We study the synchrotron radiation emitted by a rigidly rotating charged
fermion in a constant magnetic field $B$ parallel to the axis of rotation. The
rigid rotation is classical and independent of the magnetic field. The angular
velocity of rotation $\mathrm{\Omega}$ is assumed to be much smaller than the inverse
magnetic length $\sqrt{qB}$ which allows us to ignore the boundary effects at
$r=1/\mathrm{\Omega}$ . We refer to such rotation as slow, even though in absolute value
it may be an extremely rapid rotation. Using the exact solution of the Dirac
equation we derived the intensity of electromagnetic radiation, its spectrum
and chirality. We demonstrate by explicit numerical calculation that the effect
of rotation on the radiation intensity increases with the particle energy.
Depending on the relative orientation of the vectors $\mathbf{\Omega}$ and $\mathbf{B}$
and the sign of the electric charge, the rotation can either strongly enhance
or strongly suppress the radiation.