Various external and inertial torques around its axes of motion affect the real rotating object. The frictional torques on the supports of the rotating object are part of the external load. The external loads alter the properties of the gyroscope, which can be expressed using mathematical models. The frictional forces on the supports increase the angular velocities of gyroscope motions around the rotation axes. The external torque, acting toward precession, causes the gyroscope to turn. Initially, these gyroscopic effects may seem inconsistent with the known principles of mechanics. This chapter discusses mathematical models for the motions of a gyroscope with single-sided support, considering the effects of frictional forces and two load torques acting around two of the gyroscope's axes, resulting in an “anti-gravity” effect. The principles of classical mechanics describe the physics of these gyroscopic effects. The mathematical model for the gyroscope motions with the action of frictional forces and two load torques was practically tested and validated on the laboratory stand of the Super Precision Gyroscope at “Brightfusion LTD”. The theoretical calculations perfectly matched the test results.