Spinning a rod in relativistic speed This is a random question that just comes into my mind.
Say you have a rod with a length of 6 x $10^8$ m and I spin it at its mid point at 1 rad/s. By classical mechanics the end of the rod would have been spinning at a linear velocity of light speed, that is definitely impossible according to relativity. So if I am an observer that is looking at the spinning rod from above, what would I observe? Will the rate of spinning on each part of the rod different and I will observe the rod started to bend like a spiral?
 A: $v=\omega r$ only holds if the rod is a rigid body. But since we're talking about sizes where relativistic effects come into play (in fact, even without relativity), the rod can no longer be considered as a rigid body. If it still were, that would imply any force you apply on one end of the rod can propagate to the other end instantly, violating the fundamental speed limit of such propagation $c$. Once you let go of the rigid body assumption, $v\ne \omega r$ and one needs to solve the internal dynamics of the rod (e.g. knowing its Young's modulus) to see how the applied force and torque propagates along the rod, which by this time will look more like spaghetti than a straight line.
A: In addition to @Gaberber 's answer, even if we have a material in which the speed of sound is very close to that of light, the rod's farthest end cannot exceed the speed of light. In this case, the relativistic momentum/force predicts that the farther parts of the rotating rod resist more against being accelerated, and thus they move slower not to reach the speed of light. Therefore, it is possible that the rod is bent into a spiral shape as guessed by you.
