# What are the consequences of relativistic angular velocities?

If I take a rod of some radius $r$ and length $L$, and I spin this rod with angular velocity $\omega$. How would the geometry of the rod appear to an observer as one converges to $c$? What are the consequences of this to, say, electrons in a solenoid?

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– user1664196 Jan 12 at 3:17
@user1664196 Yeah, I'd be happy with whatever the limiting speed is for angular velocity (there must be one, right?). – Kevin Jan 12 at 3:24
@Raindrop Right, I noticed the paper you referenced, but it doesn't help with the specific questions I have: How would the geometry of the rod appear to an observer as one converges to c? What are the consequences of this to, say, electrons in a solenoid? – Kevin Jan 12 at 3:50
Check this research out: [Relativistic Hall Effect][2] "We examine manifestations of the relativistic Hall effect in quantum vortices and mechanical ﬂywheels and also discuss various fundamental aspects of this phenomenon." quoted from the abstract.   [2]: prl.aps.org/pdf/PRL/v108/i12/e120403 – Raindrop Jan 12 at 6:54
Relativistic contraction and related eﬀects in noninertial frames xxx.lanl.gov/abs/gr-qc/0307011 en.wikipedia.org/wiki/Ehrenfest_paradox – Raindrop Jan 12 at 7:20
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## 1 Answer

Based on Relativistic description of a rotating disk O. Gron, Am. J. Phys. 43, 869 (1975), DOI:10.1119/1.9969 [I got the link from Wikipedia references on the Ehrenfest article] I think that for a rod instead of a disk: An observer S ("momentarily at rest relative to the disk") "measures an elliptical shape for the" path of the tip of the rod, "and finds that each point of it describes a cycloid-like path, while its center moves along a straight line with constant velocity. S' ("an accelerated observer ... rotating with the" rod) observes a rod at rest, while the surroundings are rotating. He measures a circular shape for the path of the tip of the rod.

I have no idea how electrons would behave in a solenoid coiled around a rod with angular acceleration, $\omega \rightarrow cr$.

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