  We demonstrate in open microcavities with broken chiral symmetry,
quasi-degenerate pairs of co-propagating modes in a non-rotating cavity evolve
to counter-propagating modes with rotation. The emission patterns change
dramatically by rotation, due to distinct output directions of CW and CCW
waves. By tuning the degree of spatial chirality, we maximize the sensitivity
of microcavity emission to rotation. The rotation-induced change of emission is
orders of magnitude larger than the Sagnac effect, pointing to a promising
direction for ultrasmall optical gyroscopes.
