Radiation reaction for a rotating sphere with rigid surface charge

Radiation reaction in classical electrodynamics is studied using as a simple model a rotating sphere with rigid surface charge. Because of the transparent geometric nature of the problem, we obtain an exact integral expression for the "self-torque", which depends causally and linearly on the angular speed. This leads to a linear equation of motion, which does not have any runaway solutions, as long as no negative mechanical moment-of-inertia is added to the system. The results are illustrated with a few examples corresponding to predetermined motions and external torques.