Question

Obtain an expression for the angular momentum of a body rotating with uniform

angular velocity.​

Answer 1

Explanation:

L = IW

WHERE L = ANGULAR MOMENTUM

I = MOMENT OF INERTIA

W = OMEGA

Answer 2

To derive:

Express for angular momentum of a body rotating with uniform angular velocity.

Derivation:

Angular momentum is defined as the moment of linear momentum.

Let angular momentum be L.

$\therefore \: L = r \times p$

$\implies\: L = r \times (mv)$

$\implies\: L = \dfrac{m \times v \times {r}^{2} }{r} \: \: \: \: . \: . \: .(multiply \: and \: divide \: with \: r)$

$\implies\: L = m {r}^{2} \times \dfrac{v}{r}$

$\implies\: L = m {r}^{2} \times \omega$

$\implies\: L = I \times \omega$

So , angular momentum is represented as:

$\boxed{ \bold{\: L = I \times \omega}}$