Is the concept of reactive centrifugal force valid?

[Dadface]

Do you understand now how that is not the case?

The extra rope doesn't change the problem, it simply specifies some of the irrelevant details. In fact, for your design the extra rope is required in order to avoid changing the problem. As long as the external system supplies the right force to the center it is a legitimate external system for the problem and doesn't change any of the givens.

Do you feel that you understand now what it means to change the problem and why the details are irrelevant?

Dalespam,at the time of asking it was most relevant for me to ask for the details because the question was unclear and seemed to be describing an impossible situation.Looking at it in retrospect it can be seen that the question is ambiguous.You may be able to see this ambiguity if you look at your question(post 190 page 12).
As I understood the question at the time I thought that the word assembley referred to the assembley you described and since you called this the whole assembley I though that there was nothing else.
The mental pictures I formed of the event included the assembley somehow rotating in space about the end of the rope but with nothing else attached to the rope.Of course I had to ask for details.You can see something about how i interpreted your question if you read again some of my earlier posts(220 page 19 227 page14 etc)
In a later post you said that the system was not isolated.That should have given me a clue but it just washed over me at the time and I just did not spot the significance of it.Hands up to that.
In post 242 you referred to "applying an external force" to the end of the rope.At last I had been given a detail and the question made some sense,but there was another problem.I took the part description "the end of the rope" literally and by that I understood it to mean that whatever else is attached to the assembley has to be at the end of the rope and not beyond it.In other words in order to not change the linear dimensions of the new "whole assembley" the total length had to be at its original defined length of 2m.
I was puzzled by that requirement but I went along with it anyway as evidenced by my following posts.Did you not find it odd that my analysis,for example,had the mass M being positioned exactly at the end of the rope?
Eventually the relevant extra details I needed for the question to make sense came out,but sort of indirectly.It was a long time getting there.

 

[Doc Al]

I think that Doc Al might say it that way, but I wouldn't. I would say that A and B are each pulling on the rope.

I also prefer the more accurate statement that A and B each pull the rope (and, of course, that the rope pulls back on both A and B). That's the most complete statement. For some purposes it's OK to be a bit sloppy and say that "A and B pull on each other", treating the rope as merely transmitting the force. But I don't think that's a good idea for this thread, as the whole issue is to identify the forces involved most accurately.

 

[rcgldr]

The wiki article on centrifugal force states that it exists for all objects observed from a rotating frame and is equal and opposing to what would be the mass of the observed object times the centripetal acceleration of a point on the rotating frame at the same distance from the center of rotation of the rotating frame as the observed object, except the point is not moving wrt the rotating frame. Centripetal acceleration of that point is v² / r wrt to an inertial frame and centrifugal force = m (mass of object) v² / r. The corilios force exists for all objects that appear to be moving when observed from a rotating frame. For an object at "rest" in an intertial frame, the corilios force will have double the magnitude and oppose centrifugal force, resulting an apparent but fictitious centripetal force of the object as observed from a rotating frame.

My point here is that 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.

 

[Dale]

Looking at it in retrospect it can be seen that the question is ambiguous.You may be able to see this ambiguity if you look at your question(post 190 page 12).
...
In a later post you said that the system was not isolated...
In post 242 you referred to "applying an external force" to the end of the rope...
Eventually the relevant extra details I needed for the question to make sense came out,but sort of indirectly.It was a long time getting there.

I don't know if you have taken a basic physics class, but this type of problem is very common on homework or tests. Usually you are given enough information to come to a unique solution for the question asked, and no extra information.

Systems are usually not explicitly identified as isolated or non-isolated, it is inferred from the analysis itself. You are usually not told that if you want to envision things outside of the problem you are free to add a length of rope if you happen to be imagining some specific external mechanism that requires it.

The question is unambiguous because it has enough information to come to a unique solution. These other details that came out later are not things that were missing from the question, they are things that should have been part of the analysis (the non-isolated system) or only incidental to your particular specification of the external system (the extra length of rope).

 

[Andrew Mason]

I also prefer the more accurate statement that A and B each pull the rope (and, of course, that the rope pulls back on both A and B). That's the most complete statement. For some purposes it's OK to be a bit sloppy and say that "A and B pull on each other", treating the rope as merely transmitting the force. But I don't think that's a good idea for this thread, as the whole issue is to identify the forces involved most accurately.

I understand what you are saying. But you can't apply a force to something that has no mass. If the rope is massless, then the force that A applies to the rope is zero and all the forces between A and B are exerted by A on B and vice-versa.

If there is no force applied to the rope, it would effectively be force at a distance. Which is why real ropes cannot be massless. But for this problem as stated, it really is force at a distance.

AM

 

[Dale]

I thought you changed your mind on that earlier and agreed that Newtons laws do apply to massless ropes. If not, please find a mainstream scientific reference. I don't think there is any support for the claim that you cannot apply a force to something massless. Certainly an unbalanced force can't be applied, but we didn't do that here.

In any case, massless ropes, like frictionless ramps, and other such idealized devices, are understood as merely being reasonable approximations for these kinds of problems.

 

[Andrew Mason]

I thought you changed your mind on that earlier and agreed that Newtons laws do apply to massless ropes. If not, please find a mainstream scientific reference. I don't think there is any support for the claim that you cannot apply a force to something massless. Certainly an unbalanced force can't be applied, but we didn't do that here.

Well Newton's laws apply to massless ropes. It is just that if they have 0 mass any force applied to a massless rope results in zero force exerted on the rope and zero reaction force from the rope. F = ma. That's all I am saying. So we treat the rope as simply allowing force to be exerted by and on the masses that are connected to it. If B applies a pulling force on one end of a massless rope and A is the only other mass connected to the rope, the reaction of A is entirely on B. That would not be the case if the rope had mass.

In any case, massless ropes, like frictionless ramps, and other such idealized devices, are understood as merely being reasonable approximations for these kinds of problems.

Massless=negligible for the purposes of the problem at hand. I understand.

AM

 

[Dadface]

I don't know if you have taken a basic physics class, but this type of problem is very common on homework or tests. Usually you are given enough information to come to a unique solution for the question asked, and no extra information.

Systems are usually not explicitly identified as isolated or non-isolated, it is inferred from the analysis itself. You are usually not told that if you want to envision things outside of the problem you are free to add a length of rope if you happen to be imagining some specific external mechanism that requires it.

The question is unambiguous because it has enough information to come to a unique solution. These other details that came out later are not things that were missing from the question, they are things that should have been part of the analysis (the non-isolated system) or only incidental to your particular specification of the external system (the extra length of rope).

1.In the UK these types of problems are very common indeed.Circular motion is treated quantitatively in S and A level physics courses(for 17 and 18 year olds).I can't recall an actual exam question on this topic where enough information wasn't given.

2.I concur with your second point and would add that,depending on the problem,any additional information can be irrelevant,misleading and can result in the question exceeding any desired length limits.

3.The question is ambiguous in that it can be interpreted as describing an impossible event and one that cannot be analysed.Let me illustrate this by comparing your question to one I just selected.The question is from a past university of Cambridge A level exam and I will quote just a part of it:
After giving numerical information about a stone on a string the question continues..."The stone is whirled in a vertical circle the axis of rotation being at a height of 100 cm above the ground".It is easy to see similarities between this question and yours when you wrote "The whole assembley is swung about the left end of the rope"
The relevant difference between the questions is that in the first question the implication is that the structure is not just the stone and the string but that there is an additional external structure,the details of which are not necessary to answer the question,but the prescence of which is necessary for the event to occur.
In your question the event happened in zero gravity.Was it in space? Was there something else to provide the necessary external structure?If there was something else then fine,but the implication I read into your question was that the rope with masses attached was the "whole" assembley in other words there was nothing else.

 

[Doc Al]

Well Newton's laws apply to massless ropes.

Sure they do.

It is just that if they have 0 mass any force applied to a massless rope results in zero force exerted on the rope and zero reaction force from the rope. F = ma. That's all I am saying.

That's wrong. Any unbalanced force applied to a massless object would result in infinite acceleration--that just means that the net force on the massless rope must always be zero. Not that you can't exert a force on it!

The massless rope approximation just means that the tension in the rope is uniform. You can certainly pull the rope and it certainly pulls back.

If completely massless bothers you, give the rope some very small mass. See what changes.

 

[Dale]

any force applied to a massless rope results in zero force exerted on the rope

This is a self-contradiction.

 

[Doc Al]

I would say that you can apply a force but you cannot exert a force.

LOL! Get a grip, man!

You are attributing magical powers to this massless rope. Somehow it can transmit a force without exert a force.

I would prefer to say that you cannot exert a force at all on a massless rope because a massless rope cannot stretch. If it stretched, there would be a difference in force between ends while it stretched, and that can never happen with a massless rope. So the force applied to an end of the rope does not exert a force, net or otherwise, on the rope at all. For the purpose of the physics here we really are transmitting force at a distance through the concept of mechanical tension.

You are simply defining a massless rope out of existence, even though such an idealization is used all the time. The idealization just makes the analysis easier and eliminates non-essentials.

Does a real rope stretch? Sure. But our idealized massless rope is inextensible. Just for convenience. If that bothers you, let it stretch a bit. So what?

Does a real rope have mass? Sure. But our idealized rope does not. Again, just for convenience. If you like, use a real, massive rope!

You are massively (get it?) missing the point here.

 

[A.T.]

They should really give the real, "reactive" centrifugal force a new name so as to avoid confusion.

Maybe, but this is not the task of Wikipedia. On the contrary: it is against their rules to invent new terms, and put them there. You have to provide references showing that a term is already in use, so I assume there are such references for the real centrifugal force.

Personally I would prefer that the inertial centrifugal force gets a new name. "Centrifugal" is simply too general to describe this specific concept. The other inertial forces in rotating frames have specific names: Coriolis force & Euler force. Bernoulli and Lagrange seem to be the ones who identified inertial centrifugal force as a pseudo force. But this is not going to stick anyway.

 

[Andrew Mason]

That's wrong. Any unbalanced force applied to a massless object would result in infinite acceleration--that just means that the net force on the massless rope must always be zero. Not that you can't exert a force on it!

We are both saying that the forces exerted on each end MUST BE equal and opposite at all times.

I understand what you are saying. You are saying you can exert a force but you cannot exert a net force on a massless rope. I would say that you can apply a force but you cannot exert a force. It is an interesting, although for this problem immaterial, difference in the way of looking at the same thing. We are quibbling about how many angels can dance on the head of a pin.

I would prefer to say that you cannot exert a force at all on a massless rope because a massless rope cannot stretch. If it stretched there would have to be non-equal, opposing forces on the ends on the rope (ie a net force on the rope), and that cannot happen with a massless rope. So the force applied to an end of the rope does not exert a force, net or otherwise, on the rope at all. For the purpose of the physics here we really are transmitting force at a distance through the concept of mechanical tension.

Now Dale says it is a contradiction to say that one can apply a force but not exert a force on something. You are saying that "apply" and "exert" a force are the same thing. I make a distinction.

Consider the interaction between a photon and an atom when an atom releases a photon. The photon (a massless particle) carries with it momentum h/\lambda and causes a change in momentum to the atom in the opposite direction of \Delta p_e = h/\lambda. If we say that the photon exerts a force on the atom, then for Newton's third law (which is fundamental to all of physics, quantum mechanics included) to hold we would have to say that there is a force exerted on the photon. But, for reasons we both understand, it is meaningless to talk about a force being exerted on a photon.

When the photon is absorbed by another atom, a distance s away, there is a change in momentum of that atom that is equal and opposite to the change in momentum of the emitting atom. It took a finite time to accomplish that change in momentum (\Delta t =s/c). So we can say that the emitting atom exerts a force on the absorbing atom: F = \Delta p/\Delta t = hc/\lambda s. We could say that the force is applied by means of the exchange of a massless photon. We just can't say that the force is exerted on the photon.

AM

 

[Doc Al]

We are both saying that the forces exerted on each end MUST BE equal and opposite at all times.

OK.

I understand what you are saying. You are saying you can exert a force but you cannot exert a net force on a massless rope. I would say that you can apply a force but you cannot exert a force.

Sorry, but that sounds like gibberish.

I would prefer to say that you cannot exert a force at all on a massless rope because a massless rope cannot stretch. If it stretched there would have to be non-equal, opposing forces on the ends on the rope (ie a net force on the rope), and that cannot happen with a massless rope.

(1) We are talking about an idealized rope here--who cares about the details about how it stretches or doesn't stretch. (Assume an inextensible rope.)
(2) Why in the world do you think you need non-equal forces on the ends of the rope to stretch it? All you need is tension.

So the force applied to an end of the rope does not exert a force, net or otherwise, on the rope at all. For the purpose of the physics here we really are transmitting force at a distance through the concept of mechanical tension.

More self-contradictory statements. Mechanical tension is distinctly local acting. Each part of the rope exerts a force on the neighboring part.

If you're having trouble with a massless rope just use a massive one! This is really beside the point to the issues raised in this thread.

Now you say it is a contradiction to say that one can apply a force but not exert a force on something. You are saying that "apply" and "exert" a force are the same thing. I make a distinction.

Consider the interaction between a photon and an atom when an atom releases a photon. The photon (a massless particle) carries with it momentum h/\lambda and causes a change in momentum to the atom in the opposite direction of \Delta p_e = h/\lambda. If we say that the photon exerts a force on the atom, then for Newton's third law (which is fundamental to all of physics, quantum mechanics included) to hold we would have to say that there is a force exerted on the photon. But, for reasons we both understand, it is meaningless to talk about a force being exerted on a photon.

When the photon is absorbed by another atom, a distance s away, there is a change in momentum of that atom that is equal and opposite to the change in momentum of the emitting atom. It took a finite time to accomplish that change in momentum (\Delta t =s/c. So we can say that the emitting atom exerts a force on the absorbing atom. We could say that the force is applied by means of the exchange of a massless photon. We just can't say that the force is exerted on the photon.

An irrelevant digression. We are talking about classical, macroscopic contact forces here, not interactions at the atomic level.

 

[A.T.]

If you're having trouble with a massless rope just use a massive one!

Or simply consider the rotating space station scenario, without any ropes.

 

[Doc Al]

Or simply consider the rotating space station scenario, without any ropes.

Exactly. Or the merry-go-round. Nothing 'massless' in those scenarios, so no temptation to invoke 'action at a distance'.

 

[Dale]

If it stretched there would have to be non-equal, opposing forces on the ends on the rope (ie a net force on the rope)

This is not correct.

You are saying that "apply" and "exert" a force are the same thing. I make a distinction.

Do you have any reference for that distinction?

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.

 

[A.T.]

My point here is that 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.

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 (see https://www.physicsforums.com/attachment.php?attachmentid=38327&stc=1&d=1314480216").

 

[Andrew Mason]

This is not correct.

Do you have any reference for that distinction?

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.

Let's just say that you can apply a force through the rope to the mass on the other end an not quibble about whether you can apply or exert a real force to a non-real massless rope.

AM

 

[Dale]

But that implies action at a distance.

Anyway, do you now accept my analysis or have your own?

 

[Dadface]

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.

 

[Dale]

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.

 

[Andrew Mason]

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

 

[Dale]

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?

 

[Andrew Mason]

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

 

[Dale]

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.

 

[Andrew Mason]

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

 

[Doc Al]

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?

 

[Dale]

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.

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.

 

[rcgldr]

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.

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.