  We study the electromagnetic radiation by a fermion carrying an electric
charge $q$ embedded in a medium rotating with constant angular velocity
$\bf\Omega$ parallel or anti-parallel to an external constant magnetic field
$\bf B$. We assume that the rotation is "relatively slow"; namely, that the
angular velocity $\Omega$ is much smaller than the inverse magnetic length
$\sqrt{qB}$. In practice, such angular velocity can be extremely high. The
fermion motion is a superposition of two circular motions: one due to its rigid
rotation caused by forces exerted by the medium, another due to the external
magnetic field. We derive an exact analytical expression for the spectral rate
and the total intensity of this type of synchrotron radiation. Our numerical
calculations indicate very high sensitivity of the radiation to the angular
velocity of rotation. We show that the radiation intensity is strongly enhanced
if $q\bf B$ and $\bf \Omega$ point in the opposite directions and is suppressed
otherwise.
