$A$ body rotating with an angular speed of $600 \, rpm$ is uniformly accelerated to $1800 \, rpm$ in $10 \, s$. The number of rotations made in the process is ..... .

$A$ particle is revolving in a circular path of radius $25 \, m$ with a constant angular speed of $12 \, rev/min$. The angular acceleration of the particle is .......... $rad/s^2$.

$A$ 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 ......... $\sec$.

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 wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

$A$ body is revolving with a uniform speed $v$ in a circle of radius $r$. The tangential acceleration is