Worked example - gyroscope precession rate. A toy gyroscope: M = 0.1 kg, centre of mass l = 0.03 m from pivot, spin omega3 = 100 rad/s, I3 = 2 x 10^-5 kg.m^2. Step 1: spin angular momentum p_psi = I3 omega3 = 2 x 10^-3 J.s. Step 2: fast-top precession Omega_pr = M g l/p_psi = (0.1 x 9.8 x 0.03)/(2 x 10^-3) = 14.7 rad/s ~ 2.3 revolutions per second. Step 3: sanity - doubling the spin halves the precession rate (7.35 rad/s); the gyroscope 'fights' gravity more strongly when spinning faster. Nutation frequency ~ p_psi/I1 is much higher (hundreds of rad/s), appearing as a fine tremor on the slow precession circle.