Derive the relation between rotational KE 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 rotationakl kinetic energy of the rigid body is `KE=1/2 I 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=1/2 ((Iomega)^(2))/I`
`KE=(L^(2))/(2I)`