Using the average method, we derive a closed set of linear equations that d
escribes the spinning up of an harmonically trapped gas by a rotating aniso
tropy. We find explicit expressions for the time needed to transfer annular
momentum as well as the decay time induced by a static residual anisotropy
. These different time scales are compared with the measured nucleation tim
e and lifetime of vortices by Madison et al. We find a good agreement that
may emphasize the role played by the noncondensed component in those experi
ments.