I think there is some confusion between static and dynamic equilibrium here. Centrifugal "force" is simply inertia. It's much easier to visualize by considering a point mass on a massless arm. The arm has to exert a force on the mass not as a result of any applied force from somewhere else, but just as a result of needing to accelerate the mass toward the center of rotation.
atmsk90 t1_j0hgbik wrote
Reply to comment by TheSmartestBanana in Does rotation break relativity? by starfyredragon
I think there is some confusion between static and dynamic equilibrium here. Centrifugal "force" is simply inertia. It's much easier to visualize by considering a point mass on a massless arm. The arm has to exert a force on the mass not as a result of any applied force from somewhere else, but just as a result of needing to accelerate the mass toward the center of rotation.