Inertial Forces and Torques Acting on a Spinning Annulus

The many publications related to the gyroscope theory consider the action of the inertial torques on the spinning disc. All of them have simplified expressions for the inertial torques and mathematical models of the gyroscope motions do not validate by practice. Recent research in the theory of the gyroscopic effects for rotating objects solved problems with mathematical models for interrelated inertial torques generated by the spinning disc, bar, and ring and their motions. Practitioners of engineering designed gyroscopic devices with spinning rotors whose geometry can be an annulus or similar designs. Such spinning annulus generates inertial torques whose expressions differ from the disc bar and ring and hence another mathematical model describes the motions of the gyroscopic devices. The value of gyroscopic effects of the devices with spinning annulus is bigger than for the disc-type rotor. This manuscript presents mathematical models for the inertial torques generated by the spinning annulus and the interrelated angular velocities of the gyroscopic devices about axes of rotation.