Rotational motion in special relativity

From analysis of translational motion and transformation of reference frame, one conclude the upper limit of velocity cannot exceed the speed of light. In classical mechanics, the velocity by rotation is given by $vec{v}=vec{r}xvec{omega}$. Consider the case of infinite long rod, then a seemingly paradox that to prevent violating upper limit of velocity, on cannot rotate the rod as the velocity by rotation will easily exceed the limit. Can anyone give an account on relativistic correction on rotation? Namely, such as the derivation and consequence of Thomas precession?