The problem of nucleons moving independently in a rotating oscillator potential can be solved exactly by elementary methods. The resulting simple expressions for the energy and moment of inertia are valid for all angular velocities, and will be of use in estimating corrections to the finer details of the rotational spectra of nuclei. The motion is analyzed in terms of the orbits of the individual nucleons. The rotation of the average field induces particle motions with positive and negative orbital angular momenta, which are large in comparison with the angular momenta associated with the rotation of the orbits with the average angular velocity. The 'rigid' value of the moment of inertia of the independent particle motion near an equilibrium deformation results from the cancellation of these much larger orbital contributions. The orbits 'outside' closed shells contribute to the moment of inertia a value practically equal to that of a rigid body with the mass distribution of the whole nucleus. On account of cancellations, the resultant contribution of the deformed, closed-shell core is only a small fraction of the total value.