# Why does relativistic rotating rod bend?

Let's consider two inertial reference frames S and S', S' moving with velocity V relative to S (velocity V to the right with respect to S considered stationary, in X-axis direction). We have a rotating rod at rest in S (strictly speaking, only one of the endponts of the rod is at rest, the others are rotating with constant angular velocity $$\omega$$).

If we assume that this rod is capable of undergoing relativistic velocities without breaking, what would be seen from S is simply a rod which rotates with a really high velocity. No length contraction, no bending. However, what would be seen from S' is a rod such that:

(1) it translates to the left -since S' moves with velocity V to right with respect to S-

(2) it changes its length as it rotates, the length being contracted when the rod is rotating near the X-axis - which can be understood in terms of the length contraction caused by relative velocity V being close to c-

(3) it bends!!!

I cannot understand why (3) happens. When $$\omega$$ isn't relativistic, there would be no bending but only contraction (2). When $$\omega$$ is relativistic, we perceive all of (1), (2) and (3) as seen in S'.

I would like to find an explanation for (3) which rests upon solid arguments and definitions. Can (3) be explained only in terms of Lorentz Transformations, which is the approach I find most clarifiying?