Mechanical Engineering
Gyroscopic Torque
Analyze the mechanics of gyroscopic torque. Change the mass and radius of the spinning disc, the spin velocity, and the precession rate to compute the magnitude of the reactive torque vector.
Stability
Low Reaction
Based on torque output
Momentum L
17.67 N·m·s
Spin axis capacity
Status
Locked
Vector cross active
Parameters
Application Preset
Precession Sweep
Governing Equations
Moment of Inertia
I = 0.5 * m * r²
Spin Velocity
ω = (RPM * 2 * π) / 60
Gyroscopic Torque
T = I * ω * ω_p
Vector cross-product
T_vector = ω_vector × (I * ω_spin_vector)
Gyroscopic torque is directly proportional to the moment of inertia, the spin velocity, and the precession rate.
The reactive torque vector always acts perpendicular to both the spin axis and the precession axis.
Vector Cross-Product Diagram
Moment of Inertia (I)
0.0562kg·m²
Spin Vel. (ω)
314.2rad/s
Angular Momentum
17.67N·m·s
Reactive Torque
35.3N·m
Gyroscopic Torque & Momentum vs Spin Speed
Simulation Data
| Spin Speed (RPM) | Reactive Torque (N·m) | Momentum (kg·m²/s) |
|---|---|---|
| 500 RPM | 5.89 | 2.945 |
| 1450 RPM | 17.08 | 8.541 |
| 2400 RPM | 28.27 | 14.137 |
| 3350 RPM | 39.47 | 19.733 |
| 4300 RPM | 50.66 | 25.329 |
| 5250 RPM | 61.85 | 30.925 |
| 6200 RPM | 73.04 | 36.521 |
| 7150 RPM | 84.23 | 42.117 |
| 8100 RPM | 95.43 | 47.713 |
| 9050 RPM | 106.62 | 53.309 |
| 10000 RPM | 117.81 | 58.905 |