In the rotational motion of a rigid body,all particles of the body have

$A$ uniform rod of mass $m$ and length $l$ is suspended by means of two identical inextensible light strings as shown in the figure. The tension in one string immediately after the other string is cut is . . . . . . . ($g$ is the acceleration due to gravity)

$A$ thin but rigid semicircular wire frame of radius $r$ is hinged at $O$ and can rotate in its own vertical plane. $A$ smooth peg $P$ starts from $O$ and moves horizontally with constant speed $v_0$,lifting the frame upward as shown in the figure. Find the angular velocity $\omega$ of the frame when its diameter makes an angle of $60^{\circ}$ with the vertical.

How can one verify that an object is undergoing rotation about a fixed axis?

$A$ body is in pure rotation. The linear speed $v$ of a particle,the distance $r$ of the particle from the axis,and the angular velocity $\omega$ of the body are related as $\omega = \frac{v}{r}$. Thus,

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,with what acceleration will the mass fall on release?