For a rigid body in rotational motion,if the linear velocity of a particle at a distance of $2 \ cm$ from the fixed axis of rotation is $10 \ cm \ s^{-1}$,what is the angular velocity of a particle at a distance of $4 \ cm$ from the axis of rotation?

$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

$A$ uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is

The linear velocity of a rotating body is given by $\overrightarrow v = \overrightarrow \omega \times \overrightarrow r,$ where $\overrightarrow \omega$ is the angular velocity and $\overrightarrow r$ is the radius vector. If the angular velocity of a body is $\overrightarrow \omega = \hat i - 2\hat j + 2\hat k$ and the radius vector is $\overrightarrow r = 4\hat j - 3\hat k,$ then find the magnitude of linear velocity $|\overrightarrow v |$.

Between the hour hand of a clock and the rotation of the Earth about its own axis,which has a lower angular speed?

The instantaneous velocity of point $B$ of a rod of length $L = 0.5 \ m$ is $v = 3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. The angular velocity of the rod for the minimum velocity of end $A$ is: