The angular velocity of a wheel is $70\, rad/s$. If the radius of the wheel is $0.5\, m$,then the linear velocity of the wheel is ....... $m/s$.

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

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

$A$ 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

$A$ particle of mass $m$ moves along a circle of radius $r$ with constant tangential acceleration. If the kinetic energy $(K.E.)$ of the particle is $E$ by the end of the third revolution after the beginning of the motion,then the magnitude of the tangential acceleration is:

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