In the $P^{\text{th}}$ second,a particle describes an angular displacement of $\beta \text{ rad}$. If it starts from rest,the angular acceleration is:

$A$ particle moves along a circle of radius $\left( \frac{20}{\pi} \right) \, m$ with constant tangential acceleration. If the velocity of the particle is $80 \, m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is

$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?

If the equation for the angular displacement of a particle moving on a circular path is given by $\theta = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2 \ s$ from its start is ......... $rad/s$.

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)

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 :