  Motivated by recent experiments on rotating Bose-Einstein condensates, we
investigate a rotating, polarized Fermi gas trapped in an anharmonic potential.
We apply a semiclassical expansion of the density of states in order to
determine how the thermodynamic properties depend on the rotation frequency.
The accuracy of the semiclassical approximation is tested and shown to be
sufficient for describing typical experiments. At zero temperature, rotating
the gas above a given frequency $\Omega_{\rm DO}$ leads to a `donut'-shaped
cloud which is analogous to the hole found in two-dimensional Bose-Einstein
condensates. The free expansion of the gas after suddenly turning off the trap
is considered and characterized by the time and rotation frequency dependence
of the aspect ratio. Temperature effects are also taken into account and both
low- and high-temperature expansions are presented for the relevant
thermodynamical quantities. In the high-temperature regime a virial theorem
approach is used to study the delicate interplay between rotation and
anharmonicity.
