All the other answers here are good but I want to add that for your example General Relativity which handles accelerating frames of reference is the theory that deals with accelerating frames. The relativity you're referencing is special relativity. So, although rotation isn't handled by special relativity, general relativity can handle rotating frames of reference or any other accelerating frames of reference.
HonestWestern8594 t1_j0gs0p3 wrote
Reply to Does rotation break relativity? by starfyredragon
All the other answers here are good but I want to add that for your example General Relativity which handles accelerating frames of reference is the theory that deals with accelerating frames. The relativity you're referencing is special relativity. So, although rotation isn't handled by special relativity, general relativity can handle rotating frames of reference or any other accelerating frames of reference.