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What exactly is the reactive centrifugal force (split) 
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#55
Feb113, 09:12 AM

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#56
Feb113, 09:19 AM

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[itex]F_{12} = 0[/itex] [itex]F_{32} = 0[/itex] [itex]F_{13} = 1[/itex] [itex]F_{23} = 1[/itex] [itex]F_{31} = 2[/itex] [itex]F_{21} = 2[/itex] That satisfies Newton's first law, but not the third. 


#57
Feb113, 02:23 PM

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It is rotating. Everything is accelerating. We use the inertial frame to analyse forces. The absence of apparent acceleration in the noninertial frame is not real. Why are you even referring to this? This makes it very difficult for the student to distinguish between the apparent centrifugal force and the real reaction force (which you say is a static centrifugal force and I say is a nonstatic centripetal force). AM 


#58
Feb113, 03:19 PM

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I note that you have not found a reference that writes a clear mathematical expression corresponding to your version and calls that the third law. All you have is an ambiguous translation that cannot be said to clearly contradict your approach. 


#59
Feb113, 03:36 PM

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When you sand on a table, you exert a downwards force on the table. When that downwards force starts deforming the table downwards, there eventually will be a momentary reduction in that downwards force. Do you find it strange to call it a downwards force, because it creates a downwards effect when it is reduced? 


#60
Feb113, 05:19 PM

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Acceleration is the second time derivative of the body's displacement vector relative to an inertial point. If you use as your reference a noninertial point whose acceleration is constantly changing, how would you measure real acceleration? AM 


#61
Feb113, 05:31 PM

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AM 


#62
Feb113, 05:32 PM

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#63
Feb113, 05:50 PM

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#64
Feb113, 07:24 PM

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By the way, I put it that way because you insist that one can have a force that produces no acceleration as a third law reaction to one that does produce acceleration. There is nothing wrong or confused in saying the force is related to an acceleration. AM 


#65
Feb113, 07:38 PM

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EDIT: Actually, after having read the entire quote in context it seems quite clear that Newton is not supporting your view. The part of the quote you cited is not the law, but the last of three examples. First he gives the "actionreaction" formulation of the law. Then he clearly talks about forces, not accelerations, in an example of a finger pressing a stone and second example of a horse drawing a stone. Then he introduces a third example, this one clearly indicating the special case of two bodies with no other forces acting so that the force is equal to the change in momentum (by his second law). In that case your formulation is equivalent to the usual formulation, but in all of the other examples he clearly intended the usual formulation, not yours.That is why I prefer sources that use math which is clear and unambiguous. All of those that I have seen clearly contradict your position. Can you provide any unambiguous (with math) support for your position? I provided unambiguous (with math) support for mine, so I don't think it is unreasonable to require the same from you. 


#66
Feb113, 07:42 PM

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#67
Feb113, 10:17 PM

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I know it seems counterintuitive, but with no external torque the centripetal force decreases as r increases. We see this from the fact that gravity, which supplies the centripetal force for orbiting bodies, varies as 1/r^2. AM 


#68
Feb113, 10:39 PM

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I found this commentary which wrestles with this very issue. I know what you are saying but the real problem I have is that Newton talks about force in his first two laws but talks about action and reaction in his third and does not mention force. The first two laws are quite straight forward and unambiguous. But the third is not, due to his use of undefined terms. That said, we should not be too critical of any confusion Newton may have had or caused by his statement of this law. Newton's laws are a truly remarkable achievement when one considers the state of physical science at the time. AM 


#69
Feb213, 01:58 AM

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But keep in mind that the whole causation reasoning about forces is often more fuzzy intuitive mythology, than physics. It doesn't affect the quantitative results. The action doesn't cause the reaction in the 3rd law. They both happen simultaneously, and physics just says they are equal but opposite. The same is true for net force and acceleration in the 2nd law. Although we often say that the net force causes the acceleration, they both happen simultaneously, and physics just says they are proportional. 


#70
Feb213, 02:06 AM

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#71
Feb213, 02:16 AM

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#72
Feb313, 09:13 PM

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*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. 


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