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.

Let us consider a particle moving along the curve PQ under the influence of a force  let a any instant r, the particle be at A and its position vector is 

where F_ϕ is transverse component of force. Therefore torque is equal to product of radial distance and transverse component of force.

Also x = τ Fsin ϕ = F(rsin ϕ)

= Fd

Therefore, torque is equal to product magnitude of force and perpendicular distance of line of action of force from the axis of rotation.

When the size of a body is small, the centre of mass and centre of gravity coincide. 

If sin θ = 0 or r = 0

then, θ= 0°, 180°

That is, Torque = 0.