$A$ flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad/s$ to $40\pi \, rad/s$ in $10 \, s$. How many rotations did it make in this period?

$A$ particle starts rotating from rest. Its angular displacement is expressed by the following equation $\theta = 0.025t^2 - 0.1t$,where $\theta$ is in radians and $t$ is in seconds. The angular acceleration of the particle is:

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

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

Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ 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