The angular speed of the wheel of a vehicle is increased from $360 \; rpm$ to $1200 \; rpm$ in $14 \; s$. Its angular acceleration is,

$A$ car is moving at a speed of $72 \, km/h$. The diameter of its wheels is $0.25 \, m$. If the wheels stop after completing $20$ revolutions upon applying brakes,the angular retardation produced by the brakes is ....... $rad/s^2$. (in $.5$)

$A$ wheel initially at rest,begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first $2 \ s$ and a further angle $\theta_2$ in the next $2 \ s$,the ratio $\theta_1 : \theta_2$ is

$A$ wheel of radius $0.20 \ m$ starts from rest and rotates with an angular acceleration of $1 \ rad/s^2$. What will be the centripetal acceleration of a point on its circumference when it has rotated through an angle of $90^o$?

$A$ particle is rotating in a circular path and at any instant its motion can be described as $\theta = \frac{5t^4}{40} - \frac{t^3}{3}$. The angular acceleration of the particle after $10 \text{ s}$ is . . . . . . $\text{rad/s}^2$.

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1 t + \theta_2 t^2$. Then the angular acceleration of the body is