$A$ wheel is at rest. Its angular velocity increases uniformly and becomes $60 \ rad/sec$ after $5 \ sec$. The total angular displacement is ........ $rad$.

$A$ 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 . . . . . . $\text{rad/s}^2$.

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

$A$ 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

The angular speed of a flywheel is increased from $600 \text{ rpm}$ to $1200 \text{ rpm}$ in $10 \text{ s}$. The number of revolutions completed by the flywheel during this time is :

$A$ wheel has an angular acceleration of $3.0\, rad/s^2$ and an initial angular speed of $2.00\, rad/s$. In a time of $2\, s$,it has rotated through an angle (in radians) of: