Gyroscopic Precession & Angular Momentum

Mechanical Engineering

How It Works

A gyroscope consists of a rapidly spinning rotor possessing high spin angular momentum (L⃗ = I·ω_s). When an external gravitational torque (τ⃗ = r⃗ × W⃗) is applied perpendicular to the spin axis, the system resists pitching downward; instead, the torque induces a steady gyroscopic precession angular velocity (Ω_p) perpendicular to both the torque and spin vectors.

Governing Equation
τ⃗ = Ω⃗_p × L⃗ , Ω_p = τ / (I · ω_s) = (m · g · r) / (I · ω_s) , L = I · ω_s