1Q50.50 Precession with Quality Gyro

This demo aims to highlight the fundamental equation of precession, Q = IΩω, with a high precision gyroscope mounted on a counterweight.

A small, high-precision gyroscope is set on a long, thin rod with a counterbalancing weight on the far end. The rod is supported in a small rectangular frame. The gyroscope's motor and battery pack appear nearby.

Since both the moment of inertia of the gyroscope (I) and the torque produced by the counterweight (Q) are (approximately) constant, the equation says the angular speed of the precession (Ω) is inversely proportional to the angular speed of the gyroscope’s spin (ω).

This sketch of the gyroscope and the counterbalancing mass shows: the mass M, with a constant force Fg downward and the angular speed of precession capital omega; the gyroscope with angular velocity labeled lowercase omega and a constant moment of inertia I; and an equation that reads 'the magnitude of r cross F is equal to the moment of inertia times the angular speed of precession times the angular velocity."

Thus, when the gyroscope spins faster, the precession should be slower, and when the spin is slower, the precession is faster.

There is also an option to collect data from this demonstration to corroborate the equation quantitatively: there are markings on the gyroscope, so a high-frequency strobe light will allow a student to calculate the gyroscope’s angular speed. The precession’s angular speed can be calculated simply by recording the time it takes for one full revolution of the counterweight to occur, and both the torque and the moment of inertia of the gyroscope can be measured with relative ease (or, you could assume the equation is correct and use it to calculate the moment of inertia).

Location: B2-3