  Light interaction with rotating nanostructures gives rise to phenemona as
varied as optical torques and quantum friction. Here we reveal that circular
dichroism of rotating optically-isotropic particles has an unexpectedly strong
dependence on their internal geometry. In particular, nanorings and nanocrosses
exhibit a splitting of $2\Omega$ in the particle optical resonances, while
compact particles display weak circular dichroism at low rotation frequency
$\Omega$, but a strong circular dichroism at high $\Omega$. We base our
findings on a quantum-mechanical description of the polarizability of rotating
particles, which has not been rigorously addressed so far. Specifically, we use
the random-phase approximation and populate the particle electronic states
according to the principle that they are thermally equilibrated in the rotating
frame. We further provide insight into the rotational superradience effect and
the ensuing optical gain, originating in population inversion as regarded from
the lab frame, in which the particle is out of equilibrium. Surprisingly, we
find the optical frequency cutoff for superradiance to deviate from the
rotation frequency $\Omega$. Our results unveil a rich, unexplored
phenomenology of light interaction with rotating objects.
