centripetal and the fictitious centrifugal forces in the co-rotating frame) so that you can work out ellipical and hyperbolic orbits and such. The Coriolis force is present, but since it accelerates the planet orthogonal to r it's not in the 1D equation.  The rotation rate of the co-rotating frame has to change so that at each instant it matches the theta dot.  The explanation in Taylor helps to understand Goldstein, I think.  Goldstein's fictitious 1D problem has its origin always at the other body (the sun); at any time t you can fix the origin and rotation rate to be constants and get the results he states, as Taylor shows.  I'm surprised you don't seem to have followed Goldstein's analysis at all.  Dicklyon (talk) 21:29, 25 April 2009 (UTC)

I gather that you feel that the discussion of centrifugal force from this perspective has value. It would be very different in form from what was here. Why don't you try to do it? I hope the goal of illuminating the nature of centrifugal force will remain paramount. Possibly one feature of this discussion will be the dependence of centrifugal force on the frame of reference? Brews ohare (talk) 21:38, 25 April 2009 (UTC)


 * Yes; I think the short section that FyzixFighter did was a good start, but not perfect. The whole article is about the CF being dependent on the frame of reference; this section will just be the application of that idea to non-circular orbits under central force.  We don't need to do out every detail, but rather should keep it short, referencing Goldstein and Taylor for detailed derivations. Dicklyon (talk) 21:49, 25 April 2009 (UTC)

Dick, you mean 'not perfect' in the sense that he tried to tell us that centrifugal force was centripetal force? I thought it had all the makings of a very well written reduction until I read the bit where he called the centrifugal force a 'centripetal force'. David Tombe (talk) 00:10, 26 April 2009 (UTC)

Comparison table
I enthusiastically oppose any attempt to combine the centrifugal force article with the reactive centrifugal force article. They are not aspects of the same thing, as the examples in the two articles clearly demonstrate and as the table below makes abundantly clear:

The bottom row of entries in the table are particularly telling.Brews ohare (talk) 20:47, 25 April 2009 (UTC)


 * The table looks reasonably sensible. Why not include it in an article on centrifugal force to help clarify the distinction between the two views? Dicklyon (talk) 20:59, 25 April 2009 (UTC)

The only distinction between the two aspects is that one is the centrifugal force which acts on an object as per the term in the radial planetary orbital equation. The other is the effect which that object then transmits to another object on contact. They can both be treated within the context of a rotating frame of reference if you feel you need to insert a frame of reference around the situation. But you don't have to involve a rotating frame of reference. It is quite voluntary. Centrifugal force is one subject. There is no need for two articles in wikipedia. David Tombe (talk) 00:07, 26 April 2009 (UTC)


 * It's not a matter of "on contact"; contact has nothing to do with it. And the "fictious centrifugal force" is zero in an inertial frame, so what you're saying isn't consistent with physics as we know it.  But I agree there's no need for two articles. Dicklyon (talk) 02:24, 26 April 2009 (UTC)

Brews, the table doesn't clearly demonstrate that they are not aspects of the same thing. Let's take one example. It states that the so-called reactive centrifugal force applies in any frame of reference. That is true. And what is it reacting to? It certainly isn't reacting to the centripetal force because the centripetal force doesn't come into existence until the other centrifugal force, as per the planetary orbital equation, causes either a tension or a pressure. You are saying that the latter is a fictitious force that is only observable in rotating frames of reference? Yet the latter (fictitious force) is the very thing which causes the former (reactive) effect which the table says can apply in any frame of reference? David Tombe (talk) 00:17, 26 April 2009 (UTC)


 * It's the reaction to the centripetal force, which has to be there to cause the object to move in a curved path. The force of the string makes the ball's path curve, and the reaction force from the ball's acceleration keeps the string under tension.  Some authors prefer to use the term "inertial force", but sometimes mix up whether they mean the force on the object the makes it curve or the force on the string, or both (they're equal when the path is circular).  Dicklyon (talk) 02:24, 26 April 2009 (UTC)

Dick, what makes the string go taut in the first place? There is no centripetal force (apart from the negligible gravity) until the string goes taut. So what makes the string go taut in the first place? It's the centrifugal force as per the planetary orbital equation. So clearly, the centrifugal force cannot be a reaction to the centripetal force.

Equation 3-11 in Goldstein,


 * $$m\ddot r-mr\dot\theta^2=f(r)$$

applies for any centripetal force. It doesn't matter whether the centripetal force, $$f(r)$$, is (1) gravity, (2) tension in a string, or (3) both. The centrifugal force term is an independent term which is not necessarily equal to the centripetal force term. Hence, the centrifugal force cannot be a reaction to the centripetal force in any circumstances whatsoever. David Tombe (talk) 12:26, 26 April 2009 (UTC)


 * David, for your first query, what makes the strings go taut, that depends on the setup; for example, if you have a limp string, starting with the ball inside the circle (defined by radius equal to string length) and moving in a straight line, the ball will at some point reach the circle, where the string will tighten and provide whatever force is needed to keep the ball from exiting the circle.


 * On your second point, it's very true. The centrifugal force that Goldstein defines in the 1D problem (distance r) is not equal to the reactive centrifugal force except in the case of circular motion, where that net f(r) is zero.  Dicklyon (talk) 14:51, 26 April 2009 (UTC)

Dick, Yes. So it is the outward centrifugal force which makes the string go taut. The centripetal force doesn't come about until the string is taut. And yes, the centrifugal force is only equal to the centripetal force in the special case of circular motion. Whoever drew up that comparison table was trying too hard to make a case for two different centrifugal forces.


 * But there are two different centrifugal forces in use here; the fictitious force of the rotating system and the reaction force to centripetal force. When you say "The centripetal force doesn't come about until the string is taut,", that's also true of the reaction force, the force the ball exerts on the string.  It's not true of the fictitious centrifugal force that you see in the co-rotating system even while the ball is moving in a straight line with slack string.  They're just different things, which is why Brews argues they should have separate articles.  But of course, they are also closely related, as in equal for the case of circular motion. Dicklyon (talk) 19:22, 26 April 2009 (UTC)

The most common argument that they put forward for having two different centrifugal forces is that the two centrifugal forces act on different bodies. Yes. Centrifugal force acts on body A. Body A contacts body B and transmits the effect. It's a very sophomoric argument and it's hardly a basis for two wikipedia pages. But I know that you, like myself, have been advocating a unified article, and I noted that you also stated that two aspects of the same overall effect is not a basis for having two pages on wikipedia.


 * Again, contact has nothing to do with it. There are two different conceptions of centrifugal force, they act on different bodies, and they have different values, and one is "fictitious" in the sense that it doesn't exist in an inertial frame.  It's not an unreasonable argument for different articles, nonetheless I agree that one article could cover the relationship better. Dicklyon (talk) 19:22, 26 April 2009 (UTC)


 * No. They both have the same value and the transmission of the effect from A to B can only be by contact. David Tombe (talk) 19:39, 26 April 2009 (UTC)

When we get a unified article, it will be easier to discuss the problem in its entirety. Two balls connected by a string involves every single aspect of the problem. It involves gravity, albeit negligible, but that allows us to contemplate the hyperbolic orbit. Then we add the string. The outward centrifugal force pulls the string taut. The induced tension in the string then augments the inward gravity force and converts the orbit to circular.


 * Yes, we could cover that. But we'd need to get you to accept that "the outward centrifugal force" of a ball moving in a straight line with a slack string attached is a fiction induced by a viewpoint (a rotating viewpoint from where the other end of the string in anchored, perhaps); there's no actual force acting on anything in that case, as should be crystal clear as the ball is moving a straight line (neglecting gravity). Dicklyon (talk) 19:22, 26 April 2009 (UTC)


 * How can it be a fiction if it pulls the string taut? David Tombe (talk) 19:43, 26 April 2009 (UTC)


 * What is it doing before the string pulls the ball into a curved path? Dicklyon (talk) 20:04, 26 April 2009 (UTC)


 * It's not truly fictitious. The force is real, but doesn't exist in the inertial reference frame. This is usually called a 'pseudoforce'. Gravity is also a pseudoforce; and if you are in an inertial reference frame, you feel no acceleration due to gravity either.- (User) Wolfkeeper (Talk) 20:22, 26 April 2009 (UTC)


 * This "real" versus "fictitious" thing is vacuous without definitions; fictitious is defined the same as pseudo as you use it; I'm not certain which one is more common, but both are commonly used for these forces that do not exist in an inertial frame, but rather come up in applying f = ma in a non-inertial frame. I'm not at all sure what "real" is supposed to mean here; it's all real in the defined sense.  As to which way to treat gravity, that depends on whether you mean inertial in the classical or the general relativity sense, doesn't it?  I think we're pretty much stick to classical here, so gravity would not be treated as a fictitious force, but rather as a force that's felt even in an inertial frame. Dicklyon (talk) 20:34, 26 April 2009 (UTC)


 * The word 'fictitious' means that something is completely and utterly made up; Sherlock Holmes is fictitious; but centrifugal force/effect have real measurable consequences; so the term 'pseudo-force' is accurate whereas fictitious force is a misnomer.- (User) Wolfkeeper (Talk) 22:03, 26 April 2009 (UTC)


 * If that's what it means, that maybe explains David's reluctance to accept it; perhaps it's unfortunate that this fairly standard terminology is a misnomer, as you call it, but since it's what's used in the field, we should use it, too; of course, we can say it's the same as pseudoforce, and use that preferentially if that helps. It doesn't change the meaning, but may change the negative reactions to it. Dicklyon (talk) 22:36, 26 April 2009 (UTC)

I can see that you clearly understand the issues. It's only a matter of fitting a coherent and simplified article around the references. David Tombe (talk) 19:04, 26 April 2009 (UTC)


 * Indeed. Dicklyon (talk) 19:22, 26 April 2009 (UTC)

Dick, I'll have to retract that now since it looks like you don't understand the issues after all. Let's concentrate on the bit when the string is being pulled taut. (See section 9 in the reference which I have just supplied). What is pulling the string taut? David Tombe (talk) 19:36, 26 April 2009 (UTC)


 * I don't see the reference you refer to; can you repeat it? You're going elliptical on me again...  Dicklyon (talk) 20:04, 26 April 2009 (UTC)


 * Dick, see section 9 in reference 23 on the main page. It's the reference that I inserted today.


 * For the record, that's this book, pp. 78–80 or so. That all looks reasonable to me.  The centrifugal force (an "apparent force" in the rotating frame, as opposed to "true forces" in inertial frames, as this book calls them) is obviously pulling the string taut, when you look in the co-rotating frame; in the inertial frame, the it's the reaction to the force with which the string is accelerating the balls.  Dicklyon (talk) 23:14, 26 April 2009 (UTC)


 * The centrifugal pseudoforce that appears in the equations of motion when you transform them to a rotating reference frame pulls it taut!!!!!!! Do you think we made this term up? If it's in the equation of motion, is it really fictitious? No! It's real physics.- (User) Wolfkeeper (Talk) 20:22, 26 April 2009 (UTC)


 * The other way to look at it, viewing in the inertial frame, is that the string is pulling against the inertia of the ball; when the string puts a force on the ball to move it in a circle, the string is pulled by the reaction to that force; in this view, the centrifugal force is the string tension, which exists only after the string comes tight, and it's equal to the centripetal force even if the string is stretchy. In the pseudoforce view, the centrifugal force is on the ball, even before the string is tight, and is not equal to, but often close to in balance with, the centripetal force; if the string is stretchy and the ball's radius is accelerating, they're not quite in balance; if the string's not tight yet, they're way out of balance, but the centrifugal force on the ball still exists while the ball is moving in a straight line, which is why its r is accelerating outward.  Dicklyon (talk) 20:34, 26 April 2009 (UTC)


 * You can certainly look at the same thing, either as inertia in a newtonian centre of mass frame, or as a pseudoforce in the rotating frame. But calling one 'real' and the other 'fictitious' confuses a lot of people like David Tombe, because you're using English words incorrectly. They ask 'If it's fictitious how can it change anything in the rotating reference frame?'; which is a good question; if it actually was fictitious it couldn't. But it's not, it's a misnomer.- (User) Wolfkeeper (Talk) 23:29, 26 April 2009 (UTC)

Dick, it strikes me that you are trying too hard to not see the centrifugal force. Let's go back to the stage where the string is still slack. We will have an outward centrifugal force acting on the ball, as per equation 3-11 in Goldstein. Wolfkeeper calls it a pseudo-force and acknowledges that it is real. So we are making progress. Eventually this centrifugal force pulls on the string and makes the string go taut. This induces a tension in the string. That tension then causes an inward centripetal force to act, and the orbit gets pulled into a circle.

Where do you see two centrifugal forces in this scenario? And how do you reason that one of them is present in all frames of reference whereas the other is only present in a rotating frame of reference? And how do you reason that one of the centrifugal forces is reacting to anything? David Tombe (talk) 22:55, 26 April 2009 (UTC)


 * I see the centrifugal force just fine, thanks; just like Wolfkeeper I see the "apparent" or "pseudo" or "fictitious" force; calling it "real" has no obvious meaning to me; I think we all agree it's proportional to the theta-dot of the frame, whereas the force on the string doesn't depend on the rotation rate of your frame of reference. See Brews's table. Dicklyon (talk) 23:14, 26 April 2009 (UTC)

Dick, That's good that you can see the centrifugal force as per equation 3-11 in Goldstein. So who said anything about a rotating frame of reference? And where did you read in Goldstein that this force is either "apparent", "fictitious", or "pseudo"? This force can pull a string taut. And you are quite wrong when you say that the force on the string doesn't depend on the rotation rate. The force on the string, and the force in equation 3-11 are one and the same force, and that force does depend on the rotation rate. David Tombe (talk) 23:22, 26 April 2009 (UTC)


 * Goldstein uses the word "fictitious" for the co-rotating 1D system, though not explicitly for the force; but it's same as what others call those things. If you look at the ball moving in a straight line in an inertial frame, it's obviously unaccelerated and therefore has no force on it; only when you rotate to face it and measure r do you see an apparent acceleration away from you.  I suppose I can repeat this a few more times for those of you who have a mention block about it. Dicklyon (talk) 23:32, 26 April 2009 (UTC)

Dick, Goldstein states that equation 3-12 is the same equation as occurs in the equivalent fictitious 1-D problem. He does not say that either equation 3-12 or equation 3-11 is a fictitious 1-D equation. Indeed, equation 3-11 which contains the centrifugal force in its familiar form cannot possibly be a 1-D equation because of the angular velocity term. You have totally misrepresented Goldstein on this point and you have done it opportunistically and repeatedly. You have played on simplistic word association. You have seen the word 'fictitious' in a completely different context and you have opportunistically swooped in and milked it dry.

And now you are ducking the main point again. We know that there is a centrifugal force acting on the ball even before the string becomes taut. That centrifugal force eventually pulls the string taut. Where do you see two centrifugal forces? And how can centrifugal force be a reaction to anything. I have a quote from you here,

''in the inertial frame, it's the reaction to the force with which the string is accelerating the balls. Dicklyon (talk) 23:14, 26 April 2009 (UTC)''

That quote is totally nonsensical. It is a desparate attempt to try and argue the impossible. The centrifugal force is not a reaction to any other force. It exists in its own right by virtue of absolute rotation. David Tombe (talk) 23:50, 26 April 2009 (UTC)


 * The equation for the forces and accelerations along r is a 1D frame rotating at rate theta-dot. I'll take this opportunity to swoop out now; but feel free to explain what you mean by "absolute rotation" in the case of the ball moving in a straight line with a limp string attached. Dicklyon (talk) 01:43, 27 April 2009 (UTC)

Dick, You have completely avoided the question. There is an outward centrifugal force acting on the ball even before the string gets pulled taut. That is the centrifugal force as per equation 3-11 in Goldstein. It then pulls the string taut. Where do you see two centrifugal forces in all of this? And how can you see the centrifugal force as being a reaction to the centripetal force when the centripetal force doesn't even come into existence until the string has been pulled taut? And why do you feel the need to insert a frame of reference around the problem? Can you not clearly see what is going on without involving a frame of reference? David Tombe (talk) 10:05, 27 April 2009 (UTC)


 * We could explain it to you if you understood vector notation. Do you understand vector notation?- (User) Wolfkeeper (Talk) 17:18, 27 April 2009 (UTC)


 * David, your example makes it very clear what the two different centrifugal forces are. The motion is purely is linear, yet there is a centrifugal force, from the point of view of an observer watching the ball approach and recede and looking at the second derivative of the distance r as a generalized acceleration.  On the other hand, the string is slack, so since it's not pulling on the ball it feels no reaction force.  The reactive centrifugal force is zero (until the string goes tight), and "fictitious" centrifugal force is nonzero, in theis case of straight line motion.  The "fictitious" one doesn't correspond to any real curved motion or rotation, just the rotating point of view from which the observer measures the ball's location in one dimension r. Dicklyon (talk) 17:55, 27 April 2009 (UTC)

Dick, I didn't see your two centrifugal forces in that explanation. What is wrong with the simple explanation that the centrifugal force which acts on the ball then causes the ball to pull the string taut? David Tombe (talk) 20:35, 27 April 2009 (UTC)


 * What's wrong is that it's just words, with no interpretation that I can figure out. Dicklyon (talk) 23:29, 29 April 2009 (UTC)

Why do we need a frame of reference?
Tombe: Dick, You have completely avoided the question. There is an outward centrifugal force acting on the ball even before the string gets pulled taut. That is the centrifugal force as per equation 3-11 in Goldstein. It then pulls the string taut. Where do you see two centrifugal forces in all of this? And how can you see the centrifugal force as being a reaction to the centripetal force when the centripetal force doesn't even come into existence until the string has been pulled taut? And why do you feel the need to insert a frame of reference around the problem? Can you not clearly see what is going on without involving a frame of reference? David Tombe (talk) 10:05, 27 April 2009 (UTC)


 * The nail has been hit on the head. Can't what is going on be seen without a frame of reference? That is what the article has to answer clearly.


 * One key objective of mechanics is to relate "what is going on" so every observer can agree. Every observer can agree that the water in the bucket is concave. That is "what is going on".


 * Not everybody has the same explanation, however. They all try to apply Newton's laws to explain the curved surface. Some can do it using only gravity and the observed rate of rotation. Others can do it too, but gravity and the observed rate of rotation are insufficient. The worst disagreement is for the co rotating observer. Their rate of rotation is zero, but their gravity is identical to everybody elses. To explain why the water is not flat, they say there is a centrifugal force. Some observer's don't need that. Some observer's see a bit of rotation, and need a bit of centrifugal force, but not as much.


 * There's the rub. "What is going on" is the same for everybody. How they analyze and explain differs.


 * The explanation is not a "gut feeling" issue. It is an issue of calculation. The input data is the curvature of the water, and the observed rate of rotation, and the gravitational force. Using these data, explain the observed curvature using the math of Newton's laws. Set up a force equation. Calculate the result.


 * Not every observer has the same rate of rotation. Their dot-theta on the "a" side is observed dot-theta, which differs for different observers. What they put into the Force side of F=ma also differs. Some don't need centrifugal force. Some do. It depends upon the dot-theta term on the "a" side. That is input data that changes with the observer. The force side compensates. Everybody gets the same differential equation for F=ma, does the same math, and finds the same curvature, of course.


 * Scientists are prejudiced. They like fewer terms on the force side of the equation, and if they can do that by choosing some particular frame of reference, they go for it. So centrifugal force is regarded as necessary for some observers, but they are the unfortunate ones. The "reality" is that no centrifugal force is needed on a "fundamental basis". The observers for whom the "right" dot-theta is observed, the ones that need no centrifugal term on the "F" side, are the "chosen ones", the observers that see "reality".


 * This slippery slope applied to the disappearance of magnetic forces for some observers leads to special relativity. The disappearance of gravity for some observers leads to general relativity. Brews ohare (talk) 13:52, 27 April 2009 (UTC)


 * Brews, central force problems are two dimensional and we are all agreed that this is the radial equation,


 * $$m\ddot r-mr\dot\theta^2=f(r)$$


 * It is equation 3-11 in Goldstein. You are now telling us that only certain observers need the centrifugal force term. What is fundamentally different between the centrifugal force and the centripetal force such that the centripetal force can be observed by all observers, whereas the centrifugal force can only be observed by co-rotating observers? They are both rotating. They both act in the radial direction. One is inverse square law. One is inverse cube law. The different power laws account for orbital stability. David Tombe (talk) 16:11, 27 April 2009 (UTC)

The equation from Goldstein presumes a frame of reference. That begs the question. Brews ohare (talk) 18:51, 27 April 2009 (UTC)


 * Brews, the assumed frame of reference is the inertial frame of reference. All the variations of the radial and transverse unit vectors are relative to the inertial frame of reference. Rotating frames of reference don't enter into it. Why are you happy with the concept of a rotating centripetal force being viewable from the inertial frame whereas you can't cope with the idea that we might equally view a rotating centrifugal force from the inertial frame? What is this special problem with centrifugal force that makes people think that we need to be in a rotating frame in order to be able to view it? I can watch somebody swinging a bucket of water over their head and see the centrifugal force in operation. I don't need to be swinging with the bucket to see the centrifugal force. David Tombe (talk) 20:42, 27 April 2009 (UTC)


 * David, if you want to be in the inertial frame, you can't call the second derivative of r an acceleration; it's a generalized acceleration in the rotating frame or the fictitious 1D frame, but in the inertial frame it's not, as the freely-moving ball makes clear; when there's no acceleration of the ball (it's moving in a straight line), you still have a non zero r-double-dot. You can't have it both ways – either use the acceleration in the inertial frame, or use the frame in which the acceleration is r-double-dot (or has r-double-dot as a component in the 2D case). Dicklyon (talk) 20:47, 27 April 2009 (UTC)

David: I went to some length above about the bucket, and made what seems to me to be a lucid explanation of matters. You can find the mathematical details at bucket argument. You can similarly see the mathematical details of the ball & string argument at rotating spheres. The whole point is that dot-θ is an observed value, and is different in different frames. Thus, even if we all use the same radial equation, and the same origin, and see the same ball running about, our ma side of the equation differs from one to another. As there is only one equation that works, two observers with different dot-θ terms on the ma side have make their equations agree by adding different forces on the force side. That is where the centrifugal force comes in – to patch things up. Brews ohare (talk) 21:13, 27 April 2009 (UTC)


 * Dick, how come the second time derivative of r can be called an acceleration in relation to the centripetal force, even when the centripetal force is rotating? Who told you that it can't be called acceleration in relation to the centrifugal acceleration? You can call it Harry if you like but it won't make any difference to the physics. But you are actually trying to tell me that I am not allowed to call the centrifugal acceleration an acceleration. You are playing on words to avoid answering the key question. What is wrong with saying that the centrifugal force on the ball then causes the string to be pulled taut? Where are the two centrifugal forces that you are talking about? Your explanation above did not make any sense. David Tombe (talk) 22:21, 27 April 2009 (UTC)


 * What are you talking about? Under what circumstance did anyone say that it's an acceleration with respect to one force and not another?  Are you making up stuff to object to?  I'm sorry my explanations don't make sense to you; it seems to be a problem unique to you; similarly with the explanations of others that are understood except by you. Dicklyon (talk) 23:22, 27 April 2009 (UTC)

Dick, it says in the book that it's a central force equation. If the centripetal force is a force, how could the centrifugal force term in the same equation not also be a force? You have just said above that the centrifugal term is not an acceleration. And don't try to pretend that you are part of some united front. Wolfkeeper says that he believes it's a real force, whereas you have said that it is only a fiction. So don't try to pretend that your speaking as a spokesman for a group that are all saying the same thing. David Tombe (talk) 01:56, 28 April 2009 (UTC)


 * David, I never said it's "not a force", nor that it's "only a fiction." I said it's a "fictitious force", which is the other common term for what Wolfkeeper calls a "pseudoforce".  I don't really care what you want to call it, just recognize that in a non-rotating frame it goes to zero, unlike the centrifugal reaction force. Dicklyon (talk) 03:48, 28 April 2009 (UTC)

Brews, Yes, there is a different centrifugal force acting on one object relative to every point in space. That is part of the mystery of it. But we can deal with that later. At the moment we have a simple radial equation with a centrifugal term which can pull a string taut. There seems to be a great reluctance to boldly print this equation in the article without hiding it behind hedges, and then to openly and unashamedly name the terms in it. David Tombe (talk) 22:21, 27 April 2009 (UTC)


 * Dick, here is your exact quote,


 * But we'd need to get you to accept that "the outward centrifugal force" of a ball moving in a straight line with a slack string attached is a fiction Dick Lyon 19.22 hours 26th April 2009


 * Wolfkeeper says that it is real. So your united front does not exist.


 * And furthermore, you did try to argue that the centrifugal term is not an acceleration. You clearly stated above that the second time derivative of the radial distance r is not an acceleration. And I'm not going to waste time on word games as between force and acceleration. The two terms are interlinked through F = ma and so they are to all intents and purposes interchangeable in this discussion. Quibbling over force versus acceleration is another of the standard decoy methods used when people are trying to deny the existence of centrifugal force in the face of overwhelming evidence to the contrary. They swing into acceleration, or they swing into Cartesian coordinates. Anything rather than facing up to the reality that the centrifugal force pulls the string taut. David Tombe (talk) 11:36, 28 April 2009 (UTC)


 * Oops, sorry, I misspoke; I meant "is a fictional force" (in the usual sense that it's zero if viewed from an inertial frame, which is why the ball is moving in a straight line). Dicklyon (talk) 15:24, 28 April 2009 (UTC)


 * Yup, although just because it goes to zero in a stationary reference frame doesn't make it not real. Kinetic energy goes to zero in at least one inertial reference frame too. Everyone here gets this David, they may phrase it differently, but they all basically have the same understanding. David you're not editing from a good-faith position- you're trying to introduce your own OR into the article. You're trying to edit the article to be compatible with you wacky theories about how centrifugal force is the cause of magnetism or whatever. But, strangely enough, there's no good references that support that POV; so we cannot really let you insert it here, in the wikipedia, and nor can we allow you to modify/distort the article to make it more compatible.- (User) Wolfkeeper (Talk) 16:04, 28 April 2009 (UTC)


 * If you have novel physical theories you need to take them to a respected journal and publish them there, rather than trying to get them as accepted physics by editing the wikipedia.- (User) Wolfkeeper (Talk) 16:04, 28 April 2009 (UTC)


 * Wolfkeeper, you have just said that it can be zero and still be real. How can a real force of zero value pull a string taut? You have indicated that you don't comprehend this topic. The planetary orbital equation is not my own original research. It is a topic which is being sidelined because it contradicts the superficial approach to centrifugal force which dominates the modern textbooks. You have all been trying to distort the topic of planetary orbits in order to bring it into line with your own misinformed opinions which are based on the topic 'rotating frames of reference'. David Tombe (talk) 16:15, 28 April 2009 (UTC)


 * If I drive my car down the road, there is a frame of reference in which the kinetic energy of my car is zero. How can zero kinetic energy move me? That's the same logic as yours.- (User) Wolfkeeper (Talk) 18:39, 28 April 2009 (UTC)


 * Really, if we add up the megabytes of drivel you've 'contributed' to the wikipedia, how much have you cost the project, a charity in total?- (User) Wolfkeeper (Talk) 18:39, 28 April 2009 (UTC)


 * Wolfkeeper, you'd need to lay out the analogy point for point. David Tombe (talk) 20:37, 28 April 2009 (UTC)

Dick, it's not zero in any frame of reference. It pulls a string taut. Equation 3-11 in Goldstein,


 * $$m\ddot r-mr\dot\theta^2=f(r)$$

is all that is needed to comprehend the situation. The centrifugal force is an outward radial force which acts between any two objects which have mutual tranverse speed. You are introducing unnecessary complications such as rotating frames of reference, fictitious forces and one dimensional equivalent equations in order to try and mask out this simple underlying reality. David Tombe (talk) 16:07, 28 April 2009 (UTC)


 * What does that evaluate to when theta dot is zero? What is theta-dot?  Does it depend on the frame of reference, or not?  What is this force acting on when there's no string?  Why isn't it causing any acceleration? Dicklyon (talk) 17:00, 28 April 2009 (UTC)

Dick, when the theta dot is zero there won't be any centrifugal force at all. Theta dot is the angular velocity of the balls relative to the inertial frame. When theta dot is non-zero there will be a centrifugal force acting on the balls, string or no string. Such a centrifugal force acts on the Moon without the involvement of any string. That centrifugal force causes a centrifugal acceleration $$r\dot\theta^2$$.

Equation 3-11 covers every case scenario. If the centripetal term is a negligible gravity term, then the orbit is hyperbolic. If we then attach a string, the centrifugal force will pull the string taut. The tension in the string will then induce a centripetal force (on top of the already existing gravity) and a circular motion will ensue. David Tombe (talk) 18:27, 28 April 2009 (UTC)


 * Parts of that are OK; but what does it mean when you say "When theta dot is non-zero there will be a centrifugal force acting on the balls, string or no string"? Where is the acceleration corresponding to this force?  If there's a centrifugal force acting on the balls, why do they keep moving in a straight line (with no string)?  There's no acceleration (no x double dot or y double dot in the inertial frame), just an r double dot (a coordinate in a rotating 1D frame). Dicklyon (talk) 01:50, 29 April 2009 (UTC)

Dick, OK, let's drop the string and let's have a pure planetary orbit. Let's have negligible gravity and hence a hyperbolic orbit. There will be an outward radial acceleration on each of the planets, and that outward radial acceleration will have the value $$r\dot\theta^2$$. It is a two dimensional problem and not a one dimensional problem as you have claimed. If it were a one dimensional problem, then there would be no transverse motion and neither could there be any $$\dot\theta$$. David Tombe (talk) 09:25, 29 April 2009 (UTC)


 * In the case we're talking about, with negligible gravity, the "orbit" is a straight line, right? Which means that in the inertial frame, the "planet" has no acceleration, right?  Dicklyon (talk) 19:53, 29 April 2009 (UTC)

Dick, in the inertial frame, the planet moves in a straight line just as you say. It has an outward radial acceleration of magnitude $$\dot\theta$$.


 * Exactly so; but an "outward radial acceleration" is not an acceleration. The accleration is zero in that inertial frame, corresponding to the lack of force on the ball; the x double dot and y double dot (and z double dot if you want that dimension, too) are all zero, corresponding to straight-line motion, right?  By looking at "radial accleration" it's equivalent to saying rotate your measurement direction at rate theta dot to point at the ball, and meaure the generalized location, velocity, and acceleration in that rotating frame; in that frame, there's an apparent centrifugal force, unlike the zero force in the inertial frame where the acceleration is zero.  If you're claiming that the ball moving in a straight line in an inertial frame has a nonzero acceleration in that frame, then I'll have to pull my hair out in despair.  Dicklyon (talk) 23:28, 29 April 2009 (UTC)

Dick, gravity causes an inward radial acceleration, which may or may not be rotating. So why can an outward radial acceleration, as caused by centrifugal force, not also qualify as an acceleration in your books? Cartesian coordinates don't come into this. Gravity and centrifugal force are both central forces, and we use polar coordinates to deal with central forces. The two variables r and θ are both measured relative to the inertial frame and so we are dealing with the inertial frame of reference using polar coordinates. Rotating frames of reference don't enter into the problem. Gravity and centrifugal force are both radial forces and they both cause radial accelerations. And both of these radial forces are real. The centrifugal force can pull a string taut and it can undermine gravity so as to hold the planets in their orbits. And there is only one centrifugal force. The article has been split due to a lack of comprehension of the topic. David Tombe (talk) 11:03, 30 April 2009 (UTC)


 * No, actually, gravity is, from Einstein's equivalence principle, an acceleration of the reference frame. And gravity isn't always a central force either; that's only approximately true in spherically symmetric situations; in the general case you have one oddly shaped object attracting others, and the centre of gravity isn't even at the centre of mass.- (User) Wolfkeeper (Talk) 13:40, 30 April 2009 (UTC)


 * Wolfkeeper's diversion outside of classical mechanics being quite irrelevant to the point, gravity causes an acceleration that appears in the cartesian coordinates of the path of an object viewed in an inertial frame, while centrifugal force does not. If you want to use polar coordinates, you need to recognize that second derivatives of those are not accelerations, but need to be related to accelerations via the transformations that Brews has described.  If you use second derivative of r as acceleration, that only makes sense in a frame that's rotating such that r is a cartesian coordinate in that frame.  I've never seen any indication in any book, Goldstein or otherwise, that any classical physics can be made to work doing it otherwise.  What could F=ma mean if we didn't have at least this much understanding of acceleration? Dicklyon (talk) 14:56, 30 April 2009 (UTC)


 * No, no. My point is that even in newtonian terms gravity is a central force in the two-body conservative force sense, but in non symmetric cases it's not necessarily radial; the centre of mass and centre of gravity do not in general align even in newtonian calculations.- (User) Wolfkeeper (Talk) 15:02, 30 April 2009 (UTC)


 * Right, I see; it's a confusion invoked by David's mystical concept of "central" that you're trying to clear up; thanks. Gravity acts toward another body; centrifugal force acts toward whatever point you choose to measure r from. One is not dependent on the frame (but is "central" in the center of mass frame), the other is totally frame dependent, always acting toward whatever point you choose to look from.  Dicklyon (talk) 15:27, 30 April 2009 (UTC)

Dick, I'm going to ignore Wolfkeeper's diversions regarding relativity and assymetrical shapes. The concept of a central force is not a mystical concept of my creation. You have however raised a very interesting point which I have always been fully aware of. You have pointed out how centrifugal force can be relative to any arbitrarily chosen point in space whereas gravity can only be relative to a physical centre of mass. You have also correctly pointed out how centrifugal force disappears in Cartesian coordinates. That is not however the same thing as disappearing in the inertial frame.

These somewhat mysterious facts can help us to understand the underlying physical nature of centrifugal force. But at the moment I am merely trying to lay equation 3-11 from Goldstein on the table, and name the terms in it. This could be done in a very short section which would replace Brews's long section on planetary orbits. Brews's section is technically correct but it is too long winded for the purposes of this article and it also plays down the star piece, and doesn't even mention it by name.

My guess is that because centrifugal force possesses the strange properties mentioned above, such that it somewhat blends into Euclidean geometry, that this is what causes all the trouble. An equation such as 3-11 can expose it as a real outward physical force, yet on the other hand it doesn't show up in day to day situations that are described in terms of Cartesian coordinates. But that is not a reason to shy away from the reality that the $$mr\dot\theta^2$$ term in equation 3-11 is the familiar centrifugal force that holds the planets up in their orbits. David Tombe (talk) 16:38, 30 April 2009 (UTC)


 * David, you speak nonsense; you want the force to be "real", not frame dependent, but dependent on where you measure it from and on what kind of coordinate system you measure it with. This is not physics.  No wonder it's "mysterious" in your way of looking at it.  Dicklyon (talk) 18:35, 30 April 2009 (UTC)

Dick, Centrifugal force is real and it is not frame dependent. You are confusing inertial frames of reference with Cartesian coordinates. Cartesian coordinates mask the existence of the centrifugal force but they don't get rid of the reality of it. The reality of centrifugal force is expressed clearly in polar coordinates which are relative to the inertial frame. There is no need to introduce Cartesian coordinates into this debate. Cartesian coordinates hold no superiority over polar coordinates when it comes to ascertaining the reality of radial effects on either the astronomical scale or the microscopic scale.

And any rate, we don't need to discuss that. All we need to do is state equation 3-11 in Goldstein, name the terms in it, and point out that the centrifugal force term can pull a string taut and hold a planet up in its orbit. David Tombe (talk) 00:35, 1 May 2009 (UTC)

Note to Wilhelm
Wilhelm, you've suggested the clear explanations at this and this. But the latter calls the topic of this article "false", and asserts that "An evil word has worked its way into our daily vocabulary, and with it, an incorrect understanding of the way physics works. 'Centrifugal Force'." This is nonsense; there are only a few people who have that "incorrect understanding", and there's no reason to apply the term "false" to a "fictitious force" that often conveniently and correctly used in mathematical physics. It is, after all the entire topic of this article we're working on. Dicklyon (talk) 16:11, 1 May 2009 (UTC)
 * I never suggested that we should copy those pages, and I certainly did not mean to imply that in any way. I was only pointing out that these concepts can be explained in a more clear and concise way than what we currently have.  Please do not take my suggestion as a full endorsement of those pages!  Wilhelm_meis (talk) 01:58, 2 May 2009 (UTC)

A great source
I finally found a book that goes into the whole "fictitious" treatment in a smart way, including the history of different conceptions from Newton and Leibniz (who apparently first came up with Goldstein's formula for radial acceleration as a difference between the gravitational and centrifugal terms). here. Dicklyon (talk) 19:06, 1 May 2009 (UTC)


 * This source says:
 * "Newton and Leibniz are using the term centrifugal force in different senses."
 * Exactly. This article is not dealing with the Leibniz sense, and introduction of this different meaning is simply confusing, and brings nothing to the understanding of centrifugal force as opposed to a narrow designator of a term in polar coordinates that possesses no relation to a true force, including especially a complete failure to transform as a vector .Brews ohare (talk) 22:36, 1 May 2009 (UTC)


 * I don't think so. The Newton sense is the reactive force (which David says doesn't exist); the Leibniz and Goldstein sense is the pseudo-force in a 1D system along the line between two bodies (which you say is not a centrifigal force?), which is not really different from the fictitious force that this article is about, is it? Dicklyon (talk) 22:51, 1 May 2009 (UTC)


 * No Dick, the Newtonian sense as per that article is an oversimplistic sense which assumes circular motion and a centripetal force which is equal and opposite to the centrifugal force. The Leibniz sense involves an equation which is the same as the equation which would hold for the equivalent 1-D problem. You still need to accept that Goldstein did not actually say that equation 3-11 itself was a 1-D problem. Basically Leibniz was looking at the general situation whereas Newton was stuck in the special case of circular motion. David Tombe (talk) 22:56, 1 May 2009 (UTC)

Dick, That was a very interesting article. Thanks for that. It seems that all along I have been looking at the problem from the same perspective as Leibniz without realizing it. Goldstein has clearly taken a Leibniz perspective on the issue and this entire edit war was because I was trying to introduce that perspective into the article. I knew that it was in Goldstein, but this time last year when the edit war began, I didn't have access to a Goldstein and I hadn't looked at my old copy for about 27 years. And my attempts to introduce that perspective were being thwarted under false accusations of original research.

That is an excellent article. I'm glad that you have brought it to my attention. It also clears up alot of other things which I had heard over the years but never followed up. Apparently there was alot of bitterness between Newton and Leibniz. I've also read that Newton got a bit twisted about centrifugal force. On the one hand, he believed in it and advocated it in his bucket experiment, but when Hooke started using it, Newton started to change the emphasis in planetary orbits to centripetal force. I can see myself now beginning to side with Leibniz in that great historical dispute. David Tombe (talk) 22:49, 1 May 2009 (UTC)


 * Where Newton says "Centrifugal force is always equal and opposite to the force of gravity by the third law," he's clearly treating it as the reaction force; it doesn't matter if motion is circular or not. When he later uses that interpretation to criticize Leibniz by saying that his reasoning (and formula) imply r-double-dot equals zero, he's clearly misapplying one concept where the other is needed.  Obviously that would lead to a circular orbit, but he knew that a circular orbit was the wrong answer, so that's not where he was coming from.  He just didn't accept the pseudoforce that Leibniz was using implicity, as Goldstein does, by looking at derivatives of r, the coordinate in a fictitious 1D system.  Dicklyon (talk) 03:34, 2 May 2009 (UTC)

Yes Dick, he's misapplying one concept where the other concept applies, and the concept which he is applying, ie. his 3rd law of motion, never applies across centrifugal force and centripetal force. Newton was being deliberately twisted because there was a long running bitterness betwen himself and Leibniz. David Tombe (talk) 09:32, 2 May 2009 (UTC)

A basis for a new unified article. Newton v.Leibniz
Recently I made this edit,

== Proposal for a shortened section on planetary orbits ==

This very short paragraph should take the place of the existing section.

''Centrifugal force arises in planetary orbits. The radial planetary orbital equation,''

$$ \ddot r = -G(M + m)/r^{2} + l^{2}/r^{3}$$

''can be solved to show that planetary orbits are either ellipses, parabolae, or hyperbolae. See Kepler Problem. The inverse cube law term on the right hand side of the equation is the centrifugal acceleration.''

We now know that this is the approach that Leibniz and Goldstein adopted. It contains every aspect of the topic in a single equation. If the gravity is negligible the orbit will be a hyperbola. If we then connect a string between the planets, the centrifugal force will pull the string taut.

The problem is that Newton didn't want to be in agreement with Leibniz even though the evidence is that Newton's earlier writings about comet orbits suggested that he was essentially in agreement with Leibniz. Newton therefore objected to the above formula on the grounds that the radial acceleration would always have to be zero. He based this objection on his own 3rd law that action and reaction are equal and opposite, and that centrifugal force and centripetal force are an action-reaction pair.

I can't agree with Newton on this point, but it is a viewpoint which appeared in older texbooks. It appears in the 1961 edition of Nelkon & Parker but was erased in the 1971 revision.

Nevertheless, this Newtonian viewpoint seems to be the basis for the concept of 'the reactive centrifugal force'.

A single unified article on centrifugal force should discuss both these perspectives. I personally go along with the Leibniz/Goldstein approach. David Tombe (talk) 00:28, 2 May 2009 (UTC)


 * Why do you have trouble accepting both views at once? Newton is defining an action/reaction pair between centripetal and centrifugal force; lots of people do that, and it's not hard to accept.  The other concept of centrifugal force, which is not quite equal to this one when orbits aren't circular, is the "fictitious" or pseudoforce of this article, as used by Leibniz and Goldstein.  I would agree with the idea of writing an article to discuss this, but fear that you'll continue to push to screw it up by not understanding the latter concept while not accepting the former. Dicklyon (talk) 03:38, 2 May 2009 (UTC)
 * The "centrifugal" force is the reaction to the centripetal force. Just like when you stand on the ground, gravity pulls you to the earth with the force of your mass times the gravitational constant. At the same time the earth is pushing back up on your shoes with an equal and opposite force, yet no one get confused and calls that "anti-gravity". It is only confusing because it sure feels like a centrifugal force when you swing a bucket over your head, but that isn't the force you are feeling - you are feeling the centripetal force of you pulling on the rope to distort the bucket from the path it would have taken had the rope not been there. The rope pulling back against you is not a force, it is the equal and opposite reaction to a force. 199.125.109.88 (talk) 04:16, 2 May 2009 (UTC)

No Dick, Newton was being twisted on this occasion. He couldn't bring himself to accept that Leibniz was correct and that indeed Leibniz had been effectively saying what Newton had been saying earlier. The centrifugal force and the centripetal force are not in general equal. And the centrifugal force is never a reaction to the centripetal force. Newton was quite wrong to apply his 3rd law of motion to this situation.David Tombe (talk) 09:20, 2 May 2009 (UTC)


 * Anonymous 199.125.109.88, by all means adopt the Newtonian approach to the matter. Many textbooks did up until the 1960's. But it is wrong. The centripetal force in those simple circular motion scenarios doesn't come into existence until the centrifugal force has already created a tension or a pressure. Centrifugal force cannot therefore be a reaction to centripetal force, and in the general planetary orbital situation the two are not even equal to each other. Also, 199.125.109.88 it does rather look like you are getting centrifugal force and normal reaction confused. David Tombe (talk) 09:20, 2 May 2009 (UTC)
 * So now I get to go over to the local college bookstore and look up Physics texts? Doesn't Wikibooks even have a physics textbook? Wasn't the 60s when new math came out and they started saying that 2+2=3, or 4, or 5, or something else, depending on which rotating reference frame you were in (or how high you were at the moment)? I really do not think there is anything I am confusing other than why are there three articles about the same topic? Let's see Physics with Calculus/Mechanics/Rotational Motion has a section on centripetal acceleration, and A-level Physics (Advancing Physics)/Circular Motion says "Centrifugal force does not exist. There is only one force acting in circular motion, which is known as centripetal force. It always acts towards the centre of the circle." Just a guess but I suspect that was written some time long after "the 1960's". 199.125.109.88 (talk) 21:44, 2 May 2009 (UTC)

199.125.109.88 There are many textbooks and weblinks saying contradictory things about centrifugal force. The way I was taught it in physics was that centrifugal force does not exist. A circular motion example was given, and it was pointed out that all that was needed was a centripetal force to keep the object in circular motion. However, in applied maths I was taught planetary orbital theory where I learned about the radial equation which includes both inward gravity (the centripetal force) and also an inverse cube law repulsive centrifugal force whose value is independent of gravity. This second order differential equation solves to a hyperbola, a parabola, or an ellipse depending on the relative values of the centrifugal force and the centripetal force. I learned that 30 years ago, but I only learned yesterday that that was Leibniz's approach in the 17th century. Apparently Newton's approach to centrifugal force conformed to Leibniz's approach up until the year 1681. However, Newton and Leibniz had a notorious animosity towards each other over the issue of who invented calculus. When Newton saw Leibniz's radial central force equation, he objected to it. Newton claimed that his 3rd law of motion means that the centrifugal force is always equal and opposite to the centripetal force. So not only did Newton contradict Leibniz, but he also contradicted his own earlier writings on the subject. One of the two must be wrong, and I am of the opinion that Newton's application of his 3rd law to centrifugal force v. centripetal force is quite wrong, and that he only came out with that nonsense in spite of Leibniz.

That Newtonian approach was in some 1960's textbooks. It was in the 1961 Nelkon & Parker 'Advanced Level Physics'. It was used there to explain the centrifuge machine. Yet in the 1971 Nelkon & Parker, centrifugal force had disappeared and the centrifuge was explained using a totally illogical application of centripetal force. Meanwhile, the Leibniz approach to planetary orbits still exists in some classical mechanics textbooks. But the main modern thrust on centrifugal force is neither the Leibniz approach nor the Newtonian approach. The modern approach is that centrifugal force is a fictitious force which is only observable in rotating frames of reference.

I know that you have come here looking for definitive answers. But unfortunately the matter is not that simple. David Tombe (talk) 23:24, 2 May 2009 (UTC)


 * Alternatively, one can just accept that Newton's 3rd law interpretation is about the reaction force to centripetal force, and that Leibniz's equation is just the fictitious force in the 1D system along the line to the planet, and neither one is incorrect. Dicklyon (talk) 00:39, 3 May 2009 (UTC)

By transforming the problem to 1-D and then further interpreting ddot r as an acceleration (ddot any variable is OK as an acceleration in any 1D problem) one is free to interpret the remaining terms as 1-D forces. However, to take the one-D v2/r term and call it the "centrifugal force" is like calling monopoly players businessmen. There is no centrifugal force in any one-D motion. The "velocity" parameter has no interpretation in the one-D motion (it is the transverse velocity from polar coordinates and has no interpretation in 1-D). All intuitive value of the term "centrifugal force" has vanished entirely, and in its place we have introduced confused language very prone to being dragged out the one-D context and applied where it has no bearing. I don't think this peripheral, confusing abuse of language deserves any presence in this article. Brews ohare (talk) 05:37, 3 May 2009 (UTC)


 * I don't find the language confusing at all; if it was used by Leibniz and Goldstein, then it seems to me that it must have a place here. It's not really any different from the centrifugal force in any other rotating reference frame, it's just a particular frame chosen to make the two-body problem since, and it has only one interesting dimension since the motion in the dimension orthogonal to r is always 0 based on how the frame is chosen.  I'm not sure what you mean by v2/r here, however; there's no v in this problem.  The centrifugal force is express either in terms of the constant angular momentum L or the rate of change of the angle of the system, which is the instantaneous rotation rate (and the fact that the rotation rate is changing gets taken care of by the Euler and Coriolis forces cancelling, which obviously must happen, as the frame is chosen such that the body never moves off the r axis).  Dicklyon (talk) 06:31, 3 May 2009 (UTC)

Dick, you're starting to behave a bit like Newton himself. Brews is absolutely correct on this point. We are not dealing with a 1-D problem. You have been continually twisting what Goldstein said. Goldstein said that when we write the radial planetary orbital equation as per 3-12, with the centrifugal force written in the inverse cube law form, then the equation is the same as that which arises in the equivalent 1-D problem.

The fact is that Newton twisted Leibniz's formulation. Newton's interpretation is only partially correct. It is correct in that in the special case of circular motion, the centrifugal force is equal and opposite to the centripetal force. But it is incorrect in that the two are not an action-reaction pair as Newton claims. And it is incorrect in that the two are not equal in general as Newton claims. The two viewpoints are incompatible.

You had no reason to delete my historical outline of this dispute on the reactive centrifugal force page. You are clearly trying to push a point of view. You are trying to superimpose all the business about rotating frames and fictitious forces on top of the Leibniz approach which Goldstein uses. Goldstein never talks about fictitious forces or rotating frames of reference, and you are actively trying to keep the Leibniz approach off the main pages. Your edits on the reactive centrifugal force page are wrong, but of course you can depend on Wolfkeeper to back you up. It's hardly a satisfactory way to write an encyclopaedia article. David Tombe (talk) 12:48, 3 May 2009 (UTC)


 * David, since you're still very confused about what's a coordinate system effect and what's a rotation effect and how to interpret r double dot in the two systems, here is a book that explains that issue very clearly. I'm sure whether to be flattered or insulted by being compared to Newton, but really, I'm just a wikipedia editor here, and POV pushing is exactly what I'm trying to resist by moving us to where the different points of view can be integrated, compared, and constrasted; however, I don't think your POV is among those, since you are a total outlier with respect to all sources and other editors.  Dicklyon (talk) 18:43, 3 May 2009 (UTC)

Dick, my point of view is the Goldstein/Leibniz point of view. I am advocating this equation as being the single equation which unites the entire topic of centrifugal force,

$$ \ddot r = -G(M + m)/r^{2} + l^{2}/r^{3}$$

You have been consistently trying to misrepresent my position. You have been falsely alleging that I am pushing some kind of original research, and you have been continually misrepresenting what is written in Goldstein. You have consistently been claiming that equation 3-11/3-12, which is the equation that I have just written above, is a 1-D equation.

When I say that you are behaving as badly as Isaac Newton, I mean it in the sense that you are trying to undermine the Leibniz approach. The Leibniz approach is that a planetary orbit is the consequence of an inward inverse square law force of gravity acting in tandem with an outward inverse cube law centrifugal force, and the two forces are totally independent of each other and not necessarily equal in magnitude.

Isaac Newton tried to sabotage the Leibniz approach by introducing the nonsene idea that the centripetal force and the centrifugal force are an action-reaction pair, and that they are equal and opposite. That approach was found in textbooks right up until the 1960's. It was wrong, but when it was removed, it was replaced by something even worse. The appraoch which is found in most modern textbooks today is that centrifugal force is a fictitious force which is only found in rotating frames of reference. But there is absolutely no need to strap a rotating frame of reference around a situation.

Now that you have discovered the Leibniz approach via Goldstein, you have been trying to corrupt it by introducing concepts from the modern approach and imposing them on top of the Leibniz approach. You are not confused and neither am I. But you seem to have a vested interest in misrepresenting the Leibniz approach. In that respect, you are as bad as Isaac Newton. David Tombe (talk) 19:00, 3 May 2009 (UTC)


 * Actually, I quite like Leibniz's approach, and Goldstein's, and I can see why you like it, too. But your interpretation of it is twisted, as the book I just linked makes clear.  I have no vested interest in any approach, which is why I've been trying to argue that we present them all together. Dicklyon (talk) 20:14, 3 May 2009 (UTC)

Dick, can you please explain exactly in what respect I am twisting Leibniz's approach? There are actually at least three approaches to this topic.

(1) The Newtonian approach. It is partially correct but it is also badly flawed. It corrupts the Leibniz approach by the wrongful superimposition of Newton's 3rd law of motion, totally out of context. The Newtonian approach prevailed in physics textbooks up until about the 1960's. I can give you a classic example. Nelkon & Parker 'Advanced Level Physics' used it in the 1961 edition to explain the centrifuge. It was dropped by the 1971 revision. The Newtonian approach is effectively covered in the wiki article entitled reactive centrifugal force. But it is not a different topic. It is merely a blinkered view of the single topic of centrifugal force which came about because of Newton's notorious resentment of Leibniz.

(2) The modern texbook approach regarding fictitious forces and rotating frames of reference. This approach is just about tolerable so long as we are dealing with co-rotating objects. But why bother childishly strapping a rotating frame of reference around the problem? It is totally unnecessary. Then when this modern approach is extrapolated to situations in which the objects in the rotating frame are not co-rotating, it becomes a total nonsense in which the Coriolis force swings into the radial direction.

(3) There is the Leibniz approach which Newton tried to suppress. It is the approach used by Goldstein. It doesn't involve rotating frames of reference or fictititious forces. It is clearly the best approach in my opinion and this entire edit war has been due to persistant attempts by everybody but myself to keep that approach off these pages. At first they tried to say that the Leibniz approach was my original research. That's because they obviously hadn't heard of it before. They pulled out all stops to keep it off these pages. They endlessly tried to wheel in Cartesian coordinates in order to mask the centrifugal force term. FyzixFighter even hid the term inside a single vector box for radial acceleration. More recently, FyzixFighter blatantly tried to turn the centrifugal force into a centripetal force. Did he think that everybody here would be too stupid to know otherwise? At any rate, he knew he was playing to a crowd that were hostile to my attempts to introduce any approach that exposed the 'rotating frames' approach for what it is. He knew he could count on majority support. Fortunately you and Brews spotted that distortion. But nevertheless, you are now behaving as badly as Isaac Newton. You understand the Leibniz approach but you are trying to distort it. You are trying to corrupt it with nonsense concepts from (2). You clearly don't want a clean version of the Leibniz approach to appear on these pages, and you know that you have got majority support from a crowd who don't even understand the approach.

When the high school level textbooks dropped the Newtonian approach, they replaced it with an arrogant attitude that centrifugal force doesn't exist at all. They attempted to explain centrifugal force effects in terms of centripetal force which is in the complete opposite direction. Hence the situation in the literature is a shambles. That's why we see confused editors like anonymous 199.125.109.88 above.

As it stands now, wikipedia is compounding that confusing by having split the article into two different approaches under the pretext that these are two different centrifugal forces. In fact they are just two different rubbish approaches to the topic. One is in vogue right now and the other went out in the 60's. And this two year edit war has been caused by the fact that a crowd have ganged up to ensure that the 3rd way, which is the Leibniz way, does not appear on these pages. You, who should know better, are part of this. Yesterday, you erased a history section which I inserted at reactive centrifugal force. You claimed that it was my original point of view. It wasn't. It was a point of view copied out of a source which you had actually kindly provided the day before here. But obviously on reflection, you don't want that little aspect of history to be exposed.

Here is a more detailed reference giving Leibniz's position David Tombe (talk) 00:38, 5 May 2009 (UTC)


 * The more I read about Leibniz's approach, the harder it appears to be to describe it in terms of modern physics. I wonder how the first book I cited got to the equation they presented, corresponding to Goldstein's.  If you want to know do I regret starting you down this Leibniz path, yes, I do. Dicklyon (talk) 05:56, 5 May 2009 (UTC)


 * As to your description of a 3-way POV split, I see it this way: 1 is just Newton's second law; not very interesting, but not incorrect; we have the reactive centrifugal force article on it; 2 is the way all of modern physics treats centrifugal force as a fictitious force in a rotating frame, in which in combination with Coriolis force things work out correctly; 3 is a mixup of 2 with David's idiosyncratic interpretations.  And FyzixFighter was not wrong, it turns out, in his presentation of Taylor -- it just took me a while to interpret the symbol soup right with reference to Taylor; in the inertial frame, the term corresponding to centrifugal force does indeed show up as a centripetal acceleration; it is correct that it's in the opposite direction of the centrifugal force, as it has very different roles in the different frames, as the new short article section clarifies.  Try actually reading Taylor... Dicklyon (talk) 07:01, 5 May 2009 (UTC)


 * With respect to the "arrogant attitude that centrifugal force doesn't exist at all", that's nonsense; most physics writers are not arrogant, and most do not say that centrifugal force doesn't exist. You need to learn the different between being "fictitious" and not existing, and look again at who's being arrogant by rejecting all the learning of the last few hundred years. Dicklyon (talk) 07:05, 5 May 2009 (UTC)

Dick, first of all, FyzixFighter was very wrong. The centrifugal force is never the centripetal force no matter what side of the equation we write it on. Secondly, Goldstein uses the Leibniz equation. See equation 3-12 in Goldstein, and that's the way I did it in my old applied maths notes even before I ever saw a Goldstein. I didn't use Goldstein until the next year when I did gyroscopes and Lagrangian. And thirdly, the Leibniz method does not correspond to the rotating frames of reference method. In the Goldstein/Leibniz approach, the Coriolis force is always in the transverse direction. In the rotating frames approach, the Coriolis force has become loose and swings around like a weather cock on a pole.

There are clearly three approaches to this topic. Newton's approach is wrong because it equates centripetal force to centrifugal force under the terms of his third law of motion. But we know that in planetary orbits, the centripetal force and the centrifugal force both act on the same object and that they are not in general equal. You know that already because you have acknowledged it in your edits. Hence, the Newton approach is one aproach, and it is covered in wikipedia by reactive centrifugal force. It disappeared from the textbooks in the 1960's. The Leibniz approach is a different approach, and you should know that there was intense animosity between Newton and Leibniz over the priority in calculus. That is why Newton felt he had to twist Leibniz's approach, because the evidence is that Newton had an earlier stance on centrifugal force which conformed to the Leibniz approach. Then there is the modern rotating frames of reference approach. That is three different approaches. Last year Brews got the idea that the Leibniz approach was a 'polar coordinates' approach. Hence all the unnecessary extra details about polar coordinates in the article. David Tombe (talk) 11:39, 5 May 2009 (UTC)


 * If you'll read the new section, and follow up by reading the linked cited sources, you'll see exactly how to understand how a term that's a centripetal acceleration due to gravity in one (inertial) frame morphs to a centrifugal force fighting gravity in another (rotating) frame. There's no mystery here, and no opinions or mistakes, just stuff from sources.  You'll be able to see where FyzixFighter was quoting Taylor, and how it's not wrong, but a simple derivation from Newton's law, which is in complete accord with Goldstein's method. Dicklyon (talk) 15:40, 5 May 2009 (UTC)

No Dick, Never. The radial equation has both a centrifugal term and a centripetal term. They may be equal in magnitude in the special case of circular motion, but the two terms are never the same thing no matter what side of the equation they are on. You have lost all hope of making a good article because you don't want to accept that the radial equation tells the entire story. It's all too simple for you. David Tombe (talk) 01:25, 6 May 2009 (UTC)

Shortened planetary section
I took the article from about 73 K bytes to about 64 K by implementing my best cut at the proposed shortened planetary section. I think that by keeping the equations in the form F = ma it's easy to see what's being called a force and what an accleration in the different viewpoints, and it becomes clear that Taylor's "centripetal acceleration" term is the same as the "centrifugal force" term but on the other side in a different frame. That is, the inward acceleration term that (along with zero $$\ddot r$$) curves the path into a circle is the same as the pseudo-force term on the other side that keeps r constant (in the circular case, for simplicity; but more generally as shown in the equations). I don't see any point in the present article of working out the rest of the details of the planetary orbits, which I presume are covered in the three linked "see also" articles.

My hope is that most of you will be happy with this version, or will see simple ways to improve it. I fully expect one outlier to object, but that I don't care about. Dicklyon (talk) 05:51, 5 May 2009 (UTC)


 * No Dick, by equating Taylor's centripetal force with centrifugal force, you have made the whole article into a nonsense. The centrifugal force does not even equal the centripetal force in general. David Tombe (talk) 10:54, 5 May 2009 (UTC)


 * Dick, I've just looked at your edits on the main page. I'll check again, but I can't see any reference to what you say above regarding

''and it becomes clear that Taylor's "centripetal acceleration" term is the same as the "centrifugal force" term but on the other side in a different frame. '' dicklyon

I'll check again. If it's not there, then that is good because it is a totally wrong statement. David Tombe (talk) 11:26, 5 May 2009 (UTC)


 * Check Taylor; discussion of terms in equations 9.69 and 9.71, comparing the forms of the equations in the inertial and rotating frames; see highlight terms in yellow, plus the words like "fictitious" and "co-rotating" used in a precise meaningful way. Dicklyon (talk) 15:45, 5 May 2009 (UTC)

No Dick, centrifugal force is never centripetal force. David Tombe (talk) 23:41, 5 May 2009 (UTC)

Another great source
Enjoy:. Dicklyon (talk) 16:35, 5 May 2009 (UTC)


 * On a good day, that's actually linked from the article, it's not at all unusual for physics books to include this kind of stuff, and the cartoonist is a physicist as well. It's very on topic. I would have included it in the article, but the license is incompatible. Linking is allowed in cases where we can't include it.- (User) Wolfkeeper (Talk) 01:43, 6 May 2009 (UTC)

Recent revisions to Planetary Motion section
I find that recent editorial changes to this section are an improvement. I made some minor additions. Brews ohare (talk) 06:24, 7 May 2009 (UTC)


 * I just reverted your latest about instantaneously co-rotating, as I believe that it meant rotating at fixed rate, only co-rotating at one instant. In that case, the Euler force is zero and there's a Coriolis force that accelerates the object to move tangentially. But if you let the frame be totally co-rotating, not just at an instant, then the non-uniform rate of rotation induces an Euler force to cancel the Coriolis force, so there's no tangential acceleration, as indeed must be the case if you're co-rotating.  At least, that's how I read the sources.  You agree?  Dicklyon (talk) 06:53, 7 May 2009 (UTC)

Dick and Brews, As regards a co-rotating frame of reference for planetary orbits in which the angular velocity is not constant, I personally can't think of a more cumbersome and unnecessary concept. At any rate, since you have both chosen to entertain the concept, I might as well put a few facts straight. The Coriolis force and the force which you call the Euler force always cancel mathematically. I think that you both realize that. It is the law of conservation of angular momentum. However, they do not physically cancel. This may be a hard fact to grasp, but it is a reality. The Coriolis force can be observed in all non-circular planetary orbits, all vortex phenomena such as cyclones and small whirlpools, and also when a man who is sitting on a rotating stool moves his arms in and out. The Coriolis force is the observed transverse deflection of any radial motion. It is a force which changes the direction of an object, but not the speed. On the other hand, the force which you call the Euler force changes the speed of an object but not direction. Both of these forces can be visibly observed, even if they mathematically cancel each other, and they operate in tandem to yield conservation of angular momentum (or Kepler's second law of planetary motion).

Also, I hope that you have both noted that the Coriolis force is firmly fixed in the transverse direction. It does not swing around like a sign post that has become loose at the joints. I blame Gaspard-Gustave Coriolis himself for allowing this appalling state of affairs to creep into modern physics. If you study his original 1835 paper, you will see that he advocated two supplementary forces for rotating frames. The first was clearly the centrifugal force which he saw as being a force which opposes the applied (centripetal) force that would be needed to drag an object with the rotating frame. The second force was what he called the 'compound centrifugal force'. It was twice the magnitude of the centrifugal force, and Coriolis deduced its existence purely from examining mathematical transformation equations. That's when the 'compound centrifugal force' was first let off the hook and allowed to swing like a weather cock. Many years later, the compound centrifugal force 2mv×ω was given the name Coriolis Force in his honour. Coriolis should have looked more closely at his first category of supplemenatry forces and considered the case of a constrained co-rotating radial motion, such as a marble rolling radially along a groove on a rotating platform. He would have observed the induction of two equal an opposite transverse forces. One of these is the very 'compound centrifugal force' which he identified in its mathematical form and slotted into category 2. The other transverse force is what you guys call the Euler force, and it would cause the rotating platform to either angularly accelerate, or angularly decelerate, according to whether the marble was rolling in or out. Coriolis himself hence allowed the modern Coriolis force to become divorced from conservation of angular momentum, and to become linked to the inertial effects in a rotating frame of reference. And the linkage between the latter and the rotating frame transformation equations is a total shambles in modern textbooks. David Tombe (talk) 11:46, 7 May 2009 (UTC)


 * David, the Coriolis force does as you say in the planetary motion (central force one-body or two-body) problem in co-rotating frame, since the motion of the body is only along r in that case. In any more general situation, Coriolis force is still orthogonal to the motion of the body in the rotating frame, whatever direction that may be.  Any textbook covering a problem more general than your favorite one can explain it to you. Dicklyon (talk) 23:48, 7 May 2009 (UTC)

Requested move
Centrifugal force (rotating reference frame) should be moved to Centrifugal force because Centrifugal force already redirects here; it is the primary topic of "centrifugal force", and "centrifugal force" is the common name for this topic. Furthermore, the only reason I can find for the current title is that it was moved here by User:Ggsgas during a prolific move vandalism campaign last year. According to naming conventions, an article should not be disambiguated any further than necessary, and the parenthetical disambiguation here is truly puzzling. Wilhelm_meis (talk) 12:19, 30 April 2009 (UTC)
 * Retraction. I would like to retract my request to move at this time, because the situation has changed dramatically and what was a simple redirect has now become a summary-style article. I believe this summary-style approach is more useful to the reader than a move-merge.  Any new thoughts in light of these changes, anyone? Wilhelm_meis (talk) 01:08, 9 May 2009 (UTC)


 * Wilhelm meis, I fully support your request to unite centrifugal force into a single article. The reason why it was split in the first place was because of what I would consider to be a specious argument. The argument ran that the centrifugal force as per this article acts on a different body than the so-called 'reactive centrifugal force' that is dealt with in the other article.


 * But anybody with a full comprehension of the topic can see that these two effects are merely two different aspects of the one force. Centrifugal force acts on body A. Body A then pulls a string taut. It is all one single force. But those who supported splitting the article would argue that the centrifugal force that acts on body A is one force and that the pulling of the string taut by body A, due to the centrifugal force acting on body A is another force. Feel free to unite the two articles if you wish. But I guarantee that you will encounter enormous opposition based on that specious argument which I have just shown to you. David Tombe (talk) 16:44, 30 April 2009 (UTC)


 * I also support a merge; there's no reason we shouldn't discuss both the reactive and fictitious force viewpoints in one article, even though David Tombe has a very idiosyncratic view of them that we'll have to continue to defend against. Until we merge, however, let's keep the topic specificity in the title and the hatnote. Dicklyon (talk) 18:37, 30 April 2009 (UTC)


 * This version of 27 April 2008 looks like the last sensible version, which the different viewpoints are made explicit up front; after that, Wolfkeeper submerged the reactive viewpoint and moved the article to be about only the fictional viewpoint; David fought everybody else for over a year, and Brews came in and over-expanded and complicated things. Can we move back to something sensible?  Dicklyon (talk) 18:53, 30 April 2009 (UTC)


 * No Dick, that version was a total dog's dinner of confusion. David Tombe (talk) 00:41, 1 May 2009 (UTC)


 * Apart from the fact that this is a move review not a merge review, in the wikipedia articles are properly on one or or more synonymous meanings of the title. (That's the primary difference between an encyclopedia and a dictionary, the latter which usually contains multiple definitions per article, see NOTADICT). Centrifugal force (in the rotating reference frame sense) and Centrifugal force (in the reactive force to the centripetal force) are anything but synonymous; they occur at different times to different bodies, act in general at different directions and vary differently, and are defined differently and have different cardinality and are used for completely different purposes by different people. In short. Hell No.. - (User) Wolfkeeper (Talk) 00:08, 1 May 2009 (UTC)


 * Wolfkeeper, you've got it all totally wrong. David Tombe (talk) 00:39, 1 May 2009 (UTC)


 * There is no right or wrong here, there's only well referenced material. Unfortunately, you don't have any.- (User) Wolfkeeper (Talk) 13:24, 1 May 2009 (UTC)

Actually, I requested a move, not a merger. If there is consensus to merge as well, I have absolutely no problem with that, but the simple title should not be a redirect to a senselessly disambiguated title. If someone wants to propose a merger, please do, but this is supposed to be a move discussion. Can I get everyone's thoughts on moving this article to Centrifugal force? I think it's important to have two separate discussions, one for moving and one for merging. Thanks. Wilhelm_meis (talk) 23:44, 30 April 2009 (UTC)


 * Oppose. The title helps the user understand what we are talking about and helps disambiguate it when there is more than one topic that goes with that name.- (User) Wolfkeeper (Talk) 00:08, 1 May 2009 (UTC)
 * So are you arguing that this is not the primary topic of "Centrifugal force", or that there is no primary topic? It seems that there may well be consensus (with a holdout or two) that these are closely enough related topics to merit a merger, as one unified topic, but, again, I don't want to digress into a merger discussion.  I'm just trying to clarify the consensus of what is the primary topic.  Again, it makes no sense to have Centrifugal force redirect to a needlessly disambiguated title.  Either this is the primary topic or it is not.  Wilhelm_meis (talk) 04:47, 1 May 2009 (UTC)


 * Support. I support move and/or merger. Anything to get the topic unto one page. David Tombe (talk) 00:36, 1 May 2009 (UTC)


 * Comment. It is completely ridiculous to have three separate articles about the same subject, and it really constitutes a three-way wp:content fork. One article says there isn't really a force, one says it is a fictitious force, and the third says it is really a centripetal force. Make up your mind and pick one name for the article, please, not three articles. Hint: Don't call it centrifugal force - there is no such thing, and please lose the hatnote "For the general subject of centrifugal force, see Centrifugal force (disambiguation)", and especially don't try to make a disambiguation page into an article about the confusion about which of the three content forks to go to. 199.125.109.102 (talk) 04:43, 1 May 2009 (UTC)
 * Agreed. Mostly.  I would argue that we should place the article at Centrifugal force because this is the common name used in English.  If we want to talk about the misconceptions inherent to the common term, fine, by all means, let's please do that, but let's also put it where it is easy to find and usable to the general reader.  I agree that the present situation defies common sense, but we need to set aside some of our disagreements over the finer points of definition and produce something useful to the general reader.  Then we can worry about making it more technically accurate.  Of course, it also helps if we avoid original research and synthesis and stick with what is published in reliable sources.  Don't get me wrong - I'm not accusing anyone of anything, but I think several editors here have become somewhat impassioned on the subject, and perhaps could better help the project by taking a deep breath and thinking objectively about the overall quality of the article(s).  Wilhelm_meis (talk) 04:56, 1 May 2009 (UTC)


 * No, no, no, and no again, you can not call it centrifugal force even if every person on the planet who has not taken physics (and that is over 99%) calls it centrifugal force. There is no such thing, it is centripetal force. You need to redirect centrifugal force to centripetal force and point out what it really is in the article, and cover it in one article, not three. Content forks are prohibited, and that is all that these three articles are - it would be like having two articles about the earth, one insisting that it was flat, and the other insisting that it was not. 199.125.109.88 (talk) 03:13, 2 May 2009 (UTC)


 * Actually, as wikipedia editors, we don't get to decide what to call it; we're supposed to report on what things are and what they're called, not try to enforce our own logic of what things should be called. But you're confusing the centrifugal (outward-directed) and the centripetal (inward-directed) forces; that's one more POV that we haven't heard from recently. Dicklyon (talk) 03:23, 2 May 2009 (UTC)
 * Dicklyon is absolutely right on this point. It is not our place as Wikipedians to prescribe what term people ought to use, but rather to describe what term people commonly use.  Please refer to WP:UCN and WP:NOT (especially note that WP is NOT a publisher of original thought, a soapbox for advocating a particular position - and yes this applies to physics as well as politics - nor is WP a textbook.  Wikipedia is an encyclopedia, and like any other encyclopedia, intended for the GENERAL READER.  That is where these articles are most deficient.  As to the argument against moving, no one has yet explained why this article should retain its parenthetical disambiguation AND be the target of a redirect from the simplified title.  If anyone can explain that to me, then I will be satisfied enough, but otherwise, I fully intend to see this article moved to Centrifugal force.  Then the pedantic professors can resume squabbling and bickering over its content while its readability continues to suffer tremendously.  Wilhelm_meis (talk) 12:37, 2 May 2009 (UTC)


 * Support. It's a step toward reunification, so let's do it.  I disagree with Wolfkeeper's rationale "The title helps the user understand what we are talking about and helps disambiguate it when there is more than one topic that goes with that name" because I think that we should not keep the article so narrow that it can't compare and contrast the different viewpoints on centrifugal force; what we have now is a POV fork, which is generally frowned on. Dicklyon (talk) 05:34, 1 May 2009 (UTC) see new opinion below


 * There is no unification. They're completely different forces. One is a real force you get in all references frames, the other you only get in rotating ones and is a pseudoforce. One was discussed by Newton (reactive) but the rotating reference frame was completely unknown to him. One is a D'Alembert force, the other, not. The only thing they have in common is the name. They are NOT synonymous. They are NOT defined in the same way, or even similar ways. The wikipedia does not have multiple definitions of a single term unless there is significant overlap other than the name. In this case... just the same name. Oh and they point away from a centre. But different centres. Oh and reactive centrifugal force isn't associated with a coriolis force... but this one is. This is the sister article to coriolis effect, it is completely distinct from the reactive centrifugal force in every important way.- (User) Wolfkeeper (Talk) 13:12, 1 May 2009 (UTC)


 * Oppose. Given the apparent intransigence of the various people who like the different points of view, or like them separate, a better idea is to write a short article at Centrifugal force in summary style, to link the rotating frame and reaction articles that can then keep their bloated form. Dicklyon (talk) 23:51, 1 May 2009 (UTC)

Merge proposal
As long as we're working on the move question, let's also consider the merge question that opened above. I've added a mergeto on Reactive centrifugal force and a mergefrom here. I notice that Reactive centrifugal force already has a section on the fictitious force in a rotating frame; and this article has a lot of bloat; so that merge would need to get rid of a lot of stuff. I think it would be a big win, if people don't hang tightly to the current big mess. Dicklyon (talk) 05:41, 1 May 2009 (UTC)


 * Support as nominator. Dicklyon (talk) 05:41, 1 May 2009 (UTC)

As stated above, now that the situation has changed and we are looking at a summary-style article, I find this summary-style approach satisfactory. It does not bring the entire subject under the umbrella of a single article, but it gets the basics there and then people can read on to learn more if they want to. Maybe someday it can all coexist in one article, but for now at least, the summary-style approach is the best way to build consensus and make the material accessible to the general reader. Wilhelm_meis (talk) 01:13, 9 May 2009 (UTC)
 * Support . I agree.  The more I dig into this topic, the more I see that these articles really are looking at the exact same phenomenon from different perspectives (which would make them WP:POVFORKS).  The whole thing about "rotating reference frames" is just to give the observer a more subjective viewpoint to make the same "force's" effects easier to understand in certain applications.  The problem I find with it is that we have what amounts to a POV fork buried under a slew of jargon to befuddle the general reader with endless mathematical formulae, instead of explaining the concepts in a clear and concise way like this and this.  What I see is that while editors have focused on the minutiae of verbiage, the overall articles have suffered until they are barely understandable to a casual reader.  Please remember, not everyone who reads WP has a Physics degree (or even an 8th grade understanding of Math!).  I think we need to get it much more geared to the general reader.  That's my $2x10-2. Wilhelm_meis (talk) 06:22, 1 May 2009 (UTC)


 * Wilhelm, If you carefully read through the past debates, you will see that that is exactly what I have been trying to do. I have consistently argued for one single article with a short introduction describing the centrifugal force as the outward force that is associated with rotation. More recently I have been trying to get a consensus to drastically reduce the planetary orbital section to a small paragraph which simply states the central force equation 3-11 out of Goldstein's 'Classical Mechanics', names the terms in that equation, and points out the fact that the centrifugal force term can pull a string taut. As for the so-called reactive centrifugal force, there is no such thing. Those that are advocating such a concept as a separate existence are referring to the effect of pulling a string taut by virtue of it being attached to an object which is experiencing centrifugal force. David Tombe (talk) 10:38, 1 May 2009 (UTC)
 * I too would encourage people to read the archives. They mostly show that David Tombe has been spamming the talk page over a considerable period with his views, and completely misunderstands the physics. Among other things he thinks that coriolis effect only acts at right angles to the central rotation axis, whereas anyone who knows cross products (i.e. not Mr. Tombe) can immediately see that the equation says that coriolis acts at right angles to the velocity- which is by no means constrained to be radial. In short, he's in my (at least somewhat educated) opinion, a crank. A crank that has been banned for spamming his drivel here before; and with any luck will be again. He also thinks that relativity theory is wrong, and that magnetism is a form of centrifugal force. Needless to say this is not the neutral point of view. Essentially every edit he makes tries to distort the article towards this point of view. If you actually make any edit and Tombe agrees with it, there's a very high chance that you've messed up. In this case, coriolis force and centrifugal force come out of the same equation; one that does not give you reactive centrifugal force. If anything there is a much stronger case for merging coriolis and centrifugal force together- they are a pair.- (User) Wolfkeeper (Talk) 14:42, 1 May 2009 (UTC)


 * Wolfkeeper, anybody who has seen the transverse planetary orbital equation should know that the Coriolis force is exclusively a transverse force. David Tombe (talk) 22:39, 1 May 2009 (UTC)
 * Sure, that's true. For polar coordinate analysis there is an angular acceleration due to changes in the radial distance. But in rectangular coordinates (that this article is about) there's an inward and outward force when the body moves circumferentially and in general there is a force that acts at 90 degrees to the motion. If you understood this you would never make the incorrect general statements you are continuing to make. It is my opinion based on your statements over that you are incapable of understanding this article. I find this sad, but I'm not about to let you dumb the article down.- (User) Wolfkeeper (Talk) 00:34, 2 May 2009 (UTC)

Wolfkeeper, that's an argument for the Coriolis force page. It seems to me that you are incapable of understanding the implications that are inherent in the derivation that leads to the rotating frame transformation equations. If you understood that properly you would see that it is identical to the polar coordinate derivation, and that it is all one single topic and that Coriolis force is a transverse force that is linked to conservation of angular momentum and Kepler's second law. As for rectangular coordinates, the coordinate system doesn't effect any realities. But who would ever think of using rectangular coordinates for situations such as centrifugal force which are totally suited to polar coordinates? This business of continuing to introduce Cartesian coordinates is just a diversion to cloud the issue. David Tombe (talk) 10:07, 2 May 2009 (UTC)


 * I wouldn't agree that the article is tied to rectangular coordinates; the physics doesn't depend on this. But it has to be recognized that the r dimension is a dimension in a rotating reference frame, a fictitious 1D rotating system.  This is what David is unable to relate to.  And no matter how you do it, Coriolis force is a fictitious force, just like centrifugal force, that depends on velocity in the rotating system, as opposed to the centrifugal that just depends on position.  In the 1D fictitious system, it plays no role, since there's no motion except along the radial. Dicklyon (talk) 01:24, 2 May 2009 (UTC)


 * Oppose They are completely different. One is a real force, the other is a pseudoforce. They act around different centres, were invented at different times, and share only a name. The wikipedia is not a dictionary. The real force can have multiple centres in any frame, while the pseudoforce, only one. etc. etc.- (User) Wolfkeeper (Talk) 13:26, 1 May 2009 (UTC)
 * Support. I also see the two articles as describing different aspects of the same phenomenon. -AndrewDressel (talk) 13:30, 1 May 2009 (UTC)
 * Oppose. Wolfkeeper is entirely right: one is a force the other a pseudoforce; moreover, the examples given in the two articles illustrate different phenomena and different methodology. It is not going to make things clearer if some of these examples are deleted, or the contrast between them has to be continually made throughout a combined article. Finally, if there are supporters of a merger on the basis that the two topics really are one, it behooves them to explain away the differences in this table:
 * Brews ohare (talk) 22:27, 1 May 2009 (UTC)


 * Explaining the differences in that table is exactly what the article would need to do; we don't need to do it here, as nobody is claiming that these two things are "the same"; just that they are the different facets of the topic of centrifugal force. Dicklyon (talk) 22:54, 1 May 2009 (UTC)


 * As a matter of clarity, it's better to keep separate topics separate. I believe this talk page and the one on reactive centrifugal force both illustrate clearly that separation is the wiser course. For example, it took inclusion of the exploded force diagrams on the reactive force page to convince many just how the reactive force was to be understood. Brews ohare (talk) 00:23, 2 May 2009 (UTC)


 * Support. There is no such thing as the reactive centrifugal force. The effect which is being discussed in that article is a knock-on effect on another object, ultimately caused by the one and only centrifugal force. And that knock-on effect is most certainly not reacting to any centripetal force. It exists in its own right. The references in that article which use the term 'reactive centrifugal force' are not even referring to the effect which is being covered by that article. For example, the so-called reactive centrifugal force acting on the Sun is the one and only centrifugal force as per equation 3-11 in Goldstein. David Tombe (talk) 22:39, 1 May 2009 (UTC)

Other merge proposal
It has also now been proposed that this article be merged to centripetal force. Dicklyon (talk) 03:51, 2 May 2009 (UTC)


 * Support. The subject needs to be covered, and explained, in one article only, at Centripetal force. Splitting it into three POV's is prohibited. One of the first things you learn in physics is that when you swing a bucket over your head that isn't a centrifugal force you are feeling, it is a centripetal force (but how would you know, every force produces an equal and opposite reaction - Newton's Third Law of Motion). 199.125.109.88 (talk) 03:35, 2 May 2009 (UTC)


 * Oppose. You cannot merge centripetal force and centrifugal force. They are two different forces. In the planetary orbital equation, the centripetal force is gravity and it is an inward force, whereas the centrifugal force is an outward force. In general, the centripetal force is an inward force supplied by something like gravity, or the tension in a string, or the normal reaction from the floor of a rotating cylinder. Centrifugal force is an outward force that is induced by absolute rotation. There can be no question of merging centripetal force with centrifugal force. That truly would mess it all up. The only topic that all these concepts can be dealt with together in a unified fashion is Kepler's laws of planetary motion. But if you go to that page, you will see that the same obstructions are present. There is a prohibition on using the names centrifugal force and Coriolis force for two of the terms in the equations. David Tombe (talk) 09:28, 2 May 2009 (UTC)
 * See below. Referred to Jimbo. 199.125.109.88 (talk) 17:19, 6 May 2009 (UTC)

New summary article; close merge and move proposals?
I've created a brief summary-style article at Centrifugal force, which should serve to give a bit of positioning, via the table of the different points on view relevant to these topics, assuming that nearly equal and opposite forces from David and Brews don't drag it in opposite directions until it turns into another bloated POS. I think this makes all the current move and merge proposals moot, but before I remove them, please speak up if you disagree. Dicklyon (talk) 23:27, 5 May 2009 (UTC)


 * Dick, you've taken on the role of chief organiser of this article and you haven't got a clue about the topic. You are deliberately twisting what Goldstein says. Goldstein says that equation 3-12 is the same equation as occurs in the equivalent 1-D problem. Goldstein does not say that equation 3-12 is a fictitious 1-D equation. You have been told this many times but you are persisting on imposing this falsity into the article. You are deliberately falsifying this article. You have a sympathetic crowd on your side who know very little about the topic. I've reported the matter to Jimbo Wales. If he is happy enough with your collective efforts then so be it.David Tombe (talk) 23:40, 5 May 2009 (UTC)
 * What? Reported the matter to Jimbo Wales? Sorry, I have to get a chuckle from that. I see that this summary style article needs some work in a few areas, but it is a vast improvement over the existing situation.  Now, when a user who has only the vaguest idea what "centrifugal force" means searches the term, they will find something that explains it in a way that is accessible.  That, and the elimination of the simple redirect from Centrifugal force to the more disambiguated title, is all I have been advocating.  While I don't fully agree with Dicklyon's edits, I applaud his efforts to produce a common sense solution where it is so desperately needed. Wilhelm_meis (talk) 14:17, 6 May 2009 (UTC)
 * Me too. I'm sure that Jimbo will rush on over and quickly straighten this all out. Top priority for the one and only editor for all things most important to get right. However, as I see it, you have an object moving in a non-linear path and you want to know the force acting on it to make it move in such a path. Why do you need three articles to describe it? I really don't care what reference frame you are in, it is still the same force. Anyone with any knowledge of physics knows that it would go in a straight line unless a force was pulling it in which direction? Well that would be toward the axis, and not away from the axis. Hence it is properly called centripetal force. When you get into non-circular paths, you can add a section in the centripetal force article to cover that, but there is no need for a separate article, and no need to invent a separate term from the one that everyone knows so well. 199.125.109.88 (talk) 17:09, 6 May 2009 (UTC)


 * You're right that the centripetal force is what makes the object follow a curved path. But in other frames, that's not how it looks: in a rotating frame, there is an additional force, the centrifugal one, and the objet might appear stationary or following some other shape of path, possibly curved outward.  And that object also exerts an equal and opposite reactive force, centrifugally on the object that's exerting the centrifugal force on it.  I agree it shouldn't take three articles to describe it; so now we have four, and that's better, since one of them is simple enough to read. Dicklyon (talk) 17:17, 6 May 2009 (UTC)


 * Wilhelm, thanks for your support. FyzixFighter, too (see my talk page).  Hearing no objections, I'll go ahead. Dicklyon (talk) 17:17, 6 May 2009 (UTC)

Isn't creating a fourth article kind of pointy? 199.125.109.88 (talk) 17:22, 6 May 2009 (UTC)


 * See WP:SUMMARY for the guideline justification. Dicklyon (talk) 17:33, 6 May 2009 (UTC)

Wilhelm-meis, The reason why I went to Jimbo Wales was because all efforts to do the very thing that you are now advocating have been consistently thwarted. Just like yourself, I have been advocating a single article. I have been advocating a unified, shortened, and simplified article. I have explained to all here, in a few lines, exactly what centrifugal force is. It is an outward inverse cube law repulsive force which is induced by rotation. It appears in the planetary orbital equation alongside the centripetal force of gravity, and the two forces are not in general equal and opposite. They operate in tandem to produce hyperbolic, elliptical, or parabolic orbits.

I have been accused of original research in this respect, but the equation in question is found at 3-12 in Goldstein's 'Classical Mechanics'. It is also the method which was used by Gottfried Leibniz in the 17th century. Dicklyon has been trying to obfuscate this simplicity by introducing irrelevant concepts such as rotating frames of reference, equivalent 1-D problems, and fictitious forces. We now have an anonymous 199.125.109.88 who hasn't got the first clue about the subject and who is trying to tell us all that centrifugal force is the same thing as centripetal force, and he has now even got centrifugal force directed to centripetal force, and nobody has done anything about it. Everybody is being so polite to him. The situation is going from bad to worse. I can't see how you can have noticed any improvement as you claim. Administrator intervention is badly needed here.

If you believe that there should be a single unified article on centrifugal force, then let's see you do it. Let's see you put your money where your mouth is. I can't do it because it would be instantly reverted. And as regards your applauses for dicklyon's efforts to reach a common sense solution, I think that you need to open your eyes a bit more. A common sense solution would be one single article detailing the three existing approaches to the topic in summary fashion, because there is not that much that needs to be said about each approach. I could even write a short summary for the two approaches that I disagree with.

And now I've just seen that you have awarded a merit to dicklyon for his common sense approach. It's becoming like Alison Wonderland. Dicklyon actually removed my edit about the Leibniz approach from the disambiguation page. Where was the common sense there? There is far too much bonding and alliances going on here for it ever to be possible to get a sensible article. I can see that it will get alot worse yet. David Tombe (talk) 19:25, 6 May 2009 (UTC)


 * Yes, Alison Wonderland; that's me alot. Dicklyon (talk) 03:50, 7 May 2009 (UTC)
 * Indeed I did applaud Dicklyon's sensible, good-faith efforts to improve the readability of WP's coverage of "Centrifugal force" and not merely advance a particular point of view. I applaud the good-faith efforts of other editors with whom I just as frequently disagree.  It's part of civility and it helps us build consensus when we identify the good ideas that we can agree on, and act on them.  I think this article and this talk page have suffered precisely because of the inability of several editors to find common ground and build consensus.  Several editors seem to be more interested in advancing a particular view of some aspect or another of the subject, rather than working together to produce a more readable article.  The summary-style article is a good model that is frequently encouraged on Wikipedia, and in this case it may be just the thing to get some of the other editors on board with building a better article.  I hope so, and in any case he acted on it boldly, decisively, in good faith and to fairly good effect.  I hope we can all get behind this and make it an accurate, well-rounded, and easily readable summary-style article.  In this case, I do think four articles is better than three, and quite possibly better than one.  I just hope we can all set aside the personal attacks and accusations of confusion or bad faith. Wilhelm_meis (talk) 07:50, 7 May 2009 (UTC)

Wilhelm, since you don't fully agree with my edits, I hope that means I'll be seeing some improvements from you. And big thanks for the barnstar.

I think maybe we should also take the "Development of the modern conception of centrifugal force" section out of rotating frame article, make a whole new article on this interesting history, and put a short summary of it into centrifugal force. Opinions, anybody? Dicklyon (talk) 03:50, 7 May 2009 (UTC)


 * Wilhelm, Yes, I've been pushing a point of view. You should be taking a closer look at the collective efforts which have been going on to totally suppress that point of view. I think that we have all clearly identified four points of view on this subject. Any final article will therefore have to treat all four points of view. These are,


 * (1) The Leibniz approach. Centrifugal force is a real outward force induced by the actual circulation of an object. It obeys an inverse cube law and it is not in general equal to any inward centripetal force which may or may not be acting. This is the approach which is used to solve planetary orbital problems and it is found in Herbert Goldstein's 'Classical Mechanics' (1950) which is a gold standard university textbook. It was somewhat tampered with in the 2002 revision, such as to water down the Leibniz approach. The Leibniz approach is the only approach which I support.


 * (2) The Newton approach. Centrifugal force is real, and it is equal and opposite to the centripetal force. This approach appeared in textbooks up until the 1960's. Nelkon & Parker 'Advanced Level Physics' is a clear cut case of a high school textbook which used this approach and then dropped it in the 1970's. This approach is wrong in my opinion because centrifugal force is not always equal to the centripetal force, and it is not a reaction to the centripetal force. Neither can the two be an action-reaction pair, because the two forces act on the same object.


 * (3) The rotating frames transformation approach. This possibly originates with Gaspard-Gustave Coriolis in 1835. It is clearly the most common approach in modern textbooks. It considers that the centrifugal force and the Coriolis force are fictitious forces that can only be observed from a rotating frame of reference. I do not support this approach because the rotating frames are unnecessary and the maths has been set loose from the physical realities.


 * (4) Those that once adopted the Newtonian approach at (2), often replaced it with a new attitide in which centrifugal force doesn't exist. They would restrict their demonstrations to the special case of circular motion and point out how a centripetal force causes the straight line motion to curve into circular motion, and that as such, no other forces need to be involved. Hence there is no such thing as centrifugal force. I totally disagree with this point of view as it totally ignores the already existing outward centrifugal force relative to the origin, which obeys an inverse cube law relationship as per the Leibniz approach. David Tombe (talk) 12:08, 7 May 2009 (UTC)


 * Well summarized. Paraphrasing: the only correct POV is the one no longer found in textbooks, and that's due to a big conspiracy; furthermore, most of what's in textbooks is about something that doesn't exist, and that's part of the same conspiracy.


 * Another way to look at it is this: the only thing wrong with the Leibniz/Goldstein approach (1) is David's interpretation of it, since it's actually just an application of rotating reference frames (3).  Approach (2) is still also widely reported in books, but in this approach it's not the case as David says that "the two forces act on the same object,", and it's not restricted to circular or any other particular paths; it's just Newton's third law.  The "fictitious" forces (3 and 4) do exist; they are terms in the equations of motion in rotating frames, and only David confusion the notion of "fictitious" with non-existence.  These fictitious forces (centrifugal, Coriolis, and Euler) are a mainstay of machine designers, such as roboticists and such, as well as of meteorologists, and many ohters.  Dicklyon (talk) 00:07, 8 May 2009 (UTC)

Dick, the exact point where you are distorting this entire topic is where you are trying to say that the Leibniz approach and the rotating frames of reference approach are one and the same thing. They are not. Leibniz is quite clear about the fact that the centrifugal force is a real outward force induced by actual circulation of the object. The rotating frames approach puts the cause of the fictitious centrifugal force in the lap of the rotating frame of reference. The two approaches are quite definitely different. You are trying to obliterate the Leibniz approach using this specious line of argument. It's like as if you are trying to deny that the colour blue exists by saying that it is the same thing as the colour red. As for the Laurel and Hardy show going on over on the main page between you and FyzixFighter, I'll take a back seat now and watch it. You guys are desperately trying to deal with planetary orbits by strapping a rotating frame of reference around the problem. That is simply not the way to do it. You are trying too hard to blend the Leibniz approach with the rotating frames approach. At any rate, as I said below, I'll leave you to it. I do not intend to make any more edits on the main article here. Rotating frames are a rubbish concept unless they are associated with some kind of physical reality such as a rotating turntable and dragging forces. David Tombe (talk) 09:47, 8 May 2009 (UTC)

Induced by transverse motion?
David put "the centrifugal force, a force component induced by the transverse motion" where previously we had "induced by the rotating frame of reference;" with edit summary "this is an example of the distortion that has been going on. Frames of reference are not involved in the Leibniz approach. Goldstein doesn't mention them". While I agree that Leibniz didn't get there that way, and Goldstein didn't say so explicitly, it's very unclear to me what he means by "induced by the transverse motion;" is there a source that explains centrifugal force in those terms?

I reviewed Goldstein on his; he gets to the F=ma like the one in our article, from Lagrangians, but interprets it the same way, with the central force (e.g. gravity) being the only term in "the force along r" (at his 3.11) and says nothing yet about centrifugal force; he has the centripetal acceleration term in the "a" side, but doesn't call it anything. Later, in his section "The equivalent one-dimensional problem" he has modified the force by adding "the familiar centrifugal force" term, for the "fictitious one-dimensional problem", which is the same as the r coordinate in the co-rotating frame, as I thought was obvious, and which the other sources, and newer editions of Goldstein, make more explicit. This term is "induced" there to make the F=ma work out in this rotating frame of reference, whether he invokes those words or not.

I also just noticed, David, that if you go back to pages 24-25 in your 1950 Goldstein, you find that he commits the same grievous sin that I did, of calling the term in the polar-coordinates equation the "centripetal acceleration". Curiously, the index vectored me there for "centrifugal force"; the index writer must not have seen the difference in these terms. Also, the only other "centrifugal" I can find in the book is where he has "the familiar centrifugal force" term in eq. 4-107, discussing "an observer in the rotating system" and says "the centrifugal force is the only added term in the effective force," p.135-136. So here "effective" is the sum of real and what we nowadays call "fictitious" forces. Obviously, here in Goldstein, it's induced by the rotating frame of reference.

So give it up. Dicklyon (talk) 15:20, 7 May 2009 (UTC)


 * No Dick, Goldstein doesn't mention rotating frames of reference. I don't see how you can conclude from Goldstein that the centrifugal force is induced by a rotating frame of reference. Anyway, I see that I am on the wrong page here. There is another page, seldom used, called 'centrifugal force'. This page is exclusively for the rotating frames of reference approach to centrifugal force which I am not interested in. So I will leave you to it. There are a few topics on the main article here which should not be in the article, such as planetary orbits, rotating buckets of water, and centrifugal potential energy. But I'll leave it for somebody else to delete those topics. I'll not be back on this page because I don't believe that this page should exist. David Tombe (talk) 20:39, 7 May 2009 (UTC)


 * Actually, he does mention rotating reference frames, and I gave you the page number above. However, I have NOT concluded from Goldstein that centrifugal force is induced by this rotation, as he was not very clear on this point in that old edition.  I've concluded it from the wealth of other and more modern sources, and merely pointing out that there's nothing in Goldstein to contradict that common understanding; in fact, it's easy to read Goldstein as clearly supporting it, even though in the section that interests you he doesn't apply the term "fictitious" to the force, but only to the system and the potential. Dicklyon (talk) 23:34, 7 May 2009 (UTC)

Dick, you're still trying too hard to see what is not there. David Tombe (talk) 09:49, 8 May 2009 (UTC)

Redundancy in Planetary Motion
One purpose of this section is to drive home the points made elsewhere but in a context which some find more familiar. To streamline this section omits a great opportunity to say exactly what the fictitious force idea is and how it comes about. Brews ohare (talk) 23:35, 7 May 2009 (UTC)


 * Can you explain what you have in mind? No offense, Brews, but my impression of your attempts to explain things is that they usually do more to confuse and distract along marginally relevant tangents (that's centrifugal right there!), so let's go about this with the reader in mind, carefully. Dicklyon (talk) 23:38, 7 May 2009 (UTC)
 * Oh, I see it's what you and FyzixFigher are up to. Looks to me like both of you are adding more words than are needed, and I generally support the more concise ways without the tangential complications; just go carefully.  Dicklyon (talk) 23:44, 7 May 2009 (UTC)


 * Brews, if you felt that my removal of redundant material was wrong, why did you not simply reinsert the material I removed instead of blanket reverting me? A good portion of my edit was actually a rearrangement of the current text, and clarifying the connection with the previous "Derivation" subsection. I even added in a reference that was deleted in your revert. I'll redo some of the edits in pieces so that we can more precisely pinpoint were we disagreee.
 * For example the "As an aside..." comment is slightly wrong. The ensuing statements would be true for all co-rotating frames, including those for elliptical and unbound orbits. In all those frame, $$\dot\theta'$$, is zero by definition of the co-rotating frame. And maybe I'm misreading you but I wouldn't call the centrifugal force term an "ad hoc" or "fitting parameter", since if the observer knows the rotation rate of his frame, he can calculate what the pseudo-forces should be. I'd rather connect up the "ad hoc"-ness with the previous derivation rather invoke "fitting parameter" which sounds far too arbitrary. --FyzixFighter (talk) 00:41, 8 May 2009 (UTC)


 * I agree that the "aside" bit was not helpful, and somewhat wrong; certainly misleading with respect to the whole idea of co-rotating. Dicklyon (talk) 00:43, 8 May 2009 (UTC)

I'd like to know what was "somewhat wrong"; I'd agree that the remark could be made more general, but I'd say that what was said was correct. Moreover, I think the "ad hoc" thing is very pertinent and totally accurate. Get's the idea across so clearly that it makes you two wince. Brews ohare (talk) 03:26, 8 May 2009 (UTC)


 * You had written that "As an aside on the case of circular motion with r = constant, it may be noted that to the co-rotating observer, for whom the body does not rotate, there is no directly observed $$\dot\theta$$." Besides the filler words like "as an aside" and "it may be noted", there's a clear implication here that what you're saying only applies in the case of circular motion; in fact, it applies for any orbit shape, by the nature of "co-rotating".  Then later "If the observer rotates at a different rate from the particle",  which is out of place in this section.  And the bit about the observer being "forced" and things coming "out of the blue" is just adding mystical words where none are needed. There's still something in there about "ad hoc" that doesn't add anything to the discussion.  What's ad hoc about writing the F=ma equation in the co-rotating frame?  Dicklyon (talk) 04:42, 8 May 2009 (UTC)


 * Come on Brews, set your ego aside. Veiled personal insults are just as unacceptable from me and you as they are from David. I wince so much at "ad hoc" that in both my edits, the earlier one that you blanket reverted and my last series of edits, I left in most of the "ad hoc" comments. Alright, sarcasm aside - I really don't mind the "ad hoc" comments too much - I've seen similar phrasing in textbooks saying that the fictitious forces are the way we "bootstrap" Newton's Laws to work in rotating frames. "bootstrap" vs "ad hoc", meh, six vs half-dozen. Where I think your "ad hoc" was lacking was, as I tried to communicate before, in the key point of connecting it back to the proof in the "Derivation" section for why the "bootstrap"ing is valid. In other words, it wasn't clear how this "ad hoc" method connected back up to that "ad hoc" derivation. That connection is essential to helping the reader understand how this familiar example relates to the larger context of a centrifugal pseudo-/ad hoc force due to observations being made in a rotating frame. --FyzixFighter (talk) 05:12, 8 May 2009 (UTC)


 * And don't forget that these are examples. It's not necessary to go into every possible complication.  And you don't need extra links to Orbit both before and after, with a gratuitous parenthetical inviting the reader to go get more detail.  Keep it simple.  Dicklyon (talk) 05:17, 8 May 2009 (UTC)


 * As for the ad hoc, as some of the sources make clear (was it Taylor?), this works because it's the same equation; just moved a term to treat ddot r as acceleration; so I rephrased the text to clarify that, as that simple connection had been lost. Dicklyon (talk) 05:17, 8 May 2009 (UTC)

Ah well, I have been beaten to a pulp. Nonetheless, the introduction of dot theta by the rotating observer is certainly ad hoc in the meaning found at ad hoc for this simple reason: the rotating observer has no way whatsoever to establish dot theta except by fitting his data (yes, really fitting in the sense of regression analysis) in order to find what the dot theta term on the Force side has to be. Remember, the body is stationary, so he has no information about dot theta, which is not directly observable, but can only be inferred. If he can't get a fit, like the astronomers with their galactic rotation, he'll have to invent something new, like dark matter. I thought this startling state of affairs was worth mentioning because it really makes clear that a fictitious force is a different kettle of fish from a real force. The inertial observer can measure dot theta and there is nothing ad hoc about their use of Newton's laws: everything is tied down. Brews ohare (talk) 05:38, 8 May 2009 (UTC)


 * Ah well, what doesn't kill you will make you stronger. Why are you concerned about what the observer knows?  This isn't about an observer trying to figure out what's going on, it's just a description of what is, that is, of equations that describe the motion, given the parameters.  It's a whole different game to say imagine you're in that frame and don't know the parameters and try to deduce them from the motions you see.  Not a bad game, but not at all what this section is about, and not at all what any of the cited sources are about, as far as I recall. Dicklyon (talk) 05:58, 8 May 2009 (UTC)


 * Dick: To paraphrase your reply above: what I said was correct, it is interesting, but you personally find it insufficiently on topic? Pardon me. My view is that it is on topic. I'd suggest that you re-think what the article is about: it isn't about which side of the equation a term is put on - who gives a #$%* about that? Brews ohare (talk) 12:50, 8 May 2009 (UTC)


 * Not really correct in this context, since we're in the context of co-rotating frames. And this "which side of the equation a term is put on" is exactly how the sources describe the relationship between the equations of motion in the different frames, between centripetal acceleration and centrifugal force.  If you see a better way, show us the sources.  Your tendency, amply demonstrated here and at other articles, is to over-complicate and bloat articles, provoking edit wars in the process; that's something to reflect on. Dicklyon (talk) 14:25, 8 May 2009 (UTC)


 * Dick: Your assault upon my contributions is unbalanced, unproductive, uncooperative, uninformed, unwarranted, unprovoked, unkind and contrary to Wiki policies.


 * Your interpretation of the sources as an argument over "which side the term is put on" is a bit oblique. The point is the interpretation attached to which side the term is put on. This interpretation is exactly the point of my comments: put on the "acceleration side" the interpretation of the term is kinematic, that is, based upon observation of the orbit and of ω and calculation of the implied centripetal force. Placed on the "force" side the interpretation is as an inferred centrifugal force using a fitted value for ω that cannot be directly observed, in other words, a deus ex machina. I don't think any additional sources will help here; that is what the sources say, and the Wiki article should say the same. However, here's another example I've dredged up: Genz, who points out how using the possible ω of the Universe as a fitting parameter one can deduce from the flatness of a galaxy whether the Universe is rotating. To explain a little: the flatness of the galaxy depends on how fast it rotates; if the rotation of the Universe is a portion of the observed rate of rotation, the galaxy will appear to rotate at a rate different from its actual rate of rotation, so the flatness won't come out right. It's a large-scale version of the bucket argument. Brews ohare (talk) 15:14, 8 May 2009 (UTC)


 * OK, my view was a bit harsh; sorry. As for an argument over which side of the equation a term goes on, I never found or mentioned any such argument.  The sources are very clear that it works both ways equally well, with one representing forces and accelerations in the inertial frame, and the other in the co-rotating frame.  I didn't notice anything about a kinematic versus kinetic interpretation, but will be happy to take a look if you point out the source.  I have seen some of this stuff you refer to in the cosmological context, but not in the planetary orbit context; remember, this is an example, not a place to open up whole new discussions of concepts not yet introduced. Dicklyon (talk) 16:05, 8 May 2009 (UTC)

Apologies accepted. Of course "The sources are very clear that it works both ways equally well" That is a given: everyone agrees upon the observations, so they must use the same equation. The only issue is how the different observers reach their (commonly agreed upon) formulation. That is the point. Brews ohare (talk) 16:19, 8 May 2009 (UTC)

Brews, I won't be editing on this page anymore for the reason that I personally don't think that rotating frames of reference are necessary to analyze the planetary orbital problem. I would also like to show you an interchange between dicklyon and FyzixFighter that appears on FyzixFighter's talk page,

''Do you a current best version of your proposed short section? Let's go ahead and replace the long Brews section with a short one, and try to keep Brews and David from messing up the article too much from there. If I don't hear from you, I'll try to do it from the one on the talk page and maybe a few edits. Dicklyon (talk) 19:44, 25 April 2009 (UTC)''

'':Thanks for doing this. I nearly did put it in after Brews' "diatribe" which was just plain bad physics. However, some much more important real life issues (getting a couple of papers I'm co-authoring ready and submitted to journals) have taken precedence, to the point that I haven't even tried to follow any of the discussion since my last post. I'll try to find some time to review the current version, but I'm pretty sure that there won't be much that I can add if you and some of the other anti-bloat editors have been your usual excellent selves. I also never thanked you and some of the others for the feedback, support, and general words of encouragement - so thank you for that. I can't guarantee my ability to follow the editing or discussion in the next few months, but if the debate escalates to official or unofficial mediation or guided group dispute resolution, please be sure to let me know either here or via email so I can be sure to participate. Thanks again. --FyzixFighter (talk) 20:15, 5 May 2009 (UTC)''

It is quite clear from this that there is no point in attempting any further to make these pages better. Dicklyon and FyzixFighter have agreed to gang up and thwart any efforts which you or I make to improve these articles. That is how childish it has all become. In fact, if you check the record, you will see that since I opened my account, FyzixFighter has only ever come to physics pages to undermine my edits. In such a childish environment there is no hope of having any beneficial effect on these pages. David Tombe (talk) 07:00, 8 May 2009 (UTC)


 * I agree that the situation has become rather childish with all the edit warring and incivility that has gone on, but I hope everyone can hang in there and find a way to work together. The more these edit wars go on, the more the articles will suffer.  Every time anyone here reverts another's edit (right or wrong) or accuses another of anything ranging from confusion to idiocy, he has done the reader a disservice.  These articles have suffered terribly for all the squabbling and reverting.  We need to work together much better than this, and I have seen some progress on this front, but more is needed still.  Let's all set aside our egos and help each other write a better article.  If you think someone has misunderstood something, explain it better, but don't tell that person how feeble-minded you imagine them to be.  If you disagree with someone's edit, discuss it here on the talk page BEFORE reverting it.  If you disagree with someone else's philosophy, try to understand why they believe as they do.  Above all, we MUST stick closely to the verifiable sources and avoid original research and synthesis arguments.  That will create an argument every time.  Stick to the sources and provide inline citations for everything.  If you think it's getting too heavily referenced, just have a look at Swedish heraldry.  There's no such thing as too many references to reliable sources!  It just shows that you're not inserting OR or BS.  And it avoids a lot of these very arguments.  Come on guys, we can do it, just be nice and keep cool. Remember, we're just editors and this project isn't about us, it's about the READER. Wilhelm_meis (talk) 16:23, 8 May 2009 (UTC)


 * Indeed, well put. I acknowledge my regrettable tendency to get somewhat mean when running out of patience, and I'll try to keep that in check. Dicklyon (talk) 05:22, 9 May 2009 (UTC)
 * Thank you, Dick. That kind of honesty and humility is what is needed from everyone here. Wilhelm_meis (talk) 13:19, 9 May 2009 (UTC)

Brews, I removed the creeping complexity that came from introducing the "kinematic" terminology and interpretation into the planetary section; none of the sources on this topic, as far as I've seen, use anything like that approach. I didn't see anything about planetary motion in the sources you cited. I'm sure there are appropriate places to introduce kinematics, but I don't think this is it. Dicklyon (talk) 06:04, 9 May 2009 (UTC)

Interpretation of radial equation
I'd like to initiate discussion of a point of view that seems to me useful, but is not accepted by Dick. I'll do that by bringing up some older statements that have been overridden.

A co-rotating frame is one rotating with the object so that the angular rate of the frame, $$\Omega$$, equals the $$\dot\theta$$ of the object in the inertial frame. In such a frame, the observed $$\dot \theta $$ is zero, so the term $$r \dot\theta^2$$ in the acceleration is zero. In this frame, however, to adequately predict the object's motion, a $$m r \dot\theta^2$$ term must be included on the force side of the equation and the equation becomes:


 * $$F(r) + m r \dot\theta^2 = m\ddot r $$

where the $$m r \dot\theta^2$$ term is known as the centrifugal force. Because the object is not seen as rotating in the co-rotating frame, the $$\dot \theta$$ parameter in this term is not observable directly, but is inferred.


 * Footnote: For example, in the rotating spheres example, the tension in the cord between two rotating spheres is indicative of the centripetal force required by their rotation, but in a co-rotating frame this tension is used to determine the rate of rotation of the frame. See and

This notion that the angular rate appearing in the centrifugal force is inferred in the co-rotating frame because there is no way to directly observe it, seems to strike a nerve, and has been reverted. The inclusion of a footnote to support this view also is criticized as "not being about planetary motion", and therefore beside the point. (I would have thought that support of a statement was usually to the point.)

I would like to know 1) Is the point about inference understood? 2) Is it agreed upon? 3) Is it germane, and if not, why not? 4) Why is it not allowed to stand?

Secondly, and perhaps of more importance, in the co-rotating frame the above-quoted language points out that the co-rotating observer is forced to add the centrifugal term to the force inventory in order to get agreement with observation of the motion. This point is central to all discussion of fictitious force. However, instead of allowing this language, the present form of the article insists on viewing the centrifugal force as simply a transference of a term from one side of the equation to the other ("This radial equation can be rearranged"), a rather pallid and purely mathematical stance. In fact, in the co-rotating frame there is no awareness of the centrifugal term allowing "rearrangement" of the equation. Rather, the centrifugal force is discovered to be necessary and then added to the force inventory. The section on Flatness of galaxies has two examples of this behavior without the detailed math of this planetary motion section. One is the classical example from Newton and Leibniz about the oblateness of the planet as evidence that must be explained by introduction of centrifugal force, which ex post facto suggests the planet is rotating about its axis..

Perhaps the argument is "why make this point again?", but actually the purpose of all the examples is to illustrate these points over and over in various contexts. This example is not an exception.

Why has this viewpoint about the origin of the centrifugal term met with resistance? Brews ohare (talk) 14:06, 9 May 2009 (UTC)


 * Brews, I objected to this interpretation because it didn't relate at all to the sources that we were working from (Taylor, Goldstein, etc.), in which the rotation rate of the frame is known, since they start from the equations of motion in the inertial frame. Your "notion that the angular rate appearing in the centrifugal force is inferred in the co-rotating frame because there is no way to directly observe it" is a fine notion in some contexts; like we can use a Foucault pendulum or a gyroscope on our planet, or in a box, to see if our planet or box is rotating or not.  But if we already know the rate of rotation of the system, e.g. from knowing a complete description of the system in an inertial frame, then it is simple algebra to get the centrifugal force in a rotating frame; no experiments or inference need be involved.  There's nothing wrong with the concept, but it's not what this section or example is about.  We're not saying that one needs to discover a mysterious force term to add, rather, that the equations of motion, when rearranged to treat r-double-dot as acceleration, end up with that term on the force side, by simple algebra, as shown by Taylor and others.  These relationships can then be applied in either direction, to infer a rotation rate from an apparent force, or to find a force from a rotation rate; or to find a gravitational constant from a force and a rotation rate, perhaps; just solve for what's unknown in terms of what's known, for different kinds of inferences. Dicklyon (talk) 15:45, 9 May 2009 (UTC)


 * Included in the reverted snippet is the assertion "in a co-rotating frame this tension is used to determine the rate of rotation of the frame", backed up by two sources. But I don't see anything in either source that would support more than "in a co-rotating frame this tension can be used to determine the rate of rotation of the frame."  I think that distinction is the crux of the argument here. Dicklyon (talk) 15:51, 9 May 2009 (UTC)

The physical meaning of a term cannot change simply by moving it to the other side of an equation. This entire confusion has come about because of attempts to disguise the presence of centrifugal force in the radial planetary orbital equation. Brews asks "Why has this viewpoint about the origin of the centrifugal term met with resistance?" I have been asking exactly the same question and it's this very question which lies at the root of endless arguments, even over on the Kepler's laws of planetary motion page. Over on that page, we reduced it all to two equations. A radial equation and a transverse equation. Everybody agreed with the two equations. But there was precious little agreement about the names of any of the six terms in those equations. It was the same story. It was Orwellian doublethink in full swing. There was a total obstinance about admitting the presence of the centrifugal force and the Coriolis force, despite the fact that they were starring everybody in the face. But to have named them by their proper names would have conflicted with a modern education system which teaches that it is not politically correct to think of either centrifugal force or Coriolis force as being real forces. David Tombe (talk) 19:35, 9 May 2009 (UTC)


 * Of course the physical meaning doesn't change; it's just a change of frame of reference, or point of view, that affects which terms you call accelerations and which terms you call forces. There are tons of other variants, too; this particularly simple one where you just move one term across is unique to the comparison of the special frames of reference, the inertial and the co-rotating.  As the cited sources point out, they are both correct, and they both describe the same physics, just in different frames of reference; in one frame there's a centripetal acceleration term, and in the other a centrifugal force term.  In one frame, the acceleration expression is very simple (the co-rotating frame, where it's just r-double-dot), and in the other frame the force expression is very simple (that's the inertial frame, where's there's nothing but gravity).  It's all right there in the cited and linked book pages.  Dicklyon (talk) 20:55, 9 May 2009 (UTC)

Dick, it may be in a book. But there is no way that I will ever accept that a centrifugal force can ever become a centripetal force just by changing it to the other side of an equation. David Tombe (talk) 22:10, 9 May 2009 (UTC)


 * Dick: You say the following:
 * "'But if we already know the rate of rotation of the system, e.g. from knowing a complete description of the system in an inertial frame, then it is simple algebra to get the centrifugal force in a rotating frame; no experiments or inference need be involved.'"
 * Why do you take this point of view about what is known? It is more illuminating and closer to practice to take the view that centrifugal force is invoked to explain observation, rather than to assume the rotating observer already knows they are rotating and how fast they are rotating. How did they arrive at that state of awareness? Were they talking to an inertial observer? Why did they believe the other observer when they claimed to be inertial? What was done to decide who was and who wasn't an inertial observer? This point of view is succintly presented in the cited (reverted) quote at the beginning of this section. Is all that "simple algebra"? (That's a rhetorical question.)


 * Later you say:
 * "'But I don't see anything in either source that would support more than 'in a co-rotating frame this tension can be used to determine the rate of rotation of the frame.'"
 * You simply have not read these sources with attention. They are almost entirely about determining whether one is rotating and the question of absolute vs. relative rotation. That is the whole point of the rotating spheres and bucket argument.


 * Look deep into your heart, Dick. You will find a mathematician, not a physicist. Brews ohare (talk) 01:34, 10 May 2009 (UTC)


 * Perhaps I was confused. I thought we were discussing the planetary orbits section. Dicklyon (talk) 02:29, 10 May 2009 (UTC)

Disingenuous, eh? We are discussing the planetary orbits section, and your justifications, quoted verbatim above, for overriding wording for that section, and various reasons for not accepting those statements of yours. Please respond to the issues raised. Brews ohare (talk) 04:11, 10 May 2009 (UTC)


 * Well, you said I didn't read the sources closely enough, and then immediately started talking about rotating spheres and bucket argument. Which sources in the planet section did I not read closely enough?  Can you point me at the relevant sections that explain what you're getting at?  If you mean the new sources you added, point out what they have to say about the planetary orbits problem, and I'm sure we can accommodate it; I just didn't see anything.  Dicklyon (talk) 04:41, 10 May 2009 (UTC)
 * For reference, the sources are:


 * Oops, no, sorry, those were the sources for what kinematics is; also nothing about applying it to planets, as far as I could tell.
 * It was this note with refs in it:
 * Oops, no, sorry, those were the sources for what kinematics is; also nothing about applying it to planets, as far as I could tell.
 * It was this note with refs in it:


 * For example, in the rotating spheres example, the tension in the cord between two rotating spheres is indicative of the centripetal force required by their rotation, but in a co-rotating frame this tension is used to determine the rate of rotation of the frame. See and