If the Moment of inertia, rotational kinetic energy, and angular momentum are given by M, K, and L, then:

Concept:

Angular momentum: The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. Angular momentum also obeys the law of conservation of momentum i.e. angular momentum before and after is conserved.

Angular momentum, L = M × ω

Rotational kinetic energy: For a given fixed axis of rotation, the rotational kinetic energy is given by:

\(KE = {1\over 2 }* M\omega^2\)

Where M is the moment of inertia, ω is the angular velocity.

Calculation:

Angular momentum, L = M × ω.

Rotational Kinetic Energy K = \(= {1\over 2 }* M\omega^2\) ⇒ \(\omega = \sqrt{2K \over M}\)

Therefore, \(L = M * \sqrt{2K \over M} = \sqrt{2MK}~\)