  We investigate spectral properties of the operator describing a quantum
particle confined to a planar domain $\Omega$ rotating around a fixed point
with an angular velocity $\omega$ and demonstrate several properties of its
principal eigenvalue $\lambda_1^\omega$. We show that as a function of rotating
center position it attains a unique maximum and has no other extrema provided
the said position is unrestricted. Furthermore, we show that as a function
$\omega$, the eigenvalue attains a maximum at $\omega=0$, unique unless
$\Omega$ has a full rotational symmetry. Finally, we present an upper bound to
the difference $\lambda_{1,\Omega}^\omega - \lambda_{1,B}^\omega$ where the
last named eigenvalue corresponds to a disk of the same area as $\Omega$.
