Anomalous dispersion enhancement physical mechanism for Sagnac effect is described by special relativity derivation, and three kinds of definitions of minimum detectable angular rate of resonance optical gyroscope (ROG) are compared and the relations among them are investigated. The effect of linewidth broadening induced by anomalous dispersion on the sensitivity of ROG is discussed in this paper. Material dispersion-broadened resonance linewidth deteriorates the performance of a passive ROG and dispersion enhancement effect, while the sensitivity of a structural dispersion ROG is enhanced by two orders of magnitude even considering the dispersion-broadened resonance linewidth.