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Re: [Phys-l] Centrifugal redux


On 03/20/2009 08:09 AM, Rauber, Joel wrote:

I'd add the proviso that you may choose whatever frame you like to do
calculations; however, you may not choose whatever frame you like as
your rest-frame. Or perhaps more precisely stated, you may not
choose whatever frame you like for a rigid objects Center-of-Mass
rest frame. That is uniquely determined.

No, it is not uniquely determined, as we can see from the following:
Today a certain object is at rest in the frame of the space station.
Tomorrow the same object is at rest in some terrestrial frame.


I don't understand the above objection. I would still maintain that the rest frame is uniquely determined. I'm talking about the object's rest frame. Just because that unique frame may coincide with the space station frame today and with the terrestrial frame tomorrow is a statement about the time dependence of what other frames may coincide with the objects rest frame, it's not a statement about the object's rest frame.

These are not equivalent. Assuming we arrange to have them coincide
as to position, they will have wildly different velocity and wildly
different acceleration.

I think I agree with the above, which is why I don't think the previous example is a contra-indication to the uniqueness of the rest frame of the object.


The concept of "rest frame" is not particularly profound and the
term is not particularly clear. Usually it is better to say "lab
frame" if you mean lab frame, or "comoving frame" if you mean
comoving frame.


Profoundness, may in many contexts be a matter of taste. My rest frame is very profound to me.

I agree if I mean instantaneously co-moving frame, I should say so. But I intentionally did not want to refer to a co-moving frame and therefore didn't refer to one.

A particle is always at rest relative to its own comoving frame.
Things like _proper time_ are defined in the comoving frame.


I think both of the above statements are important and profound, even if the first one may seem almost trivial (though I don't think it is; I interpret a lot of the work of Mach as representing that the first statement is far from trivial).

Being at rest in its own frame does *not* mean that the particle is
unaccelerated!

I agree and I did not claim that it did.