B M Sharma Solutions for Chapter: Rigid Body Dynamics: Part 1, Exercise 1: CONCEPT APPLICATION EXERCISE

A $100 \mathrm{cm}$ rod is moving on a horizontal surface. At an instant, when it is parallel to the $x$ -axis its ends $A$ and $B$ have velocities $20 \mathrm{cm}/\mathrm{s}$ and $30 \mathrm{cm}/\mathrm{s}$ as shown in the figure. Find its angular velocity of the rod.

A ball of radius $R=20 \mathrm{cm}$ is moving with combined translation and rotation. If the velocity of centre of mass of ball is $v_C=10 \mathrm{m}/\mathrm{s}$ and spins with an angular speed $\omega =10 \mathrm{rad}/\mathrm{s},$ find the speeds of $P$ and $Q.$

A rod of length $l$ has a velocity $v$ at $P.$ Find the velocity at $Q$ and the angular velocity of the rod.

If the ends of a rod of length $l$ have velocities ${\overrightarrow{v}}_A$ and ${\overrightarrow{v}}_B,$ find the velocity of mid-point of the rod.

A flat rigid body is moving in $x-y$ plane on a table. The body lies in the $x-y$ plane. At an instant it was found that some of the velocity components of its three particles $A,$ $B$ and $C$ were $v_{Ax}=4 \mathrm{m}/\mathrm{s}, v_{Bx}=3 \mathrm{m}/\mathrm{s}$ and $v_{cy}=-2 \mathrm{m}/\mathrm{s}$ respectively. At the instant the three particles $A, B$ and $C$ were located at $(0, 0), (3, 4)$ and $(4, 3)$ (all in metre) respectively in a co-ordinate system attached to the table.

(a) Find the velocity of $A, B$ and $C.$
(b) Find the angular velocity of the body.

The rod of length $l=1 \mathrm{m}$ rotates with an angular velocity $\omega =2 \mathrm{rad} {\mathrm{s}}^{-1}$ and the point $P$ moves with velocity $v=1 \mathrm{m}{ \mathrm{s}}^{-1}$ and acceleration $a=1 \mathrm{m}{ \mathrm{s}}^{-2}.$ Find the velocity and acceleration of $Q.$

The angular velocity and angular acceleration of the pivoted rod are given as $\omega$ and $\alpha$ respectively. Find the $x$ and $y$ components of acceleration of $B.$