  We study theoretically the polarization dynamics in a ring-shape bosonic
condensate of exciton-polaritons confined in a rotating trap. The interplay
between the rotating potential and TE-TM splitting of polariton modes offers a
tool of control over the spin state and the angular momentum of the condensate.
Specific selection rules describing the coupling of pseudospin and angular
momentum are formulated. The resonant coupling between states having linear and
circular polarizations leads to the polarization beats. The effect may be seen
as a polariton analogy to the electronic magnetic resonance in the presence of
constant and rotating magnetic fields. Remarkably, spin beats are induced by a
purely mechanical rotation of the condensate.
