The latest studies of gyroscopic properties show their physics are compound in origin. Inertial torques acting on the spinning body contain eight interacted components operating by the centrifugal, common inertial, Coriolis forces, and the change in the angular momentum that entailed by the ratio of the angular velocities of the rotating bodies around their axes. These system of inertial torques and the ratio of the angular velocities construct the fundamentals of gyroscope theory. Rotating objects in engineering constitute a vast group of machine components of different forms (disc, cylinder, ring, sphere, cone, paraboloid, propeller, etc.). The movable rotating parts manifest the gyroscopic phenomena, which dynamics remain not adequately explained. The motions of the rotating components of different mechanisms are described analytically by the action of their center mass. Such models do not well match with practice tests and do not satisfy industrial requirements. Researchers did not examine the action of the distributed rotating masses that create several inertial forces. The new studies have shown the origin of gyroscope phenomena are compound. Gyroscopic manifestations are a result of the activity of the interacted inertial torques carry out by the rotating mass of bodies. These inertial torques are based on the activity of the centrifugal, common inertial, and Coriolis forces and the change in the angular momentum. The ratio of the angular velocities of the rotating body around the axes of motions is linked to all inertial torques. The pointed inertial torques and the ratio of the angular velocities construct the basis of gyroscopic effects. The method for formulating of inertial torques created by masses of rotating bodies is applicable to any object. It can be axial symmetric as a spinning disc, cylinder, ring, cone, spheres, paraboloid, propeller, etc., and nonsymmetrical rotating objects. This work contains the mathematical models and ratio of the angular velocities of the spinning disc that examined by tests. The new analytical formulation for the gyroscope phenomena solves all gyroscopic problems and discovers new approaches in classical mechanics.
