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

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:

$A$ wheel has a speed of $1200$ revolutions per minute and is made to slow down at a rate of $4 \ rad/s^{2}$. The number of revolutions it makes before coming to rest is

An object moves along a circle with normal acceleration proportional to $t^\alpha$, where $t$ is the time and $\alpha$ is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

The ratio of the angular speed of a second-hand to the hour-hand of a watch is (in $: 1$)

$A$ grinding wheel attains a velocity of $20 \ rad/s$ in $5 \ s$ starting from rest. Find the number of revolutions made by the wheel.