How many revolutions must a wheel complete to attain an angular velocity of $20 \, rad/s$ in $5 \, s$ starting from rest?

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

The linear speed of the tip of the seconds hand of a wall clock is $1.05 \, cm \, s^{-1}$. The length of the seconds hand is nearly ........ $cm$.

$A$ car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$. The angular acceleration of the wheel is ........ $rad/s^2$.

The angular speed of a flywheel is increased from $600 \text{ rpm}$ to $1200 \text{ rpm}$ in $10 \text{ s}$. The number of revolutions completed by the flywheel during this time 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?