  The possibility of effectively inverting the sign of the dipole-dipole
interaction, by fast rotation of the dipole polarization, is examined within a
harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on
the stationary states in the Thomas-Fermi limit, in the corotating frame, as
well as direct numerical simulations in the Thomas-Fermi regime, explicitly
accounting for the rotating polarization. The condensate is found to be
inherently unstable due to the dynamical instability of collective modes. This
ultimately prevents the realization of robust and long-lived rotationally tuned
states. Our findings have major implications for experimentally accessing this
regime.
