Gyroscopic couple (C ):

Let w be angular velocity of a disk.

Let wp be angular velocity of precession (rotation of axis of spin)

Let the axis of spin be rotated by an angle dθ in time dt

L1 = Iw

L2 = Iw + Iw sin(dθ) ≈ Iw + Iw x dθ

C $= \text{Rate of change of angular momentum} \hspace{2cm} \text{(by definition)} \\ = dL/dt = (L2-L1)/dt= Iw dθ/dt$

When dθ and dt are very small,

Wp = dθ/dt

Hence,

C = I w wp