Question about the rotating disc

[Fredrik]

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.

 

[Dale]

You have to perform more work than that. At a minimum there is work that goes into deformation of the material, and there is also the work on increasing the KE of the disk.

 

[Entropia]

Yes, the answer is yes. In special relativity, the concept of Born rigid objects does not hold. This means that when we rotate the disc, the different parts of the disc will experience different accelerations, leading to a deformation of the disc. Therefore, in order to get the disc rotating, we would have to perform work that takes into account the elasticity of the disc. This work would depend on the material properties of the disc and the amount of deformation that occurs during rotation. So, in short, the work required to rotate the disc would not be solely dependent on the initial velocity and the rotational speed, but also on the elasticity of the disc.