  Angular momentum balance is examined in the context of the electrodynamics of
a spinning charged sphere, which is allowed to possess any variable angular
velocity. We calculate the electric and magnetic fields of the (hollow) sphere,
and express them as expansions in powers of $\tau/t_c \ll 1$, the ratio of the
light-travel time $\tau$ across the sphere and the characteristic time scale
$t_c$ of variation of the angular velocity. From the fields we compute the
self-torque exerted by the fields on the sphere, and argue that only a piece of
this self-torque can be associated with radiation reaction. Then we obtain the
rate at which angular momentum is radiated away by the shell, and the total
angular momentum contained in the electromagnetic field. With these results we
demonstrate explicitly that the field angular momentum is lost in part to
radiation and in part to the self-torque; angular momentum balance is thereby
established. Finally, we examine the angular motion of the sphere under the
combined action of the self-torque and an additional torque supplied by an
external agent.
