Gyroscopic exercise tool

The device consists of a tennis ball-sized plastic or metal shell surrounding a free-spinning mass, with an inner heavy core, which can be spun by a short rip string or using a self-start mechanism by means of rewinding it against a spring to give it potential energy.

Once the gyroscope inside is going fast enough, the person holding the device can accelerate the spinning mass to high rotation rates by moving the wrist in a circular motion.

To increase the angular velocity of the ball, the sides of the groove exert forces on the ends of the axle.

The user can apply a torque on the ball by tilting the shell in any direction except in the plane of the groove or around an axis aligned with the axle.

The direction and speed of the shift can be found from the formula for the precession of a gyroscope: the applied torque is equal to the cross product of the angular velocity of precession and the angular momentum of the spinning mass.

The direction of the torque does not matter, as long as it is perpendicular to the plane of rotation of the ball.

The friction of the ring increases on the side opposite to the plane of rotation.

The only restriction to this process is that the relative speed of the surface of the axle and the side of the groove due to precession,

, must exceed the relative speed due to the rotation of the spinning mass,

, where I is the moment of inertia of the spinning mass, and ω is its angular velocity.

Since angular acceleration will occur regardless of the direction of the applied torque, as long as it is large enough, the device will function without any fine-tuning of the driving motion.

These factors allow beginners to learn to speed up the rotation after only a few minutes of practice.

is the kinetic coefficient of friction, it can be shown that the torque spinning up the mass is a factor of