Derive an expression for kinetic energy in rotation and establish the relation between rotational kinetic energy and angular momentum.

Explanation

Let a rigid body of moment of inertia I rotate with angular velocity`omega `
The angular momentum of a rigid body is,` L= I omega `
The rotational kin e tic energy of the rigid body is,` KE= 1/2 1 omega^2`
By multiplying the numerator and denominator of the above equation with I, we get a relation between L and KE as,
` Ke = 1/2 (I^2 omega ^2)/(I ) = ।/2 (( omega )^2)/(I)`
` KE = (L^2)/( 2l)`