$A$ grinding wheel attains a velocity of $20 \ rad/s$ in $5 \ s$ starting from rest. Find the number of revolutions made by the wheel.

If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$,then its linear velocity is (in $\text{m/s}$):

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

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

$A$ flywheel starts from rest and rotates with a constant angular acceleration of $3.0 \ rad/s^2$. An observer notes that it covers an angle of $120 \ rad$ in a time interval of $4.0 \ s$. How long had the wheel been rotating before the observer started the observation?

If the speed of a particle moving in a circle of radius $2 \ m$ is given as $v = 2t + 2$,then its centripetal acceleration after $1 \ s$ will be ......... $m/s^2$.