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:

The angular acceleration of a wheel is $3 \ rad/s^2$. If its initial angular velocity is $2 \ rad/s$,what is the angular displacement (in $rad$) covered by it in $2 \ s$?

$A$ 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?

If the frequency of an object in uniform circular motion is doubled,its acceleration becomes

The ratio of angular speeds of the minute hand and the hour hand of a watch is:

$A$ particle moves along a circle of radius $\left( \frac{20}{\pi} \right) \, m$ with constant tangential acceleration. If the velocity of the particle is $80 \, m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is