We identify a new mechanism of internal dissipation of rotational kinetic e
nergy in spinning dust grains, arising from the reorientation of nuclear an
gular momentum, e.g., spins of protons. Grain rotation induces magnetizatio
n of the nuclear spin system, with net alignment of nuclear spins parallel
to the grain angular velocity. When the grain does not rotate around a prin
cipal axis, the nuclear magnetization vector precesses in grain-body coordi
nates, resulting in dissipation of energy. The analogous process involving
electron spins was discovered by E. M. Purcell and termed "Barnett relaxati
on." We revisit the physics of the Barnett relaxation process and correct t
he estimate for the Barnett relaxation rate. We show that nuclear relaxatio
n can be orders of magnitude more important than Barnett relaxation. This f
inding implies that the processes of "thermal flipping" and "thermal trappi
ng" are important for a broad range of grain sizes.