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I know that, at least for a point mass or a rigid body travelling at constant velocity, in special relativity kinetic energy T is defined as: T = E - Mc^{2}where E is the body's total energy and M its invariant mass.

I have a problem in undestanding how to define T in the case of a spinning body. I assume the body has cylindrical simmetry around its axis of rotation, that its centre of mass is still, that it has uniform density even during spinning and that we could neglect internal tensions.

I have problems in doing that because M now depends on its spinning speed (it also depends on "how" it speeds because we can't simply make the assumption of rigid body, in general, but let's forget these complications for the moment). Infact E = Mc^{2}in this case, and this means kinetic energy would be zero according to that definition. Presumably we should instead define kinetic energy as: T = E - mc^{2}where m is the body's mass when it's not spinning at all. Does it make sense?

If then we don't neglect the energy due to internal elastic tensions E_{el}, should we count it as kinetic energy or not? If not, should we then say that T = E - mc^{2}- E_{el}?

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# Kinetic energy of a spinning body

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