What exactly is the reactive centrifugal force (split)

by A.T.
Tags: centrifugal, force, reactive, split
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P: 6,345
 Quote by A.T. Here is your error. Only the L of the entire system must be constant. The L of the astronaut doesn't have to be constant.
The space station would have to apply a torque to the astronaut to increase his angular momentum effectively maintaining the astronaut's angular speed. So the space station would have to have a large moment of inertia compared to the astronaut: Iss >> R^2Mast. In that case you are right.

Let's suppose there is one astronaut who weighs 100 kg including his suit, and he is lying on the floor of a circular rotating space station of radius R and mass 1100 kg. It is made of aluminum except for the section directly opposite him which is made of lead that has a mass of exactly 100 kg more than the aluminum floor under/outside the astronaut.

The centre of mass of the space station is not the geometric centre. Let's say its centre of mass is Δr from the geometric centre. But the centre of rotation, with the astronaut, is the geometric centre.

The question is: what provides the centripetal force that causes the centre of mass of the space station to rotate about the geometric centre?

AM
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 Quote by DaleSpam We are talking about the force ON the floor (the reactive centrifugal force), so of course it disappears if the floor completely dissolves. The deformation of the floor is in the outward direction which requires a force on the floor in the outward direction*. This force is the reactive centrifugal force. *EDIT: actually, on further thought I realized that I am making an incorrect generalization from statics. What is required is a shear stress in the radial direction and/or a tension in the circumferential direction. In this specific case the stress is caused, in part, by the reactive centrifugal force, but it is not a general requirement.
So you seem to be saying that the reason the astronaut makes the dent is, at least in part, because of his inertia. This would be shown by the dent itself. If the dent is not a perfectly radial dent then it has to be caused by inertia. I say the dent will be on an angle, indicating that with the momentary loss of force of the floor the astronaut simply continued moving in a straight tangential line until the solid part of the floor moved in and deflected him.

 You are taking one specific case and making an incorrect generalization. In this case, we are dealing with a massive space station, not a hula hoop. The ω of the space station is nearly independent of the astronaut's r, even in the absence of an external torque. Thus, the formula I posted (F=mωēr) is the correct one for this situation. The centripetal force increases with increasing r. Again, you are taking one specific case and making an incorrect generalization. In this case, we are not dealing with gravity and a 1/rē force, we are dealing with material deformation which essentially follows Hooke's law (a force proportional to Δr) up to the point where you start getting plastic deformation (a force independent of r).
Actually, I should have said that Fc is proportional to 1/r^3, if angular momentum is conserved: Fc = L^2/mr^3. But your point is well taken: with a massive space station where Iss >> r^2Mast the angular speed would not decrease significantly with the astronaut's increase in r. So, AFTER the Astronaut's feet again reached a solid floor the centripetal force would be greater by a factor of Δr/r because ω does not change.

But surely the essential physics doesn't depend on how massive the space station is compared to the astronaut. Let's say there are 2 floors, the inner one being 10 cm thick and made of material that will turn to jello 1 cm at a time when someone presses a switch. Each time the astronaut completes a circle, someone presses the switch. What you will end up with is a series of dents in the jello moving at an angle opposite to the direction of rotation. Each time the floor turns to jello, the Astronaut keeps moving on a tangent until the next non-jello layer moves inward 1 cm to stop him. If it was the centrifugal reaction force that caused the dents, the dents would be completely radial would they not?

AM
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 Quote by Andrew Mason So you seem to be saying that the reason the astronaut makes the dent is, at least in part, because of his inertia.
No, that is not what I am saying at all. A dent forms due to stresses in the material. In dynamics there can be stresses due to the floor's own inertia, but any stresses attributable to the astronaut will be through the reaction force.

 Quote by Andrew Mason This would be shown by the dent itself. If the dent is not a perfectly radial dent then it has to be caused by inertia. I say the dent will be on an angle, indicating that with the momentary loss of force of the floor the astronaut simply continued moving in a straight tangential line until the solid part of the floor moved in and deflected him.
How do you propose that the astronaut's inertia will cause stress in the material? Please provide a reference to support the claim.

 Quote by Andrew Mason Actually, I should have said that Fc is proportional to 1/r^3, if angular momentum is conserved: Fc = L^2/mr^3. But your point is well taken: with a massive space station where Iss >> r^2Mast the angular speed would not decrease significantly with the astronaut's increase in r. So, AFTER the Astronaut's feet again reached a solid floor the centripetal force would be greater by a factor of Δr/r because ω does not change.
Thank you!

 Quote by Andrew Mason Let's say there are 2 floors, the inner one being 10 cm thick and made of material that will turn to jello 1 cm at a time when someone presses a switch. Each time the astronaut completes a circle, someone presses the switch. What you will end up with is a series of dents in the jello moving at an angle opposite to the direction of rotation. Each time the floor turns to jello, the Astronaut keeps moving on a tangent until the next non-jello layer moves inward 1 cm to stop him. If it was the centrifugal reaction force that caused the dents, the dents would be completely radial would they not?
No. When the astronaut is co-rotating the reaction force is purely centrifugal, but if the astronaut is not co-rotating then the reaction force may have some tangential component as well (think about the Coriolis force in the rotating frame). Any deformation of the material due to the Astronaut will always be via the reaction force, whether that is purely centrifugal or otherwise.
P: 3,170
 Quote by Andrew Mason The question is: what provides the centripetal force that causes the centre of mass of the space station to rotate about the geometric centre?
Acceleration of the centre of mass is a function of the net force, not of an individual force provided by something. An individual force has a point of attack, which together with its direction determines if it is centrifugal or centripetal. The net force doesn't have a physical point of attack, but can be thought of as acting on the center of mass. Therefore you can have one individual centrifugal force acting, and yet a centripetal acceleration of the center of mass.
P: 3,170
 Quote by Andrew Mason So you seem to be saying that the reason the astronaut makes the dent is, at least in part, because of his inertia.

It doesn't matter how many indirect causes you can list for the deformation. The direct cause of the deformation is the local centrifugal force exerted by the astronaut on the wall. So that centrifugal force has a direct physical effect.
 Mentor P: 15,560 Andrew Mason, In A.T.'s drawing below, do you disagree about the existence of any of the forces, or is your disagreement entirely about the labeling?
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 Quote by DaleSpam In A.T.'s drawing below, do you disagree about the existence of any of the forces, or is your disagreement entirely about the labeling?
It seems to be about labeling and the problem that: You can have an individual force acting outwards and inward acceleration of the CoM of some arbitrarily chosen part of the system. But at the same time that outwards force can have real, physical outwards effects, like outwards acceleration/deformation of some other arbitrarily chosen part of the system.

The best way to avoid this conflict, is to ignore all the effects the force might have on arbitrarily chosen parts, and simply consider what is independent of how you split up the system: The force's point of attack and direction. This leads to the label "centrifugal".
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 Quote by DaleSpam No, that is not what I am saying at all. A dent forms due to stresses in the material. In dynamics there can be stresses due to the floor's own inertia, but any stresses attributable to the astronaut will be through the reaction force. How do you propose that the astronaut's inertia will cause stress in the material? Please provide a reference to support the claim.
A dent signifies that there has been movement. If the dent is due to a force overcoming stress, the motion results from that force exceeding the stress momentarily. That can never happen here. My point in using the jello was to eliminate the force and the stress and show that there would be a dent in the jello that essentially traces the inertial path of the astronaut.

Our disagreement is not that there is a force between the astronaut and the space station. We don't disagree on its direction either. We just disagree on what that reaction force does. You say it is just a force that results in centrifugal tension in the space station. I say that it actually accelerates the space station in the direction opposite to the direction that the astronaut is accelerating. In other words, it accelerates the space station toward the centre of rotation.

My position is that by calling it a centrifugal reaction force giving rise only to a tension is incorrect and it also makes it extremely difficult to distinguish from the fictitious centrifugal force. The centrifugal force or pull from the outside is postulated as the source of the tension in the space station.

AM
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P: 6,345
 Quote by A.T. Acceleration of the centre of mass is a function of the net force, not of an individual force provided by something. An individual force has a point of attack, which together with its direction determines if it is centrifugal or centripetal. The net force doesn't have a physical point of attack, but can be thought of as acting on the center of mass. Therefore you can have one individual centrifugal force acting, and yet a centripetal acceleration of the center of mass.
Ok. Then you are saying that the reaction force causes centripetal acceleration but you still want to call it a centrifugal force. The centripetal acceleration multiplied by the mass of the spacestation is equal and opposite to the centripetal acceleration x the mass of the astronaut. So the astronaut's centripetal force and its reaction force are both "net" forces.

The direction is what it is. It is opposite to the centripetal acceleration of the astronaut, which is the direction of the acceleration of the space station. It cannot ever cause motion to occur outward from the centre of rotation so I am not sure why anyone would want to call it centrifugal. While it acts, it accelerates mass toward the centre of rotation.

When Newton describes forces moving things he is implicitly if not explicitly referring to the accelerations of their centres of mass or centres of gravity, not the direction of tensions within the bodies themselves. Those are trivial details and they don't matter - until one gets into the world of rotating masses.

AM
P: 3,170
 Quote by Andrew Mason We just disagree on what that reaction force does...it accelerates the space station ...
Read post #76. Learn to distinguish between an individual force and the net force.
P: 3,170
 Quote by A.T. Acceleration of the centre of mass is a function of the net force, not of an individual force provided by something.
 Quote by Andrew Mason Ok. Then you are saying that the reaction force causes centripetal acceleration ...
Mentor
P: 15,560
 Quote by Andrew Mason A dent signifies that there has been movement. If the dent is due to a force overcoming stress, the motion results from that force exceeding the stress momentarily.
Sure, Newton's 2nd law.

 Quote by Andrew Mason That can never happen here.
Why not?

 Quote by Andrew Mason My point in using the jello was to eliminate the force and the stress and show that there would be a dent in the jello that essentially traces the inertial path of the astronaut.
Even in jello there is a reaction force. Jello has a very low yield strength, so the force will be small, but it is still that reaction force which causes the deformation of the Jello. By using jello you have made the reaction force small (not zero), but you have also made it particularly sensitive to the force.

 Quote by Andrew Mason Our disagreement is not that there is a force between the astronaut and the space station. We don't disagree on its direction either.
OK. That force that we both agree exists is called the "centrifugal reaction force". It is how that term is defined. You may not like the name, and you may have excellent reasons for disliking the terminology (e.g. for extended bodies a centrifugal reaction force can cause centripetal acceleration), but nevertheless that is the standard terminology.

 Quote by Andrew Mason We just disagree on what that reaction force does. You say it is just a force that results in centrifugal tension in the space station. I say that it actually accelerates the space station in the direction opposite to the direction that the astronaut is accelerating. In other words, it accelerates the space station toward the centre of rotation.
I don't disagree about the acceleration which falls under Newton's 2nd law (although in A.T.'s example the space station's COM is not accelerating).

I disagree only with your interpretation of Newton's 3rd law where you try to claim that the 3rd law reaction to the centripetal force on one astronaut is the centripetal force on the other astronaut. All of the remaining discussion has been about your attempts to justify that interpretation, either by re-defining Newton's third law with reference to his use of the word "action" or by asserting that the centrifugal reaction force does not have any physical effects besides centripetal acceleration.

I think that it is clear that the reactive centrifugal force exists in some cases, in those cases it is the 3rd law pair of a centripetal force, it is always a real force, it exists in all frames and can do all of the things that you would expect of a real force including material deformations and other such things.

I also agree that the terminology can be confusing. It is clearly a topic that many students struggle with. Personally, I don't even like the "action/reaction" terminology, but it is out there and people should know what it means.
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 Quote by DaleSpam (although in A.T.'s example the space station's COM is not accelerating).
Unless you include the other astronaut in the space station. So it depends on an arbitrary definition of objects, what the "effect" on an object's COM might be. That's why it is not a good idea to base a general naming on some object’s COM acceleration. The logic behind the centrifugal-name does not depend on how you cut the system into pieces.

And if more forces are acting, it is even more difficult to attribute a particular effect, to a certain force. That's why it is not a good idea to base the naming on effects in general. The logic behind the centrifugal-name does not depend on other forces, and what effects they might cause together.
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 Quote by A.T. No. Read it again.
You have quoted only part of what I said. The "net" force IS ALWAYS the mass x its acceleration. The astronaut's entire reaction force is equal and opposite to its mass x its acceleration and that is exactly equal to the mass x acceleration of the space station. It is by its very nature a "net" force.

AM
P: 3,170
 Quote by Andrew Mason The astronaut's entire reaction force is equal and opposite to its mass x its acceleration and that is exactly equal to the mass x acceleration of the space station. It is by its very nature a "net" force.
No, it is not the same. They have a different point of attack. See post #76.
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 Quote by A.T. No, it is not the same. They have a different point of attack. See post #76.
I don't see the significance of the point of attack.

Maybe I am missing something here. Stop me if you think I am saying anything that is incorrect.

1. For a rigid body that is not rotating and whose centre of mass is not accelerating, the sum all forces acting on it is 0. Since no part of the body is accelerating, the sum of all forces acting on each part of such a body is 0.

2. For a rigid body that is rotating and whose centre of mass is not accelerating, the sum of all forces acting on it is 0. Since each part of the body is accelerating, the sum of all forces acting on each part of the body is equal to the mass of such part multiplied by its (centripetal) acceleration. (Since the sum of all such mass x accelerations must be 0, a rotating free body always rotates about an axis through its centre of mass).

3. The space station with the single astronaut lying on the floor (as I described in my post #73) is a rotating rigid body whose centre of mass is not accelerating. Therefore:
• the sum of all forces acting on each part is equal to the centripetal acceleration of that part multiplied by the mass of such part.
• For any arbitrary division of the space station (including contents) into two parts, the sum of all forces acting on each part is equal to the mass of such part multiplied by its (centripetal) acceleration and
• The sum of the mass x (centripetal) acceleration of each of the two parts = 0.
• Thus, the mass x (centripetal) acceleration of any part is equal and opposite to the mass x centripetal acceleration of the other part.

4. Therefore the mass x acceleration of the astronaut = -mass x acceleration of the rest of the space station

5. Since the force applied by the space station to the astronaut = the mass x the (centripetal) acceleration of the astronaut, the equal and opposite force applied by the astronaut to the space station = the mass x (centripetal) acceleration of the rest of the space station = sum of all the forces acting on all the parts of the rest of the space station.

AM
P: 3,170
 Quote by Andrew Mason I don't see the significance of the point of attack.
It's a naming convention, not a matter of great significance. See post #85 for my reasons to prefer the common convention over yours.
Mentor
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 Quote by Andrew Mason The sum of the mass x (centripetal) acceleration of each of the two parts = 0.
This is not generally true. If you take two parts which are near each other or two parts which are opposite but not equally massive then their change in momentum may not be equal and opposite.

 Quote by Andrew Mason 5. Since the force applied by the space station to the astronaut = the mass x the (centripetal) acceleration of the astronaut, the equal and opposite force applied by the astronaut to the space station = the mass x (centripetal) acceleration of the rest of the space station = sum of all the forces acting on all the parts of the rest of the space station.
This is true if you consider the opposite astronaut to be part of the space station (which is valid). In that case the centrifugal reaction force applied by the right astronaut to the space station is indeed equal to the mass x centripetal acceleration of the "space station & left astronaut".

The statement is not true if you consider the opposite astronaut not to be part of the space station (which is also valid). In that case the centrifugal reaction force applied by the right astronaut to the spact station is not equal to the mass x centripetal acceleration of the space station.

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