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

The angular speed of a truck wheel is increased from $900 \, rpm$ to $2460 \, rpm$ in $26 \, s$. The number of revolutions made by the truck engine during this time is (assuming the acceleration to be uniform).

$A$ 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 . . . . . . .

If a wheel starting from rest is rotating with an angular acceleration of $\pi \ rad \ s^{-2}$,then the number of rotations made by the wheel in the first $6 \ s$ is:

$A$ grinding wheel attains a velocity of $20 \ rad/s$ in $5 \ s$ starting from rest. Find the number of revolutions made by the wheel.

$A$ flywheel at rest is to reach an angular velocity of $24 \ rad \ s^{-1}$ in $8 \ s$ with constant angular acceleration. The total angle turned through during this interval is (in $rad$)