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

$A$ particle $P$ is moving in a circle of radius $a$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$,the angular velocity of $P$ about $A$ and $C$ are in the ratio:

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

The angular speed of Earth around its own axis is ......... $rad/s$.

$A$ 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:

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their angular speeds $\omega_{1}$ and $\omega_{2}$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_{1}$ to the linear speed of $m_{2}$ is: