  In classical electrodynamics for rotating with variable angular velocity
charged rigid sphere are found: the exact values of electromagnetic fields, the
flux of radiating energy and the exact integral equation of rotation including
the terms of self-rotation. The analysis of this eq. shows that on one hand,
there is no "runaway" solutions, peculiar to the Lorentz-Dirac eq. of radiating
point particle, on the other hand, there appear new problems, among them is the
nonexistence of solution for some external moments of force.
