Find $\mathrm{K}\mathrm{E}$ of the rotating composite rod comprising two rods of mass $m$ and $2m$ and each of length $l=1m$. Assume $\omega =10$ rad $s^{-1}$ and $m=1\mathrm{k}\mathrm{g}$ .

A uniform rod smoothly pivoted at one of its ends is released from rest. If it swings in vertical plane, find the, maximum speed of the end $P$ of
the rod.

A rigid body is made of three identical uniform thin rods each of length $L$ fastened together in the form of letter $H.$The body is free to rotate about a fixed horizontal axis $\mathrm{AB}$that passes through one of the legs of the$H.$ The body is allowed to fall from rest from a position in which the plane of $H$ is horizontal. What is the angular speed of the body, when the plane of $H$ is vertical. 

A uniform spherical shell of mass $M$ and radius $R$ rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of the shell, over a pulley of rotational inertia $I$ and radius $r$ and is attached to a small object of mass $m$ that is otherwise free to fall under the influence of gravity. There is no friction of pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance $h$ from rest? Use work-energy considerations.

A uniform rod of length $l$ is released from rest such that it rotates about a smooth pivot. Find the angular speed of the rod when it becomes vertical.

A uniform disc of mass $m$ is fitted (pivoted smoothly) with a rod of mass $m/2$ . If the bottom of the rod is pulled with a velocity $v$ , it moves without changing its angle of orientation and the disc rolls without sliding. Find the kinetic energy of the system $(\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{}+\mathrm{}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c})$ .