# Is the concept of reactive centrifugal force valid?

• Andrew Mason
In summary, the article is incorrect in its assertion that the reactive centrifugal force is always centrifugal. It depends on the context.
Some of the similar style problems I'm familiar with make the same type of simplifying assumptions so,for example,you might read an opening to a question something like " a small body of mass m is fixed to the end of a light inextensible string"...etc.In fact we make simplifying assumptions for every analysis we carry out.We can't take everything into account and some factors might be considered to have negligible or irrelevant effects on what we wish the analysis to reveal.
I think it would be interesting to see an extended problem where it would be necessary to account for the properties of the rope(s) and possibly other factors but in my opinion this would be best dealt with by starting another thread.

I think it would be interesting to see an extended problem where it would be necessary to account for the properties of the rope(s) and possibly other factors but in my opinion this would be best dealt with by starting another thread.
I would be glad to participate in that, and I agree that it would be best in another thread. Such problems are often easier in the rotating frame.

DaleSpam said:
In any case, are you finally in agreement with my analysis, or do you wish to propose your own? After we have pinned that down, then I am glad to analyze any other scenario of your choosing.
I agree with your answers to the questions asked in your massless rope, and mass A, B scenario (set out post #190) except that I would not say that the force of B on A should be characterised as a centrifugal force.

Similarly, I would not characterise as centrifugal the net force of the moon on a mass on the moon's surface on a line joining the centres of mass of the Earth and moon. I gather you would call it centrifugal because technically it is away from the earth-moon barycentre.

AM

Andrew Mason said:
I agree with your answers to the questions asked in your massless rope, and mass A, B scenario (set out post #190) except that I would not say that the force of B on A should be characterised as a centrifugal force.
It points away from the center of rotation, therefore it is centrifugal by definition.

Do you want to analyze another scenario? If so, which one?

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DaleSpam said:
It points away from the center of rotation, therefore it is centrifugal.

Do you want to analyze another scenario? If so, which one?
Let's make it simple. Two 1 kg masses, A and B, tethered by a 2 metre long massless rope rotating with a speed of 1 revolution / sec. Is there a force of B on A? If so, what is the direction of the force of B on A?

AM

Andrew Mason said:
Let's make it simple. Two 1 kg masses, A and B, tethered by a 2 metre long massless rope rotating with a speed of 1 revolution / sec. Is there a force of B on A? If so, what is the direction of the force of B on A?
No, but there is a force of B on the rope which is directed outwards and a force of the rope on A which is directed inwards.

DaleSpam said:
No, but there is a force of B on the rope which is directed outwards and a force of the rope on A which is directed inwards.
Ok. We obviously have a different interpretation of what is meant by the force of A on B.

I will define what I mean by the force of A on B. The force of A on B is a vector whose magnitude and direction is determined by

$$\vec{F}_{A-B} = m_B\vec{a}_{p-B} - m_A\vec{a}_{p-A}$$ where p is a point in an inertial frame of reference.

1. the mass of B multiplied by the acceleration of B (a vector) with respect to an inertial point

2. MINUS the mass of A multiplied by the acceleration of A with respect to the same point.

Conversely, the force of B on A is:

$$\vec{F}_{B-A} = m_A\vec{a}_{p-A} - m_B\vec{a}_{p-B}$$ where p is a point in an inertial frame of reference.

Can you now answer my question about the direction of the forces between A and B?

AM

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Andrew Mason said:
Ok. We obviously have a different interpretation of what is meant by the force of A on B.
A does not exert a force on B, the rope does.
I will define what I mean by the force of A on B. The force of A on B is a vector whose magnitude and direction is determined by

$$\vec{F}_{A-B} = m_B\vec{a}_{p-B} - m_A\vec{a}_{p-A}$$ where p is a point in an inertial frame of reference.
In what sense would this quantity be any kind of force on B?

Andrew Mason said:
I will define what I mean by the force of A on B. The force of A on B is a vector whose magnitude and direction is determined by

$$\vec{F}_{A-B} = m_B\vec{a}_{p-B} - m_A\vec{a}_{p-A}$$ where p is a point in an inertial frame of reference.
Do you have any mainstream scientific reference for this definition of force?

I think that most of the difficulty in this conversation stems from your penchant for refusing to use standard terms in the standard way. Btw, this is also a good way to fail a freshman physics class, even if you actually do understand the physics.

Andrew Mason said:
Can you now answer my question about the direction of the forces between A and B?
There is no force between A and B. A zero vector has no defined direction.

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rcgldr said:
In the case of an object not moving wrt to a rotating frame, then the centrifugal force wrt the rotating frame is the same as the reactive centrifugal force wrt an inertial frame. In this case the centrifugal force is real and the same in both frames, resulting in an outwards force exerted on whatever surface of the rotating frame that causes the object to travel in a circular path wrt inertial frame.

A.T. said:
Just to clarify: In this specific case they happen to have the same direction and magnitude, but this doesn't make it "the same force". They act on different objects.
Yes, the fictitious centrifugal force acts on the astronaut, while the reactive centrifugal force is the force the astronaut exerts on the wall of the space station. In the rotating frame, what is the force that the astronaut exerts on the wall called, is it still reactive centrifugal force? This would make sense since the fictitious centrifugal force is a single force without an equal and opposing force.

The analogy would be gravity with the astronaut standing on the Earth in a inertial frame. In this case there are equal and opposing attractive forces due to gravity between astronaut and earth. There are also equal and opposing compressive forces between the astronauts feet and the surface of the earth.

It would seem the main difference is unlike gravity, fictitious centrifugal force doesn't have an equal and opposing force. It's just a mathematical method used to compensate for the rotating frame.

DaleSpam said:
Do you have any mainstream scientific reference for this definition of force?
You seem to be hung up on this rope for some reason. So I just figured I should define this interaction in terms of the real masses and their accelerations. That way we are only concerned about real forces on real masses and not the angels who are holding hands in between them.

To make it conceptually easier to see, would it help to put a massless ball, C, at the centre of mass of these two 1 kg masses that are 2m apart and rotating (ie. 1 m. from each of A and B)?

I think that most of the difficulty in this conversation stems from your penchant for refusing to use standard terms in the standard way. Btw, this is also a good way to fail a freshman physics class, even if you actually do understand the physics.
Some professors like to discourage non-conformist approaches to physics. Feynman did his best to change things but it takes time.

There is no force between A and B. A zero vector has no defined direction.
So are you saying I can't add what you say is the force of A on the rope to the force of the rope on B to get the force of A on B? Or are you saying those forces really add up to zero?

AM

rcgldr said:
It would seem the main difference is unlike gravity, fictitious centrifugal force doesn't have an equal and opposing force. It's just a mathematical method used to compensate for the rotating frame.
It has an equal and opposing force in the rotating (non-inertial) frame - the force that is keeping it in (eg the passenger presses into the door of the car because he is trying to flee the centre of rotation due to centrifugal force and the car presses back as a centripetal reaction force) when the car goes around a curve. That is the classic example of the fictitious centrifugal force, because, of course, there is no acceleration outward. I don't see the difference between that pseudo centrifugal force and the so-called reactive centrifugal force.

AM

Andrew Mason said:
It has an equal and opposing force in the rotating (non-inertial) frame - the force that is keeping it in (eg the passenger presses into the door of the car because he is trying to flee the centre of rotation due to centrifugal force and the car presses back as a centripetal reaction force) when the car goes around a curve. That is the classic example of the fictitious centrifugal force, because, of course, there is no acceleration outward. I don't see the difference between that pseudo centrifugal force and the so-called reactive centrifugal force.
The pseudo centrifugal force acts on the passenger, giving him zero net force in the noninertial rotating frame. The so-called reactive centrifugal force acts on the door of the car, and is a real force exerted by the passenger.

As rcgldr stated, the pseudo centrifugal force is not part of a 3rd law pair. Realize that 3rd law ('action/reaction') pairs act on different bodies.

In this example with the passenger in a car going around a curve: The door of the car exerts a real centripetal force on the passenger; the 3rd law pair to that force is a real force exerted by the passenger on the door. In the inertial frame, there is a net force on the passenger producing his centripetal acceleration. Viewed from the rotating frame, in which there is no acceleration, there is an additional pseudo centrifugal force acting outward on the passenger, giving him zero net force. That pseudo force has no agent (it's not a real force) and has no 3rd law pair.

Andrew Mason said:
You seem to be hung up on this rope for some reason. So I just figured I should define this interaction in terms of the real masses and their accelerations. That way we are only concerned about real forces on real masses and not the angels who are holding hands in between them.
Yet you seem to want an 'angel' connecting the masses so you can claim that A exerts a force directly on B even though they are not in contact.

How about you stop the nonsense and use a real rope! With mass. What do you think changes now?

And stop making up nonsense definitions ('non-conformist' ) that you think will support your strange notions. Stick to standard physics.

Andrew Mason said:
You seem to be hung up on this rope for some reason.
It is rather important. Without the rope there is no force on A or on B. That makes it pretty clear that the interactions are with the rope.

Andrew Mason said:
To make it conceptually easier to see, would it help to put a massless ball, C, at the centre of mass of these two 1 kg masses that are 2m apart and rotating (ie. 1 m. from each of A and B)?
It is your scenario. Feel free to specify it however you wish. But I will analyze whatever situation you choose using Newtons laws, not Andrew Masons laws.

Andrew Mason said:
So are you saying I can't add what you say is the force of A on the rope to the force of the rope on B to get the force of A on B?
Yes, that is what I am saying.

Doc Al said:
Yet you seem to want an 'angel' connecting the masses so you can claim that A exerts a force directly on B even though they are not in contact.

How about you stop the nonsense and use a real rope! With mass. What do you think changes now?
The complexity of the problem. Now you have a string of positively and negatively charged masses each prescribing rotation about each other and exerting centripetal forces on each other about their respective centres of mass with the net result of attractive forces between one end and the other toward the middle.
And stop making up nonsense definitions ('non-conformist' ) that you think will support your strange notions. Stick to standard physics.
"Standard" physics does not get hung up on the physics inside massless ropes. "Standard" physics treats centrifugal forces as pseudo forces. "Standard" physics does not distinguish between a "reactive centrifugal force" and a centrifugal "force". "Standard" physics says that all forces, including reactive forces, in a two body rotation are centripetal.

AM

It certainly seems clear that "reactive centrifugal forces" is an unfortunate term, but there's nothing formally wrong with it. The expression just means "whatever force appears when a body is constrained to accelerate perpendicular to its velocity", and it points "centrifugally" toward the instantaneous center of the motion. But since we already have the perfectly good term "centripetal force", and the term "centrifugal force" means something very different, there doesn't seem like any good reason to talk about "reactive centrifugal forces." All the same, there's nothing wrong with the concept, it's just awkward given the ways those other words are used. These comments would seem to apply independently to details of the mass distribution in a rope.

Andrew Mason said:
"Standard" physics treats centrifugal forces as pseudo forces. "Standard" physics does not distinguish between a "reactive centrifugal force" and a centrifugal "force".
I hope you understand my incredulity, but given the fact that you are 0 for 5 (or more) in providing any references supporting any of your previous positions I have a hard time believeing that you have the slightest idea what standard physics says. Do you have any mainstream scientific reference for these claims?

I agree that standard physics does not get hung up on massless ropes. There is no hangup since the standard rules apply, as you yourself have admitted (and then ignored your own advice). I also agree that all forces, including reactive forces, in a two body rotation are centripetal. Of course, there is more to physics than two body rotations.

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Ken G said:
It certainly seems clear that "reactive centrifugal forces" is an unfortunate term, but there's nothing formally wrong with it. The expression just means "whatever force appears when a body is constrained to accelerate perpendicular to its velocity", and it points "centrifugally" toward the instantaneous center of the motion.
Away from the center, not toward.
Ken G said:
But since we already have the perfectly good term "centripetal force",
That's toward the center
Ken G said:
and the term "centrifugal force" means something very different,
Yes, away from the center.
Ken G said:
there doesn't seem like any good reason to talk about "reactive centrifugal forces."
If the 3rd law reaction to centripetal force is centrifugal, the term makes perfect sense.

DaleSpam said:
I have a hard time believeing that you have the slightest idea what standard physics says.
To be fair: He put "standard" in quotes, indicating he means his own definition of "standard physics".
DaleSpam said:
there is more to physics than two body rotations.
Not to his "standard" physics.

rcgldr said:
In the rotating frame, what is the force that the astronaut exerts on the wall called, is it still reactive centrifugal force?
I see no reason to change it's name depending on the reference frame. The force by the wall on the astronaut is usually still called "centripetal force" in the rotating frame. Another hint that usually neither "centripetal" nor "centrifugal" implies the corresponding acceleration (there is none in the co-rotating frame).
rcgldr said:
The analogy would be gravity with the astronaut standing on the Earth in a inertial frame. In this case there are equal and opposing attractive forces due to gravity between astronaut and earth. There are also equal and opposing compressive forces between the astronauts feet and the surface of the earth.
That is correct for Newton's gravity. In General Relativity however the ground frame becomes non-inertial accelerating upwards, and gravity becomes an inertial force without a counter part.

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DaleSpam said:
I also agree that all forces, including reactive forces, in a two body rotation are centripetal. Of course, there is more to physics than two body rotations.
All rotations can be viewed as a group of multiple two body rotations. See my post #328.

AM

DaleSpam said:
I think that most of the difficulty in this conversation stems from your penchant for refusing to use standard terms in the standard way.
It's a great way to create endless arguments out of nothing.

Andrew Mason said:
All rotations can be viewed as a group of multiple two body rotations. See my post #328.
That was by no means a general proof, and there were still centrifugal forces on each end of the rope.

A.T. said:
Away from the center, not toward.
You're right, it's not the centripetal force, it's the action/reaction pair to the centripetal force. Of course, the centripetal force is a net force, so if there's more than one contributing, then we have more than one reactive centrifugal force.
If the 3rd law reaction to centripetal force is centrifugal, the term makes perfect sense.
I guess I've just never seen any example where the concept was actually useful.

If the 3rd law reaction to centripetal force is centrifugal, the term makes perfect sense.

Ken G said:
I guess I've just never seen any example where the concept was actually useful.

That would depend on what you mean by useful. Does acceleration perpendicular to velocity really need a special term (centripetal)?

As an example where both forces could be considered reaction forces, consider the case of a rocket free of any external forces using it's engine to travel in an circular path at a constant speed. At the engine, there's a centripetal force accelerating the rocket inwards, and an equal and opposing "centrifugal" force accelerating the ejected mass (spent fuel) outwards.

rcgldr said:
That would depend on what you mean by useful. Does acceleration perpendicular to velocity really need a special term (centripetal)?
Yes, because there are many situations where you know the acceleration, and it helps to have a name for the force you are looking for to provide that acceleration. When are we separately seeking the "reactive" centripetal force, once we know the centripetal force? We'll already have all the forces on the body, so we'll also have all their action/reaction pair forces, there's just nothing left to do. But I'll grant you that there is probably some situation we could imagine where a label for this force would be of use, it just doesn't seem generally useful enough to be worth it. Every label comes with some "overhead", around taking the time and effort to include it in the jargon of the field. If a label isn't worth that time and effort, it is appropriate to drop it from the lexicon.
As an example where both forces could be considered reaction forces, consider the case of a rocket free of any external forces using it's engine to travel in an circular path at a constant speed. At the engine, there's a centripetal force accelerating the rocket inwards, and an equal and opposing "centrifugal" force accelerating the ejected mass (spent fuel) outwards.
Right, but to me that's a classic example of where I don't need the concept of a reactive net force. I just want the force holding the rocket in a circle, and I don't need a label for the reaction forces because I already know them all, I just switch some signs. Imagine we had two sources of thrust, and engine and retro rocket, say. The concept of centripetal force would be useful because we would only know, from the motion, the sum of the forces of those two rockets, and that sum needs a name. Why does the reaction need a name? If we then find some way to solve for the two rocket forces, we still don't need a name for the sum of their reaction force-- we already know the two individual reaction forces and have no interest in their sum. It just seems like a way to label something we would always already know and need no help in describing.

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Ken G said:
I guess I've just never seen any example where the concept was actually useful.
I agree in the sense that reactive centrifugal froce is not a "concept" on the same footing as the inertial centrifugal force. See my remarks here:

Ken G said:
If a label isn't worth that time and effort, it is appropriate to drop it from the lexicon.
This is not about physics anymore and should be discussed on the Wikipedia page, but I disagree for two reasons:

1) Wikipedia is not a minimal collection of only "very badly needed terms". It is a broad collection of terms that are used.

2) There is a lot of resources on the web which try to explain the term "centrifugal force" and end up implicitly confusing the inertial with the reactive one. The clear distinction drawn by Wikipedia helps to clear up the confusion (unless someone is willfully ignorant and prefers to redefine all other terms just to defend his flawed idea that they are the same thing)

Ken G said:
Why does the reaction need a name?
It doesn't need one. You can name it F6. But apparently some authors prefer to give it an more explanatory name. That's why it is in Wikipedia. To avoid the confusion with such generic names the concept of the inertial centrifugal force should get a more specific name as I wrote here:

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Ken G said:
If a label isn't worth that time and effort, it is appropriate to drop it from the lexicon.
I agree in principle, but it is simply not possible in practice. Once a term is part of the lexicon it becomes impossible to drop it because older texts will still refer to it as will some people who read those older texts, some of whom will write newer texts still using the term. The only thing to do is to understand the term correctly (for when others use it) and then not use it yourself.

rcgldr said:
That would depend on what you mean by useful. Does acceleration perpendicular to velocity really need a special term (centripetal)?
I think acceleration that is constantly perpendicular does. A non-rotating rocket thrusting perpendicular to its direction of motion does not create a central force.
As an example where both forces could be considered reaction forces, consider the case of a rocket free of any external forces using it's engine to travel in an circular path at a constant speed. At the engine, there's a centripetal force accelerating the rocket inwards, and an equal and opposing "centrifugal" force accelerating the ejected mass (spent fuel) outwards.
Or you could put a mass on a compressed spring and let it rotate while the spring expanded. These are examples of forces away from the centre. But these are not the forces resulting from rotation.

AM

DaleSpam said:
I agree in principle, but it is simply not possible in practice. Once a term is part of the lexicon it becomes impossible to drop it because older texts will still refer to it as will some people who read those older texts, some of whom will write newer texts still using the term. The only thing to do is to understand the term correctly (for when others use it) and then not use it yourself.
One word: Phlogiston. Physicists have pretty much eradicated this outmoded/invalid concept.

Two more words: Relativistic mass. While relativistic mass is not an invalid concept, it is in most cases a unnecessary concept (what's wrong with energy?) that tends to create more confusion that it solves. Physicists have been trying to eradicate the concept of relativistic mass for quite some time now. Since the main thrust of this thread is some silly wikipedia article, it is noteworthy that the wiki article on relativistic mass does denote (deep down in the article, but hey, it is present) that the concept of relativistic mass is outdated. There is no such indication in the article on reactive centrifugal force.

D H said:
One word: Phlogiston. Physicists have pretty much eradicated this outmoded/invalid concept.
I wouldn't put reactive centripetal force in this category. Phlogiston is a wrong concept and was disproven experimentally. The reactive centripetal force is not wrong, just not terribly useful or general.

D H said:
Two more words: Relativistic mass. While relativistic mass is not an invalid concept, it is in most cases a unnecessary concept (what's wrong with energy?) that tends to create more confusion that it solves. Physicists have been trying to eradicate the concept of relativistic mass for quite some time now.
This was exactly the example I was thinking of. While it is not wrong, it is confusing and unnecessary. However, it has proven to be annoyingly persistent and I think impossible to remove despite the best efforts of a large part of the community for decades. Even Einstein stopped using it early last century, so it has been out of favor for several times longer than it ever was in favor. Yet, you still see it in pop-sci books and even in modern textbooks.

D H said:
it is noteworthy that the wiki article on relativistic mass does denote (deep down in the article, but hey, it is present) that the concept of relativistic mass is outdated. There is no such indication in the article on reactive centrifugal force.
The reason, once again, is that "reactive centrifugal force" is not a term that describes a general concept that could be outdated. It is rather an explanatory combination of words describing a quite problem-specific quantity, and is merely meant to distinguish it from the inertial centrifugal force.

The usage could still be identified as outdated or unnecessary.

A.T. said:
The reason, once again, is that "reactive centrifugal force" is not a term that describes a general concept that could be outdated. It is rather an explanatory combination of words describing a quite problem-specific quantity, and is merely meant to distinguish it from the inertial centrifugal force.
The distinction being that there is no non-reactive centrifugal force acting ON the thing that is applying the "reactive centrifugal force". Because if there was and you removed the thing that it is applying its "reactive centrifugal force" to, it would accelerate outward. (We all seem to agree that a mass cannot accelerate outward due to rotational forces).

So this "reactive centrifugal force" has to be a reaction to the centripetal acceleration that it is experiencing from something farther from the centre in a radial direction. If that is the case, then the "reactive centrifugal force" is always toward another mass. Also, this more radially distant mass is necessarily rotating about the former.

So this means the "reactive centrifugal force" is a force exerted by a mass in the direction of another mass that it is also rotating about.

As long as that is how you use "reactive centrifugal force", you are fine. Good luck in trying to explain to a physics student why physicists do not call that a centripetal force.

AM

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