  We identify a new mechanism of internal dissipation of rotational kinetic
energy in spinning dust grains, arising from the reorientation of nuclear
angular momentum, e.g., spins of protons. Grain rotation induces magnetization
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 principal axis,
the nuclear magnetization vector precesses in grain body coordinates, resulting
in dissipation of energy. The analogous process involving electron spins was
discovered by Purcell and termed ``Barnett relaxation''. We revisit the physics
of the ``Barnett relaxation'' process and correct the estimate for the Barnett
relaxation rate. We show that nuclear relaxation can be orders of magnitude
more important than Barnett relaxation. This finding implies that the processes
of ``thermal flipping'' and ``thermal trapping'' are important for a broad
range of grain sizes.
