  We describe a resonator based optical gyroscope whose sensitivity for
measuring absolute rotation is enhanced via use of the anomalous dispersion
characteristic of superluminal light propagation. The enhancement is given by
the inverse of the group index, saturating to a bound determined by the group
velocity dispersion. We also show how the offsetting effect of the concomitant
broadening of the resonator linewidth may be circumvented by using an active
cavity. For realistic conditions, the enhancement factor is as high as 106. We
also show how normal dispersion used for slow light can enhance relative
rotation sensing in a specially designed Sagnac interferometer, with the
enhancement given by the slowing factor
