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

$A$ body moves with a constant angular velocity on a circle. What is the magnitude of its angular acceleration?

$A$ particle of mass $10 \text{ g}$ moves along a circle of radius $6.4 \text{ cm}$ with a constant tangential acceleration. If the kinetic energy of the particle becomes $8 \times 10^{-4} \text{ J}$ by the end of the second revolution after the beginning of the motion, the magnitude of the tangential acceleration is (in $\text{ m/s}^2$)

$A$ wheel is at rest. Its angular velocity increases uniformly and becomes $60 \ rad/sec$ after $5 \ sec$. The total angular displacement is ........ $rad$.

If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$,then its linear velocity is (in $\text{m/s}$):