For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?

What is pure translational motion?

$A$ uniform disc with mass $M = 4\,kg$ and radius $R = 10\,cm$ is mounted on a fixed horizontal axle as shown in the figure. $A$ block with mass $m = 2\,kg$ hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block,the cord does not slip and there is no friction at the axle. The tension in the cord is . . . . . . $N$. (Take $g = 10\,m/s^2$)

$A$ cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. $A$ rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

For every particle of a rigid body in rotational motion,which of the following is true?

When a ceiling fan is switched off,its angular velocity falls to $\frac{1}{3}$ of its initial value while it makes $24$ rotations. How many more rotations will it make before coming to rest?