  We study the rotational properties of a Bose-Einstein condensate confined in
a rotating harmonic trap for different trap anisotropies. Using simple
arguments, we derive expressions for the velocity field of the quantum fluid
for condensates with or without vortices. While the condensed gas describes
open spiraling trajectories, on the frame of reference of the rotating trap the
motion of the fluid is against the trap rotation. We also find explicit
formulae for the angular momentum and a linear and Thomas-Fermi solutions for
the state without vortices. In these two limits we also find an analytic
relation between the shape of the cloud and the rotation speed. The predictions
are supported by numerical simulations of the mean field Gross-Pitaevskii
model.
