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:

$A$ wheel rotates with a constant acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions it makes in the first ten seconds is:

The angular speed of a flywheel moving with uniform angular acceleration changes from $1200\,rpm$ to $3120\,rpm$ in $16\,s$. The angular acceleration in $rad/s^{2}$ is: (in $\pi$)

The angular speed of a wheel increases from $600 \, rpm$ to $1200 \, rpm$ in $10 \, s$. What is the angular acceleration?

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. At what time will the magnitude of its centripetal acceleration and tangential acceleration be equal?

Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ is: