Imagine a thought experiment: You have a rod 10 ft or 10 light nanoseconds long. On each side you have perfectly synchronized super high-speed cameras looking at the surface of the rod.
You rotate the rod from the left. On the left side the camera records that the rod started to rotate at T-left= 0. On the right side (other side), when would the other camera see the start of rotation? What would T-right be at the start of rotation as recorded by the right hand camera?
If we were to communicate the information of the start of rotation via a beam of light, it would take 10 ns to get to the other camera. So, T-right would equal 10 ns. Would communicating the same information via a physical rod beat a beam of light? Wouldn't that violate the idea that C is the absolute speed limit on everything, including information (outside of quantum entanglement)? Are there relativistic time dilation effects at play here? Would the rotation propagate through the rod in a wave form?
This is just a thought experiment, so let's assume that the rod is made from an absolutely rigid material and there are no spring effects or other purely mechanical effects.