Gyroscope Precession Calculator
Enter the rotor mass properties and spin rate to predict the slow precession motion that balances gravitational torque, plus the time for one full wobble of the axis.
How the precession math is derived
A spinning gyroscope resists tipping because its angular momentum vector reacts to external torque. The gravitational torque on the rotor is , where is the mass, is gravity, and is the lever arm to the center of mass. The rotor’s angular momentum is , with as the moment of inertia and the spin rate in rad/s. Precession arises because the torque changes the direction of at the rate .
Substituting the expressions gives , which the calculator converts into degrees per second and the time for one full precession cycle . The tilt angle helps estimate the lateral displacement of the spin axis per cycle, making it easier to anticipate clearance needs for gimbals or reaction wheels.
Example precession scenarios
| Scenario | Mass (kg) | Lever arm (m) | Spin rate (RPM) | Precession period (s) |
|---|---|---|---|---|
| Spinning top on table | 0.35 | 0.04 | 5200 | 22.8 |
| Reaction wheel on satellite test rig | 3.2 | 0.18 | 4200 | 91.4 |
| Heavy flywheel balancing demo | 12.0 | 0.25 | 3200 | 158.7 |
Plan the rest of your stabilization test
Combine these precession predictions with the Robot Arm Torque Calculator, Torsional Pendulum Period Calculator, and Magnetic Field Energy Density Calculator to ensure gimbals, test stands, and magnetic dampers can handle the loads. Knowing the precession period makes it easier to schedule telemetry sampling and video capture for lab demonstrations or outreach events.