Explanation

(d) The angular momentum is measure for the amount of torque that has been applied over time the object. For a particle with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as
$L = I\omega$ …(i)
Where $I$ is moment of inertia of particle and $\omega$ the angular velocity.
Also, $K = \frac{1}{2}I\omega^{2}$ …(ii)
Where $K$ is kinetic energy of rotation.
From Eqs. (i) and (ii), we get
$L = \frac{2K}{\omega^{2}}\omega = \frac{2K}{\omega}$
$L^{'} = \frac{2\left( \frac{K}{2} \right)}{2\omega} = \frac{1}{4}\ \left( \frac{2K}{\omega} \right) = \frac{L}{4}$
Note In a closed system angular momentum is constant.