What exactly is the reactive centrifugal force (split)by A.T. Tags: centrifugal, force, reactive, split 

#73
Feb313, 10:52 PM

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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 



#74
Feb413, 04:09 AM

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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 nonjello 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 



#75
Feb413, 06:27 AM

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#76
Feb413, 06:33 AM

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#77
Feb413, 06:38 AM

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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. 



#78
Feb413, 06:49 AM

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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? 



#79
Feb413, 08:01 AM

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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". 



#80
Feb413, 10:25 AM

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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 



#81
Feb413, 10:55 AM

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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 



#82
Feb413, 11:02 AM

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#83
Feb413, 11:07 AM

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#84
Feb413, 12:04 PM

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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 redefining 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. 



#85
Feb413, 12:34 PM

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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 centrifugalname does not depend on other forces, and what effects they might cause together. 



#86
Feb413, 01:28 PM

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AM 



#87
Feb413, 02:59 PM

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#88
Feb513, 07:20 AM

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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:
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 



#89
Feb513, 07:46 AM

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#90
Feb513, 08:48 AM

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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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