[UPSC IFoS 2021] Rigid Body Dynamics (Q189, 8M)

(i) Define the angular velocity \omega of a rigid body rotating about some axis.

(ii) Then derive the relation \vec{v} = \vec{\omega} \times \vec{r} for the velocity of a point in the body with position vector \vec{r} relative to an origin on the axis. Draw a diagram explaining all the vectors.