A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown. $C$ is the pivot, $O$ the centre of the circle in which the pendulum bob moves and $\omega$ the constant angular velocity of the bob.

In the above problem if $\overrightarrow{L}$ is the angular momentum about the axis $CO,$ then, 

A circular wooden loop of mass $m$ and radius $R$ rests flat on a horizontal frictionless surface. A bullet, also of mass $m,$ and moving with a velocity $V,$ strikes the loop and gets embedded in it. The thickness of the loop is much smaller than $R.$ The angular velocity with which the system rotates just after the bullet strikes the loop is

A solid sphere rolls on an inclined plane without slipping. The ratio of rotational energy and total energy is