The angular velocity of a flywheel making $120$ revolutions per minute is:

If the angular velocity of a merry-go-round is $60^o/s$ and you are $3.5\,m$ from the centre of rotation,your linear velocity will be

$A$ man is running with constant speed along a circular path of radius $2 \sqrt 2 \, m$. He completes $1$ round in $10 \, s$. Find the instantaneous speed at $2.5 \, s$.

The ratio of the angular speed of the hour hand of a clock to the angular speed of the minute hand is .......

What is uniform circular motion? By using a proper figure,derive the equation for centripetal acceleration $a_c = \frac{v^2}{r}$ for uniform circular motion. Show that its direction is towards the center.

$A$ particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$,the ratio of instantaneous velocity to its average velocity is $\pi : x \sqrt{2}$. The value of $x$ will be $.........$