  Using the average method, we derive a close set of linear equations that
describes the spinning up of an harmonically trapped gas by a rotating
anisotropy. We find explicit expressions for the needed to transfer angular
momentum as well as the decay time induced by a static residual anisotropy.
These different time scales are compared with the measured nucleation time and
lifetime of vortices by the ENS group. We find a good agreement that may
emphasize the role played by the non-condensed component in thoses experiments.
