The shaft of a motor rotates at a constant angular velocity of $3000 \ rpm$. The number of radians it has turned through in $1 \ s$ is (in $\pi$)

$A$ body is whirled in a horizontal circle of radius $20 \,cm$. It has an angular velocity of $10 \,rad/s$. What is its linear velocity at any point on the circular path in $m/s$?

$A$ particle is moving on a circular path with constant speed $v$. It moves between two points $A$ and $B$,which subtend an angle $60^{\circ}$ at the centre of the circle. The magnitude of the change in its velocity and the change in the magnitude of its velocity during motion from $A$ to $B$ are respectively ..........

In uniform circular motion,

When a particle moves in a uniform circular motion,it has:

$A$ 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: