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

For a particle in uniform circular motion,the acceleration $\vec{a}$ at any point $P (R, \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$-axis and $v$ is uniform speed):

The shaft of a motor rotates at a constant angular velocity of $3000 \ rpm$. The number of radians it has turned through in $1 \ s$ is (in $\pi$)

What is the physical quantity represented by the unit $rpm$? Express it in $rad/s$.

$A$ fan is making $600$ revolutions per minute. If after some time it makes $1200$ revolutions per minute,then the increase in its angular velocity is

The length of the second's hand in a watch is $1 \, cm$. The change in velocity of its tip in $15 \, seconds$ is