Physics ★★☆ Moderate

🌀 Gyroscope Precession

A fast-spinning gyroscope doesn't fall — it precesses. Gravity's torque τ = r×mg rotates the angular momentum vector, making the spin axis sweep a cone at rate Ω = mgr / (I·ω). Slow the spin and watch precession speed up.

Spin ω: 20.0 rad/s
Precession Ω: 0.00 rad/s
Period T:
L = Iω:
τ = mgr·sinθ:

🔭 Physics of Precession

When gravity pulls the gyroscope's centre of mass downward, it exerts a horizontal torque τ = r × F perpendicular to both the spin axis and vertical. Instead of falling, angular momentum changes direction: dL/dt = τ, so the spin axis sweeps a cone — a phenomenon called steady precession.

Ω_prec = mgr·sinθ / (I·ω·sinθ) = mgr / (I·ω)

Key insight: precession rate Ω is inversely proportional to spin ω — a slower gyroscope precesses faster. This is why well-thrown tops stay upright, and explains the 26,000-year wobble of Earth's axis.