The angular velocity of a wheel is $70\, rad/s$. If the radius of the wheel is $0.5\, m$,then the linear velocity of the wheel is ....... $m/s$.

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with angular acceleration $\alpha$. The magnitude of the average velocity in the time it completes the small angular displacement $\theta$ is

$A$ wheel has a diameter of $1 \ m$. If it makes $30$ revolutions per second,then the linear speed of a point on its circumference will be:

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 $\text{m/s}$):

$A$ fan is rotating with an angular speed of $300 \text{ rpm}$. The fan is switched off,and it takes $80 \text{ s}$ to come to rest. Assuming constant angular deceleration,the number of revolutions made by the fan before it comes to rest is:

$A$ wheel rotates with a constant acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions it makes in the first ten seconds is: