special relativity - Is there a physical upper limit on how fast a physical object can rotate?

Objects can not travel faster than the speed of light.

Angular velocity is $\omega = \frac{s \times v}{|s|^2}$

It seems to me that for infinitely small objects (like electrons) there is no limit on how fast objects can rotate.

It seems wrong to me that it is theoretically possible to generate more magnetic effects and similar by rotating than by linear movement though.

I recall that sufficiently fast rotating black holes can form naked singularities. If rotation is limited to below that amount then that might be a limit on how fast things can rotate?