Define angular momentum. Derive an expression for it in vector form.

Angular momentum of a rotating body is measure of the quantity of angular motion contained in the body. It is also called moment of linear momentum of the body.

Due to rotational inertia possessed by the body about the axis of rotation, the rotating body cannot change its angular momentum itself. The torque produced by applied force on the rotating body changes its angular momentum and rate of change of angular momentum is equal to torque on the body, i.e.

Let us consider a body moving in XY plane. The torque on the body revolving in XY plane is,

τ_z =xF_y-yF_x ...(1)

Let p_x and v_x be the X-component and p_y and v_y be the Y component of linear momentum and velocity of body in XY plane respectively.