  We present a method to determine the critical rotational frequencies for
superfluidity of both uniform and trapped Fermi gases across wide Feshbach
resonance. It is found that as one approaches the resonance from the BCS side,
beyond a critical scattering length, pairing is so robust that superfluidity
cannot be destroyed by rotation. Moreover, the critical frequency has a
sequence of jumps revealing the appearance of Landau levels, which are
particularly prominent for systems up to a few thousand particles. For
rotational frequency below an "ultimate" critical frequency, defined to be the
lowest frequency at which the center of the cloud goes normal, a trapped gas
has a superfluid core surrounded by a normal gas, as seen in recent
experiments.
