The notion of the rotational frequency shift, an analog of the Doppler
shift, is introduced. This new frequency shift occurs for atomic syst
ems that lack rotational invariance, but have stationary states in a r
otating frame. The rotational frequency shift is given by the scalar p
roduct of the angular velocity and the angular momentum of the emitted
photon in full analogy with the standard Doppler shift which is given
by the scalar product of the linear velocity of the source and the li
near momentum of the photon. The rotational frequency shift can be obs
erved only in a Mossbauer-like regime when the angular recoil is negli
gible.