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 $B.$

A cylinder of radius $5 \mathrm{m}$ rolls on a horizontal surface. If the velocity of its center is $25 \mathrm{m}/\mathrm{s}.$ Find its angular velocity and velocity of the point $A.$

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.