Spinning gyroscope (bicycle wheel), force, and zero torque exerted by angular momentum

   This paper (preprint) shows the author’s analysis which unveils a problem related to the motion of a spinning gyroscope (bicycle wheel). The classical mechanics formula for torque exerted by the angular momentum of a spinning gyroscope (bicycle wheel) tells that a magnitude of the torque is zero when a gyroscope spins at a uniform (constant) angular speed because a gyroscope angular acceleration is zero. Hence, the torque exerted by a gyroscope angular momentum cannot act against a torque exerted by the Earth gravitation based on the formula. The gravitation pulls a gyroscope (bicycle wheel) down to the Earth surface. As a result, the zero torque, which is exerted by a gyroscope angular momentum, cannot prevent the gyroscope from falling from Position #1 to Position #2, see Figure 1. There appears a practical problem - impossibility to calculate a force (torque) needed to change a plane of the spin of the uniformly spinning gyroscope.