Dynamics & Robotics
Gyroscopic Precession
Interact with parameters governing gyroscopic precession. Adjust rotor mass, radius, speed, and shaft leverage to witness how torque and angular momentum govern the precession rate.
Rotor Type
Solid Cylinder
I = 0.5 * m * R²
Gravity Force
39.2 N
Downward force
Status
Ready
Simulation stable
Parameters
Rotor Preset
Precession Sweep
Governing Equations
Moment of Inertia
I = 0.5 * m * R²
Angular Momentum
L = I * ω
Gravitational Torque
τ = m * g * r
Precession Rate
Ω_p = τ / L = (m * g * r) / (I * ω)
Higher spin speeds (ω) increase angular momentum (L), which stabilizes the gyroscope and reduces the precession rate.
Increasing shaft length (r) increases gravity torque, resulting in faster precession.
3D Vector Diagram
Moment of Inertia (I)
0.0648kg·m²
Angular Momentum (L)
10.18kg·m²/s
Gravitational Torque
9.81N·m
Precession Rate
9.20RPM
Precession Rate vs Spin Speed
Simulation Data
| Spin Speed (RPM) | Precession (RPM) | Momentum (kg·m²/s) |
|---|---|---|
| 500 RPM | 27.61 | 3.393 |
| 1450 RPM | 9.52 | 9.839 |
| 2400 RPM | 5.75 | 16.286 |
| 3350 RPM | 4.12 | 22.733 |
| 4300 RPM | 3.21 | 29.179 |
| 5250 RPM | 2.63 | 35.626 |
| 6200 RPM | 2.23 | 42.072 |
| 7150 RPM | 1.93 | 48.519 |
| 8100 RPM | 1.70 | 54.965 |
| 9050 RPM | 1.52 | 61.412 |
| 10000 RPM | 1.38 | 67.858 |