If the length of the second's hand in a stop clock is $3 \, cm$,the angular velocity and linear velocity of the tip are:

$A$ wheel initially at rest,begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first $2 \ s$ and a further angle $\theta_2$ in the next $2 \ s$,the ratio $\theta_1 : \theta_2$ is

$A$ particle moves from point $P_1$ to $P_2$ along a circular path with constant speed $v$. If the angle subtended by the arc $P_1P_2$ at the center is $90^{\circ}$,what is the change in velocity?

$A$ 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:

$A$ 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 .......... $rad/s^2$.

$A$ 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?