Question

Obtain formula L = I ω for the angular momentum of the rigid body.

Answer 1

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Answer 2

Answer:

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

Explanation:

The rigid body consists of a large number of particles.

Let $m_{1}, m_{2}, m_{3}$ etc., be the masses of the particles situated at distances$r_{1}, r_{2}, r_{3}$, …. etc., from the fixed axis. All the particles rotate with the same angular velocity, but rotate with different linear velocities depending on the values of ‘r’.

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

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

The angular momentum of a rigid body (L) = ∑$mr^{2} w.......(1)$

But, Σ$mr^{2$ = moment of inertia of the rigid body = I

Therefore,

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

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