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

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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) = m1 r12ωm2 r22ω…
The angular momentum of a rigid body (L) = (m1 r12 + m2 r22….) ω

The angular momentum of a rigid body (L) = Σ mr2ω …………………(1)

But, Σmr2 = 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 kgm2rad/s or kgm3/s

 

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