All particles of a body move in circular paths when its axis of rotation.........

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.)

$A$ thin rod is hinged at point $O$ and is in an unstable equilibrium position. It falls under the influence of gravity due to a slight disturbance. It makes angles of $60^{\circ}$,$90^{\circ}$,and $180^{\circ}$ with the vertical in positions $(2)$,$(3)$,and $(4)$ respectively. If $\omega_2$,$\omega_3$,and $\omega_4$ are the angular velocities in these positions,then:

$A$ mass $m$ is suspended from a string wrapped around a frictionless pulley. The pulley has a mass $M$ and radius $R$. If the pulley is a uniform circular disk and the string does not slip on the pulley,what is the acceleration of the mass?

$A$ rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time,when the rod makes an angle $\theta$ with the horizontal,the velocity of the $COM$ of the rod is $v_0$. The velocity of the end of the rod in contact with the surface at that instant is:

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