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In this paper, we report, for the first time, on the effects of two counterpropagating laser beams in a passive ring resonator to be used as a key element of an integrated optical angular velocity sensor, in order to optimize the design of the whole sensor. The ring resonator is modeled and the analytical expressions of the power transfer function for both drop- and through-port configurations are derived. At both drop and through ports, the two counterpropagating beams provide an increase of the amplitude of the transfer function, while at the through port, we observed also a mode suppression due to a physical effect similar to the Vernier effect. A parametric analysis has been carried out to optimize the sensor design. A minimum angular velocity as low as a few degrees per hour has been achieved, which is suitable for aerospace applications.