$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

Four identical point masses $m$ are joined by light strings of length $l$ and arranged to form a square frame. The center of the table coincides with the center of the arrangement. If the arrangement rotates with a constant angular velocity $\omega$,find the tension in each string.

The pulley shown in the figure is made using a thin rim and two rods of length equal to the diameter of the rim. The rim and each rod have a mass of $M$. Two blocks of mass $M$ and $m$ are attached to two ends of a light string passing over the pulley,which is hinged to rotate freely in a vertical plane about its centre. The magnitude of the acceleration experienced by the blocks is . . . . . . (assume no slipping of the string on the pulley.)

The moment of inertia of a solid flywheel about its axis is $0.1\,kg\cdot m^2$. $A$ tangential force of $2\,kg\cdot wt$ is applied around the circumference of the flywheel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m$,find the angular acceleration of the solid flywheel (in $rad/s^2$). (Take $g = 9.8\,m/s^2$)

$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ disc rotating about its axis from rest,acquires the angular speed $100 \, rev/s$ in $4 \, s$. The angle rotated by it during these four seconds (in radian) is ...... $\pi$.