$A$ particle starting from rest moves in a circle of radius $r$. It attains a velocity of $V_{0} \; m/s$ in the $n^{\text{th}}$ round. Its angular acceleration will be

$A$ wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2 \text{ s}$ it rotates through an angle $\theta_1$ and in the next $2 \text{ s}$ it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ 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:

$A$ particle is revolving in a circular path of radius $25 \, m$ with a constant angular speed of $12 \, rev/min$. The angular acceleration of the particle is .......... $rad/s^2$.

$A$ 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 $10 \text{ g}$ 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 $\text{ m/s}^2$)