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We show that the knowledge of the time dependent response of a trapped gas,subject to a sudden rotation of a confining harmonic potential, allows for thedetermination of the moment of inertia of dipolar supersolid configurations.While in the presence of one-dimensional arrays of droplets the frequency ofthe resulting scissors oscillation provides accurate access to the value of themoment of inertia, two-dimensional like configurations are characterized by amulti-frequency structure in the rotating signal, reflecting the presence ofsignificant rigid body components in the rotational motion. Using the formalismof response function theory and simulations based on the so-called extendedtime dependent Gross-Pitaevskii equation, we point out the crucial role playedby the low frequency components in the determination of the moment of inertiaand of its deviations from the irrotational value. We also propose a protocolbased on the stationary rotation of the trap, followed by its sudden stop,which might provide a promising alternative to the experimental evaluation ofthe moment of inertia.

Moment of Inertia and Dynamical Rotational Response of a Supersolid Dipolar Gas