The angular displacement of a body performing circular motion is given by $\theta = 5 \sin \frac{\pi t}{6}$. The angular velocity of the body at $t = 3 \ s$ will be $\left[\sin \frac{\pi}{2} = 1, \cos \frac{\pi}{2} = 0\right]$.

$A$ wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2 \text{ s}$ it rotates through an angle $\theta_1$ and in the next $2 \text{ s}$ it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is . . . . . . .

The angular acceleration of a body, moving along the circumference of a circle, is :

$A$ wheel of radius $30 \ cm$ is driven by a belt. Its initial angular speed is $2 \ rev/s$. Starting at this speed,it comes to rest after a length of $25 \ m$ of the belt has passed over the wheel. The angular deceleration of the wheel is ....... $rad \ s^{-2}$.

$A$ disc,initially at rest,is rotated about its axis with a uniform angular acceleration. In the first $2 \ s$,it rotates through an angle $\theta$. In the next $2 \ s$,the disc will rotate through an angle:

$A$ racing car is travelling along a track at a constant speed of $40\ m/s$. $A$ $T.V.$ cameraman is recording the event from a distance of $30\ m$ directly away from the track as shown in the figure. In order to keep the car under view in the position shown,the angular speed with which the camera should be rotated is ........ $rad/s$.