B M Sharma Solutions for Chapter: Rigid Body Dynamics: Part 1, Exercise 2: CONCEPT APPLICATION EXERCISE

A disc of radius $R=\frac{1}{2} \mathrm{m}$ is rolling on a plank. If the disc is moving on the plank with angular velocity $\omega =2 \mathrm{rad}/\mathrm{s}$ and speed $v_c=2 \mathrm{m}/\mathrm{s}.$ Find the speed of the plank for pure rolling.

A uniform disc of radius $R$ rolls perfectly over two horizontal plank $A$ and $B$ moving with velocities $v$ and $2 v,$ respectively. Find the
(a) velocity of $\mathrm{CM}$ of the disc.
(b) angular velocity of the disc

A cotton reel rolls without sliding such that the point $P$ of the string has velocity $v .$ Find the:
(i) velocity of its centre $C$
(ii) angular velocity of the cotton reel.

Two wheels $1$ and $2$ of radii $r_1$ and $r_2$ are connected by a belt. If the belt does not slide over the wheels, find the:

(i) speed of a point on the belt.
(ii) angular velocity of the wheel $2.$
(iii) acceleration of $P$ relative to $Q.$

A cylinder of radius $r$ rolls perfectly with a speed $v$ on a concave surface of radius $R.$ Find the acceleration of the bottom of the rolling body.

Shown in the figure is a rod which moves with $v=2{ \mathrm{ms}}^{-1}$ and rotates with $\omega =2\pi$ ${\mathrm{rads}}^{-1}.$ Find the instantaneous axis of rotation.

Find the position of instantaneous centre of rotation and angular velocity of the disc in the following cases as shown. Radius of disc is $R$ in each case.

A rotating disc moves in the positive direction of $x$ -axis as shown. Find the equation $y\left(x\right)$ describing the position of the instantaneous axis of rotation if at the initial moment the centre $C$ of the disc was located at origin after which

(a) it moved with constant acceleration $\text{'}a\text{'}$ (initial velocity zero) while the disc rotating anticlockwise with constant angular velocity $\omega .$
(b) it moved with constant velocity $v$ while the disc started rotating anticlockwise with a constant angular acceleration $\alpha$ (with initial angular velocity zero).