Consider a disc in the framework of special relativity. It's initially at rest in an inertial frame, and then you get it rotating in a way that respects the symmetry of the circle (e.g. by turning a thin rod through its center). There's no way that the acceleration of the different parts of the objects can be Born rigid. Does this mean that we have to perform an amount of work that depends on the disc's elasticity to get it rotating? I'm pretty sure that the answer is yes, but I'd like someone to confirm it or prove me wrong.