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Well... kind of hard to translate in English so bare with me :).

Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$.

That means that for any $ω$, there is an $r$ sufficiently big that $c = ω r_c$. That would mean that for an $r > r_c$, the speed of the point would be higher than $c$.

But we also know that c is limit. So... where is the mistake?

I'm presuming that it has something to do with the "limit" between classic mechanic approach and relativistic approach.

AccidentalFourierTransform
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zozo
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    Nothing to do with quantum mechanics, but rather with special relativity. This is one of the reasons, why absolutely rigid bodies are not possible in relativistic mechanics. One question you can ask, is how does the outer edge of the wheel know, that the center is rotating at $\omega$? If the wheel is on a shaft that starts rotating, how long before the rim of the wheel realises, that something is driving it from the center? – LLlAMnYP May 04 '16 at 09:24
  • So basically you say the wheel would act "fluid" - like an whirlpool (its edge would rotate with almost c regardless ω and r)? P.S. Why not post it as an answer (and can you add/quote proof pls?). I actually thought that would happen, but can't find any way to prove it. – zozo May 04 '16 at 10:06
  • This is not exactly a trivial problem. I didn't even begin to mention, the effects of relativistic contraction of different parts of the wheel from the point of view of an observer just standing next to the middle of the disc, or an observer in a non-inertial, rotating frame, standing on the disc. Since the theory of relativity is not my training, I'd leave the answering to someone else. But this is a classic problem, I'm sure there's something even in wikipedia. – LLlAMnYP May 04 '16 at 10:12
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    Check out the Ehrenfest paradox, it's exactly about this problem. https://en.wikipedia.org/wiki/Ehrenfest_paradox – LLlAMnYP May 04 '16 at 10:16
  • I know is not trivial :). I'm just trying to "trivialize" it a bit (as I said I thought something like that would happen, also I was sure some1 researched this and is a solved problem but could not find it). Got what I was searching for, tyvm guys. – zozo May 04 '16 at 12:23

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The link given by LLlAMnYP for the Ehrenfest paradox gives the classical physics rational :

Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of material

So one cannot construct such a rigid body, even before one can reach velocities close to c. I want also to stress, contrary to a comment, that quantum mechanics is important, because all the macroscopic properties of materials, as is the velocity of sound, emerge from the underlying quantum mechanical organization of atoms and molecules.

The forces holding solids together are electromagnetic quantum mechanical exchanges, and any impulse for the turning wheel cannot travel faster than the velocity of light. The velocity of sound is dependent on the quantum mechanical exchanges on the lattice of the solid.

anna v
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  • Exactly what I was looking for. Regarding the comment about quantum mechanics, it had sense the way I originally posted the question (I was "multitasking" and typed wrong). – zozo May 04 '16 at 12:19