B M Sharma Solutions for Chapter: Rigid Body Dynamics: Part 2, Exercise 5: CONCEPT APPLICATION EXERCISE

A rod of mass $m$ spins with an angular speed $\omega =\sqrt{g/l}$ , Find its

(a) kinetic energy of rotation.
(b) kinetic energy of translation
(c) total kinetic energy.

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 rod of mass $m$ and length $l$ is kept vertical with the lower end clamped. It is slightly pushed to let it fall down under gravity. Find its angular speed when the rod is passing through its lowest position. Neglect any friction at the clamp. What will be the linear speed of the free end at this instant?

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 solid uniform disc of mass $m$ and radius $R$ is pivoted about a horizontal axis through its centre and a small body of mass $m$ is attached to the rim of the disk. If the disc is released from rest with the small body, initially at the same level as the centre, find the angular velocity when the small body reaches the lowest point of the disk.

A copper ball of mass $m=1 \mathrm{k}\mathrm{g}$ with a radius of $r=10 \mathrm{c}\mathrm{m}$ rotates with angular velocity $\mathrm{\omega }=2 \mathrm{rad} {\mathrm{s}}^{-1}$ about an axis passing through its centre. What work should be performed to increase the angular velocity of rotation of the ball two-fold?

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 $(\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{}+\mathrm{}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c})$ .

The steel balls $A$ and $B$ have a mass of $500 \mathrm{g}$ each and are rotating about the vertical axis with an angular velocity of $4 \mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{-1}$ at a distance of $15 \mathrm{c}\mathrm{m}$ from the axis. Collar $C$ is now forced down until the balls are at a distance of $5 \mathrm{cm}$ from the axis. How much work must be done to move the collar down?