Optical resonators of whispering gallery modes are dielectric axially symmetric resonators with smooth edges that support the existence of whispering gallery modes due to full internal reflection from the resonator surface. Centrifugal forces caused by the rotation of material objects can lead to their mechanical deformation. This is true for resonators of the whispering gallery modes, and when this occurs, the variation of the radius of the working section of the cavity takes place. As is known, the frequencies of whispering gallery modes are inversely proportional to the radius of the working section. Thus, under the influence of centrifugal forces, a reciprocal (the same for opposite directions of the cavity circuit bypass by light) shift of the whispering gallery modes frequencies occurs. Optical methods allow to determine this shift with high accuracy. This can be used in practice for measuring angular velocity and create a miniature angular rate sensor. However, the reciprocal nature of the shift does not allow to judge about the sign of the angular rate (clockwise or counterclockwise rotates the object). In this paper, we propose to solve this problem by applying the initial displacement of the output characteristic point (bias). The perspectives of applying both constant and alternating sign initial displacements are considered. Also, this approach should allow to increase sensitivity to low angular velocities and reduce the nonlinearity of the output characteristic.