# What is the expression for Angular momentum of a Rigid body rotating about an axis?

Posted in ROTATIONAL MOTION | Email This Post |A rigid body rotates about a fixed axis. The rigid body consists of a large number of particles.

Let m1, m2, m3 etc., be the masses of the particles situated at distances r1, r2, r3 , … etc., from the fixed axis. All the particles rotate with the same angular velocity, but with different linear velocities depending on the values of ‘r’.

The angular momentum of a rigid body (L) = m_{1} r_{1}^{2}ω_{ + }m_{2} r_{2}^{2}ω…

The angular momentum of a rigid body (L) = (m_{1} r_{1}^{2} + m_{2} r_{2}^{2}….) ω

The angular momentum of a rigid body (L) = Σ mr^{2}ω …………………(1)

But, Σmr^{2} = moment of inertia of the rigid body = I

Therefore,

Angular momentum of a Rigid body = I × ω……putting value of I in (1)

Angular momentum of a Rigid body = moment of inertia of the rigid body ( I) x × angular velocity (ω)

The S.I. unit for angular momentum is kgm^{2}rad/s *or* kgm^{3}/s