$A$ scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$.

The position vector of a particle is $\vec{r} = (a \cos \omega t)\hat{i} + (a \sin \omega t)\hat{j}$. The velocity of the particle is

If $\omega_1$ is the angular velocity of the hour hand of a clock and $\omega_2$ is the angular velocity of the Earth,then the ratio $\omega_1 : \omega_2$ is

$A$ particle is performing uniform circular motion. The velocity of the particle at an instant of time is $(6 \hat{i} - 2 \hat{j}) \ m/s$ and the angular velocity is $\vec{\omega} = (a \hat{i} + b \hat{j}) \ rad/s$. Then the value of $\frac{b}{a}$ is:

The displacement of a body when it covers a distance of $C / 4$ (where,$C$ is circumference) along the circumference of a circle of radius $r$ with a uniform speed $u$ is

$A$ wheel of radius $30 \ cm$ rotates about its axis and undergoes an angular displacement of $30^\circ$. The linear distance covered by the wheel is .......