  We study theoretically and numerically the effect of rotation on resonant
frequencies of microcavities in a rotating frame of reference. Cavity rotation
causes the shifts of the resonant frequencies proportional to the rotation rate
if it is larger than a certain value. Below the value, a region of rotation
rate exists where there is no resulting the frequency shifts proportional to
the rotation rate. We show that designing cavity symmetry as $C_{nv}$ ($n\ge
3$) can eliminate this region.
