Let consider a system of n particles of masses m_{1}, m_{2} … …m_{n} situated at distances r_{1}, r_{2} … …r_{3} respectively from the axis of rotation (Figure).

Let v_{1}, v_{2}, v_{3 }… … be the linear velocities of the particles respectively, then the linear momentum of first particle = m_{1} v_{1}.

Since v_{1} = r_{1} ω; the linear momentum of first particle = **m _{1} (r_{1} ω)**

The moment of linear momentum of first particle = linear momentum x perpendicular distance

= (m_{1} r_{1} ω) x r_{1}

angular momentum of first particle = **m _{1} r_{1}^{2} ω**

Similarly,

Angular momentum of second particle = **m _{2} r_{2}^{2} ω**

Angular momentum of third particle = **m _{3} r_{3}^{3} ω** and so on.

The sum of the moment of the linear momentum of all the particles of a rotating rigid body taken together about the axis of rotation is known as the angular momentum of the rigid body.