$A$ wheel rotating at an angular velocity of $1200 \ rpm$ is slowed down at a constant angular acceleration of $4 \ rad \ s^{-2}$. How many revolutions will the wheel make before coming to rest?

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,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

$A$ flywheel starts from rest and rotates with a constant angular acceleration of $3.0 \ rad/s^2$. An observer notes that it covers an angle of $120 \ rad$ in a time interval of $4.0 \ s$. How long had the wheel been rotating before the observer started the observation?

$A$ car wheel rotates at $1200$ revolutions per minute. On pressing the accelerator,it rotates at $4500$ revolutions per minute in $10 \ s$. The angular acceleration of the wheel is ...

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