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,
τz =xFy-yFx ...(1)
Let px and vx be the X-component and py and vy be the Y component of linear momentum and velocity of body in XY plane respectively.
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.
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 Fϕ 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.