The maximum angular velocity is unfortunately bounded above by the tensile strengths of materials. Steel ball bearings are the traditional rotor, and even they

The maximum angular velocity is unfortunately bounded above by the tensile strengths of materials. Steel ball bearings are the traditional rotor, and even they come apart at unsatisfying (from a relativistic perspective) rotation rates. For this game, it's all about tensile strength. Even solid diamond, graphene, or nanowhatchmacallit won't do much better. Nanotubes are ~100x stronger than Kevlar, which will only win you a factor of 10 in rotation frequency. If you can, the gravitational waves radiated from a spinning object increase in power like frequency^4. The prize is sitting there for anyone who can do it.