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

Derive an expression for kinetic energy in rotation and establish the

1.	Derive an expression for kinetic energy in rotation and establish the relation between rotational kinetic energy and angular momentum.
Answer» Solution :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= 1/21 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^2omega ^2)/(I )= ।/2(( omega )^2)/(I)` ` KE = (L^2)/( 2l)`