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

$A$ 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 $90^o$?

$A$ wheel undergoes a constant angular acceleration from time $t=0$ to $t=20 \ s$ and thereafter angular acceleration is zero. If angular velocity at $t=2 \ s$ is found to be $5 \ rad/s$, then the number of revolutions made by the wheel in the time interval $t=0 \ s$ to $t=50 \ s$ is

$A$ 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 direction of angular acceleration of a body moving in a circle in the plane of the paper is

$A$ particle performing $U.C.M.$ of radius $\frac{\pi}{2} \ m$ makes $x$ revolutions in time $t$. Its tangential velocity is