Why can a spinning gyroscope precess instead of tipping straight down?

A spinning wheel supported at one end of its axle can sweep sideways rather than simply tip straight down. This motion is precession: the spin axis itself turns around another axis. Gravity is still acting, and the support still carries the assembly; spinning has not switched either force off.

The rotor’s spin angular momentum is approximately L = Iω along its axle, where I is moment of inertia and ω is spin angular speed. Gravity acting at the offset center of mass creates a torque about the support. For the horizontal axle shown, that torque is perpendicular to the spin angular momentum.

Because torque equals the rate of change of angular momentum, a perpendicular torque changes its direction. In the slow, steady-precession approximation, the axle sweeps around the vertical while the spin magnitude changes little. Its precession rate is Ω = mgr/(Iω), with r measured from the support to the center of mass.

The supplied example uses m = 1 kilogram, g = 10 meters per second squared, r = 0.1 meter, I = 0.02 kilogram meter squared and ω = 100 radians per second. Thus L is 2 kilogram meters squared per second, torque is 1 newton meter and Ω is 0.5 radian per second.

Faster spin therefore gives slower precession for these same inputs. This is not a general promise that any spinning object stays upright. Friction, startup motion, changing tilt and nutation, a bobbing of the axis, require a fuller analysis than the stated steady approximation.