$A$ car wheel rotates at $1200$ revolutions per minute. On pressing the accelerator,it rotates at $4500$ revolutions per minute in $10 \ s$. The angular acceleration of the wheel is ...

$A$ particle is revolving in a circle of radius $2 \ m$ with angular velocity $\omega = t^2 - 4t + 8 \ rad/s$. The time when the speed of the particle becomes $8 \ m/s$ is ......... $\sec$.

$A$ particle moves along a circle of radius $r$ with constant tangential acceleration. If the velocity of the particle is $v$ at the end of the second revolution after the motion has started,then the tangential acceleration is

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with angular acceleration $\alpha$. The magnitude of the average velocity in the time it completes the small angular displacement $\theta$ is

The relative angular speed of the hour hand and minute hand of a clock is (in $rad/s$):

$A$ 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 . . . . . . .