Is the concept of reactive centrifugal force valid?

[Doc Al]

In fact usually static examples are used introducing Newton's 3rd Law:

Unfortunately that reference is very badly worded:

The book lying on the table is exerting a downward force on the table, while the table is exerting an upward reaction force on the book. Because the forces are equal and opposite, the book remains at rest.

The first sentence is describing Newton's 3rd law pairs. The second sentence implies that it is those third law pairs that produce equilibrium. Yikes!

 

[A.T.]

I disagree. Your making it balanced is an obfuscating complication.

Putting aside the question why a well balanced space station is "more complicated" than a wobbling one, let me point out that the balancing is not needed to prove my point. Even in the unbalanced case it would still be true that:

Frcf has the same direction, as the vector from rotation center to the point of application of Frcf. Therefore Frcf is a centrifugal force

I didn't make it balanced because I had to, but because it leaves no room to weasel around. That's why you try to change the scenario:

Consider... [Some scenario. Where is the reactive centrifugal force now?]

This is the same flawed line of argument Andrew exhausted pages ago. Nobody ever claimed that the reactive centrifugal force exists in every possible scenario.

The concept of a reactive centrifugal force to a centripetal force does not jibe with Newtonian mechanics in the case of point masses.

Wrong as DaleSpam already explained.

So when does the concept of reactive centrifugal force to a centripetal force apply? When you over-complicate and obfuscate things.

Well, if any scenario more complex that two point masses is "over-complicated" for you, then indeed you should not bother with reactive centrifugal forces.

 

[A.T.]

The first sentence is describing Newton's 3rd law pairs. The second sentence implies that it is those third law pairs that produce equilibrium. Yikes!

Indeed. That formulation can lead to the wrong understanding I pointed out to harrylin few pages ago. Ironically their question 3 is exactly about that potential flaw in reasoning they seem to imply themselves.

But my point was simply that this static scenario is a typical example of Newton's 3rd Law, used in many books.

 

[Andrew Mason]

A.T. is correct here, Andrew. The force that the wall exerts on A.T. and the force that A.T. exerts on the wall are exactly the kind of pair-wise forces that Newton's third law addresses. Force is subject to the superposition principle. The F in F=ma is the net force acting on the object (or on A.T. in this case). The reason A.T. doesn't accelerate when he leans against the wall is because other forces are in play.

If there is no acceleration (by having sufficient friction between AT and the floor and wall), all forces are balanced and inter-connected. It seems to me somewhat arbitrary to choose which force pairs are third law pairs and which are not. But I think I see your point: if the other forces are removed (ie if there was no/insufficient static friction (on the wall or floor) the wall (along with the Earth it is connected to) and AT would exert equal and opposite forces on each other each would accelerate away from each other in a horizontal direction. Those forces then would definitely be third law force pairs.

AM

 

[harrylin]

..Once you get to the non-inertial frame there are fictitious forces. You cannot remove those fictitious forces and correctly determine the trajectory.

I'm sorry if you cannot determine the trajectory without them, but I already referred to and indicated how to do that without introducing anything fictitious. If you want to get more explanation then please start a topic on it.

 

[A.T.]

If there is no acceleration (by having sufficient friction between AT and the floor and wall), all forces are balanced and inter-connected. It seems to me somewhat arbitrary to choose which force pairs are third law pairs and which are not.

What is arbitrary for Newton's 3rd, is the definition of objects (e.g. me, wall ,floor). This arbitrariness is a great feature, because it allows to use the law on different levels of abstraction.

But I think I see your point: if the other forces are removed (ie if there was no/insufficient static friction (on the wall or floor) the wall (along with the Earth it is connected to) and AT would exert equal and opposite forces on each other each would accelerate away from each other in a horizontal direction. Those forces then would definitely be third law force pairs.

Provide a reference that demands acceleration as a result from the Newtons 3rd force pair.

 

[Dale]

I'm sorry if you cannot determine the trajectory without them, but I already referred to and indicated how to do that without introducing anything fictitious.

Then you misunderstand the method you used. Your method is exactly the method which introduces the appropriate fictitious forces for a given non-inertial coordinate system. It introduces them whether you call them fictitious forces or not.

 

[A.T.]

The concept of a reactive centrifugal force...

It occurs to me, that the problem you and Andrew might be having, is simply exaggerated expectations. You seem to think that "reactive centrifugal force" is supposed to be some general concept, like the inertial centrifugal force which appears in every rotating frame.

But in fact it just a trivial naming convention applicable in a subset of cases involving rotation, where the local reaction to the centripetal force points away from the rotation center. I would not even call it a "concept". The concept here is Newtons 3rd.

 

[Andrew Mason]

The drawings are correct, this analysis is not correct. The 3rd law pairs are, as A.T. drew them, between each astronaut and the space station. This can be seen by placing scales or pressure plates at the foot of each astronaut. Each scale registers a 3rd law pair, so there are four forces.

There are gazillions of forces if you want to look at each atom and the forces between them. [There is the force of gravity between the atoms, as well, which we are ignoring. There are also the tidal forces between the astronaut and the space station because of differences in their centripetal acceleration due to slight difference in their radii of rotation, which we are ignoring].

What you have to do is ask: what is accelerating? In this case, all the molecules of the space station and astronauts are accelerating toward the centre of rotation. So all forces on a molecule must sum to a net force on each molecule equal to the centripetal force it is experiencing due to its centripetal acceleration. So we don't have to worry about the intermolecular forces. We just need to worry about the net force that causes acceleration. So the diagram should show the net force vector for each molecule. That will be a vector pointing toward the centre whose magnitude is mv^2/r.

Let's suppose that there are two space stations rotating about a common axis line but not mechanically connected. Initially, the first one has no astronauts and the second has the two astronauts shown. One astronaut then jumps onto the other space station. What happens? Do the stresses between the molecules in the second space station increase? The answer is: no they don't. The centre of rotation just changes.

If both astronauts jump at the same time, do the stresses increase? The answer is: yes they do. Now if you want to suggest that the additional stresses occur because of a centrifugal force that the astronaut exerts on the space station, why does it only occur if both astronauts are on the space station but not if only one is present?

AM

 

[A.T.]

There are gazillions of forces if you want to look at each atom and the forces between them.

Yes, but who wants that? As I already said: What is arbitrary for Newton's 3rd, is the definition of objects (e.g. me, wall ,floor). This arbitrariness is a great feature, because it allows to use the law on different levels of abstraction.

What you have to do is ask: what is accelerating?

Is this still about the "reactive centrifugal force"? Because I still haven't seen that reference stating that Newtons 3rd Law applies only to net forces resulting in acceleration.

So the diagram should show the net force vector for each molecule.

I don't know if that's a good idea. D H thinks it is already over-complicated.

 

[rcgldr]

One astronaut then jumps onto the other space station. What happens? Do the stresses between the molecules in the second space station increase?

You've just increased the mass of a rotating system, so the stresses increase overall, or locally increase in the vicinity of the single astronaut (and decrease elsewhere), depending if angular velocity or angular momentum was preservered during the transfer.

 

[Dale]

There are gazillions of forces if you want to look at each atom and the forces between them.

Sure, I did a similar analysis in my post 119 to D_H. In such a situation there are also clearly reactive centrifugal forces for many of the atoms, as I described above.

However, that does not detract from the correctness of A.T.'s drawing. Given the partitioning of the system into 3 objects (two astronauts and the space station) then the forces are correct as drawn. You can certainly do a different partitioning, but that does not make A.T.'s diagram incorrect.

So all forces on a molecule must sum to a net force on each molecule equal to the centripetal force it is experiencing due to its centripetal acceleration.

Certainly, nobody has ever said otherwise. We are not saying that the net force is centrifugal, simply that some of the individual forces are.

So the diagram should show the net force vector for each molecule.

Have you never done a free-body diagram before? Net forces are not drawn on a free-body diagram, and you only draw the external forces for each object. The drawing is correct.

 

[Andrew Mason]

Sure, I did a similar analysis in my post 119 to D_H. In such a situation there are also clearly reactive centrifugal forces for many of the atoms, as I described above.

However, that does not detract from the correctness of A.T.'s drawing. Given the partitioning of the system into 3 objects (two astronauts and the space station) then the forces are correct as drawn. You can certainly do a different partitioning, but that does not make A.T.'s diagram incorrect.

Certainly, nobody has ever said otherwise. We are not saying that the net force is centrifugal, simply that some of the individual forces are.

Have you never done a free-body diagram before? Net forces are not drawn on a free-body diagram, and you only draw the external forces for each object. The drawing is correct.

?? But if the bodies are accelerating you have to show the forces on them that cause acceleration. All the molecules in space station are accelerating, along with the astronauts. What forces produce that acceleration?

Eliminate the astronauts. Does that eliminate the acceleration of the matter in the space station? Where is the centrifugal force on the molecules in the space station then? Answer: there is no centrifugal force.

AM

 

[Dale]

?? But if the bodies are accelerating you have to show the forces on them that cause acceleration.

Which A.T. did.

Note that the space station is not accelerating. This can be seen from the fact that the forces on the space station (labeled Frcf on A.T.'s diagram) are balanced.

All the molecules in space station are accelerating, along with the astronauts. What forces produce that acceleration?

Did you not read my post 119 to D_H? I laid that out very carefully.

Eliminate the astronauts. ...

That is a different scenario and therefore a different diagram.

 

[A.T.]

Eliminate the astronauts. (...)

And the space station too. That should finally eliminate those pesky centrifugal reaction forces.

Where is the centrifugal force on the molecules in the space station then?

All over the place. Some molecules of the space station will still experience individual interaction forces from other molecules of the space station, which have a centrifugal component.

 

[Andrew Mason]

Which A.T. did.

Note that the space station is not accelerating. This can be seen from the fact that the forces on the space station (labeled Frcf on A.T.'s diagram) are balanced.

The space station is accelerating.

Every molecule in the space station is accelerating. They are just not all accelerating in the same direction. The centre of mass is not accelerating but the centre of mass is a mathematical abstraction.

You could say the same thing about two billard balls when they are colliding. The centre of mass does not accelerate. But that does not mean there is no acceleration. The physics are very different during the collision than before and after, even though there is absolutely no change to the motion of the centre of mass.

AM

 

[Andrew Mason]

And the space station too. That should finally eliminate those pesky centrifugal reaction forces.

All over the place. Some molecules of the space station will still experience individual interaction forces from other molecules of the space station, which have a centrifugal component.

Reduce the space station to a circular string of molecules. What object of matter is causing this centrifugal "force" on a given molecule? What is exerting it and what is that object exerting the centrifugal force on?

AM

 

[Dale]

Reduce the space station to a circular string of molecules. What object of matter is causing this centrifugal "force" on a given molecule? What is exerting it and what is that object exerting the centrifugal force on?

You still haven't read post 119, have you?

 

[Dale]

The space station is accelerating.

No, it isn't. The net external force on the space station is 0, so by Newton's second law it is not accelerating.

Every molecule in the space station is accelerating. They are just not all accelerating in the same direction. The centre of mass is not accelerating but the centre of mass is a mathematical abstraction.

Everything in physics is a mathematical abstraction, that is hardly a counter-argument. When you use Newton's 2nd law to determine the acceleration of some system the thing which is accelerating is the system's center of mass. Are you attempting to reject Newton's 2nd law since it describes the behavior of a mathematical abstraction?

 

[D H]

But in fact it just a trivial naming convention applicable in a subset of cases involving rotation, where the local reaction to the centripetal force points away from the rotation center. I would not even call it a "concept". The concept here is Newtons 3rd.

I disagree. Then again, I might be being a bit irrational; I truly despise the name "reactionary centrifugal force". That said, I'm not a big fan of the term "centripetal force", either. "Centripetal acceleration" is fine; it is a kinematic description of motion. Forces are out of the picture in kinematics -- so why are we dragging forces into the mix?

For the sake of argument, let's drag it into the mix. For point masses and when viewed from the perspective of an inertial frame, the reaction to a centripetal force is also centripetal while the reaction to a centrifugal force is also centrifugal. I don't see how you can argue it is anything but.

So at best, if the term "reactionary centrifugal force" has any meaning (to me it doesn't; and no, your pictures don't sway me), it only has meaning some times. Other times the third law reaction to a centripetal force is centripetal.

 

[Dale]

So at best, if the term "reactionary centrifugal force" has any meaning ..., it only has meaning some times. Other times the third law reaction to a centripetal force is centripetal.

I agree with this.

 

[Andrew Mason]

You still haven't read post 119, have you?

I have. I and have said I disagree with that analysis.

In the rotating uniform circle of molecules example, each molecule only has two forces acting on it. These are the molecular bonding forces from each laterally adjacent molecule. These forces are equal in magnitude and sum to the centripetal acceleration of the molecule. Now, you can say that each molecule is pulling on each other, so for each pull of molecule A on adjacent molecule B, there is an equal and opposite pull by molecule B on A. But the geometry shows that those forces cannot be equal and opposite. The fact that they are both accelerating in slightly different directions shows that they are not equal and opposite. So this "centrifugal force" that you postulate cannot be equal and opposite to the the centripetal force that the molecule experiences.

The equal and opposite force is the force acting on the molecule that is diametrically opposite. The centripetal force on that diametrically opposite molecule is the "reaction" force to the centripetal force on the first. Neither is centrifugal.

AM

 

[A.T.]

Reduce the space station to a circular string of molecules.

Why so complicated? Reduce the space station just two molecules orbiting each other.

And what are trying to prove here? Nobody ever claimed that the reactive centrifugal force exists in every possible scenario. I told you that in post #18 already. I know this is about rotation, but you overdoing that going in circles a bit now.

 

[olivermsun]

In a 2 body system, where gravity is causing the objects to orbit in a circular path, the Newton third law pair of forces is the gravity force that each object exerts on the other. From each object's perspective, the gravity force that accelerates each object is towards the center of the orbit, so both gravity forces are centripetal.

So after 9 pages... what's wrong with this explanation again?

 

[Dale]

I have. I and have said I disagree with that analysis.

Sorry, I missed that. What was your disagreement with my analysis in 119?

Now, you can say that each molecule is pulling on each other, so for each pull of molecule A on adjacent molecule B, there is an equal and opposite pull by molecule B on A. But the geometry shows that those forces cannot be equal and opposite.

It is not me who says that, it is Newton's 3rd law. Are you disputing/disagreeing with Newton's 3rd law? If not then you should revise your comments because they communicate a disagreement with Newton that I hope is unintentional.

PS. I have not claimed that a centrifugal reaction force exists in all cases, so showing examples where it doesn't exist is just a red herring. The point is that in some cases they do exist, and A.T.'s example is one of those cases. The ring and the 2 orbiting point masses do not have centrifugal reaction forces, but A.T.'s astronaut example does have them. You need to address A.T.'s example on its own merits. It is a relatively simple scenario that Newton's laws can easily be applied to.

 

[A.T.]

I truly despise the name "reactionary centrifugal force".

Why make it political?

That said, I'm not a big fan of the term "centripetal force", either.

Now it's not only against Wikipedia put pretty much every physics book on the planet?

So at best, if the term "reactionary centrifugal force" has any meaning (to me it doesn't; and no, your pictures don't sway me), it only has meaning some times.

The term has always a meaning according to the definition. But you will not always find something that fits that definition

Other times the third law reaction to a centripetal force is centripetal.

Yes, that what I was saying all the time. It depends on the scenario.

 

[A.T.]

...so for each pull of molecule A on adjacent molecule B, there is an equal and opposite pull by molecule B on A. But the geometry shows that those forces cannot be equal and opposite.

You lost me here. Are they equal and opposite or not?

The equal and opposite force is the force acting on the molecule that is diametrically opposite.

So the reaction to the force by an adjacent molecule, is the force on a diametrically opposite molecule, which doesn't even have a direct interaction with the considered molecule? Now, that is an interesting combo, to be sold as Newtons 3rd force pair.

 

[Andrew Mason]

I truly despise the name "reactionary centrifugal force". That said, I'm not a big fan of the term "centripetal force", either. "Centripetal acceleration" is fine; it is a kinematic description of motion. Forces are out of the picture in kinematics -- so why are we dragging forces into the mix?

I think you may have hit the nail on the head. [Others, including me, have been hitting a few thumbs]. This addresses the point that AT made, which I have not yet properly answered, questioning whether Newton's third law is only about accelerations. Newton spoke about "action" and "reaction", after all. He did not really deal with static forces. Static forces are, by definition, equal and opposite - otherwise they would not be static.

I think our discussion shows that we really run into problems if we try to apply Newton's third law to static forces. It becomes really difficult, if not arbitrary, to select third-law force pairs. Not so when there are accelerations. There can never be only one acceleration. There must always be a "reaction" acceleration. One mass accelerating all by itself is not possible under the laws of physics as we presently know them.

If we ask, where is the acceleration that is the third law reaction to the astronaut's centripetal acceleration, the answer is clear that it has to be a centripetal acceleration because that is the only kind of acceleration that occurs.

So at best, if the term "reactionary centrifugal force" has any meaning (to me it doesn't; and no, your pictures don't sway me), it only has meaning some times. Other times the third law reaction to a centripetal force is centripetal.

I think you are being too charitable. The reaction to a centripetal acceleration cannot be a static centrifugal force - ever.

AM

 

[Doc Al]

I think you may have hit the nail on the head. [Others, including me, have been hitting a few thumbs]. This addresses the point that AT made, which I have not yet properly answered, questioning whether Newton's third law is only about accelerations. Newton spoke about "action" and "reaction", after all. He did not really deal with static forces. Static forces are, by definition, equal and opposite - otherwise they would not be static.

You are mixing up Newton's 3rd law, which is about forces not acceleration, with the 2nd law which deals with net force and the resulting acceleration. Things are 'static' only if the net force on them is zero--this has nothing to do with Newton's 3rd law.

Don't try to read into the rather archaic terminology of 'action' and 'reaction'--you cannot learn physics from a dictionary.

I think our discussion shows that we really run into problems if we try to apply Newton's third law to static forces. It becomes really difficult, if not arbitrary, to select third-law force pairs.

It's actually rather trivial.

Not so when there are accelerations. There can never be only one acceleration. There must always be a "reaction" acceleration. One mass accelerating all by itself is not possible under the laws of physics as we presently know them.

Again you confuse Newton's 2nd and 3rd laws.

If we ask, where is the acceleration that is the third law reaction to the astronaut's centripetal acceleration, the answer is clear that it has to be a centripetal acceleration because that is the only kind of acceleration that occurs.

Gibberish. Let's keep it simple: A exerts a force on B, thus B exerts an equal and opposite force on A. That's Newton's 3rd law. No mention of acceleration.

 

[Dale]

I think our discussion shows that we really run into problems if we try to apply Newton's third law to static forces.

It sounds like you do not understand basic Newtonian mechanics. Newtons third law has no problem with static forces. Newtons third law is used extensively in statics, and it is absolutely required for analyzing the stresses in a beam or structural member.

In fact, looking in my statics textbook the strong form of Newton's 3rd law is introduced on page 6. It is followed by an explanatory paragraph asserting "This principle holds for all forces, variable or constant, regardless of their source and holds at every instant of time. Lack of careful attention to this basic law is the cause of frequent error by the beginner."