  Distintictive features of supersolids show up in their rotational properties.
We calculate the moment of inertia of a harmonically trapped dipolar
Bose-Einstein condensed gas as a function of the tunable scattering length
parameter, providing the transition from the (fully) superfluid to the
supersolid phase and eventually to an incoherent crystal of self-bound
droplets. The transition from the superfluid to the supersolid phase is
characterized by a jump in the moment on inertia, revealing its first order
nature. In the case of elongated trapping in the plane of rotation we show that
the the moment of inertia determines the value of the frequency of the scissors
mode, which is significantly affected by the reduction of superfluidity in the
supersolid phase. The case of isotropic trapping is instead well suited to
study the formation of quantized vortices, which are shown to be characterized,
in the supersolid phase, by a sizeable deformed core, caused by the presence of
the sorrounding density peaks.
