Gyroscope Precession
Tip a spinning top and gravity pulls it down, yet it does not topple. Instead the whole axis swings slowly around the vertical, tracing a cone. This is precession. The reason is that a fast spin gives the top a large angular momentum pointing along its axis, and gravity, instead of tipping the axis over, can only push that arrow sideways: the axis chases the push and goes around. The faster it spins, the harder it is to push, so the precession is slower. In the leading-order limit the precession rate is Ω = M g r divided by the spin angular momentum, independent of how far it leans. The scene shows the flywheel spinning, tilted, and precessing, with gravity and the direction it drifts; the diagnostic is the precession rate against the spin rate, the curve every gyroscope, bicycle wheel, and the wobble of the Earth itself lives on.
WHAT TO TRY
- Drag the spin rate up: the flywheel spins faster and the precession visibly slows, the operating point sliding down the curve.
- Drag it down toward 20: the precession speeds up until it is no longer slow compared to the spin, where the simple formula starts to break.
- Change the tilt: the cone gets wider or narrower, but the precession rate does not change, the lean cancels out of the formula.
- Raise the mass, the arm r, or gravity: each scales the torque Mgr, so the precession speeds up in proportion (the hyperbola lifts and the operating point climbs). Drop gravity to the Moon's 1.6 and it crawls.
- Watch the gravity arrow point straight down while the axis drifts sideways, not downward: that sideways drift is the whole effect.