gyroscopic motion

Gyroscopic motion is the counterintuitive behavior of a fast-spinning body when you try to tip it: instead of falling in the direction you push, its axis swings off sideways, at right angles to the push. Push down on the front of a spinning bicycle wheel held by an axle and it turns left or right, not down. This sideways dodge is the hallmark of gyroscopic motion, and it is why a spinning top does not simply topple.

It follows directly from the rotational Newton's law, torque = rate of change of angular momentum, N = dL/dt. For a rapidly spinning body L points along the spin axis and is large. A torque N perpendicular to L cannot change the length of L, only its direction, so L (and the axis) rotates toward the torque -- perpendicular to the applied force. This is steady precession, and for a heavy top of mass M with its center of gravity a distance r from the pivot, the precession rate is Omega = M g r / (I_3 omega_3): the faster it spins, the slower and more stable the precession. The related resistance to being tilted at all is called gyroscopic rigidity.

Gyroscopic motion is everywhere once you see it: a spinning top or gyroscope that refuses to fall, a bicycle or motorcycle that is easier to balance at speed, a rifled bullet or a thrown football holding its aim, and the gyrocompass and inertial navigation systems that keep aircraft, ships, and spacecraft oriented without any external reference. The same physics also produces gyroscopic reaction forces that stress the bearings of turbine rotors and ship engines when the vehicle turns.