$A$ 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?

Two blocks of mass $1\ kg$ and $2\ kg$ are connected with each other by a spring of spring constant $60\ N/m$. If the velocity given to the block of mass $2\ kg$ at the natural length is $6\ m/s$,find the maximum velocity of the $1\ kg$ block in the subsequent motion (in $m/s$).

$A$ small particle of mass $m$ is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius $a$. All motion occurs essentially in the horizontal plane. If the angular velocity of the cord is $\omega_0$ when the distance from the particle to the tangency point is $r_0$,then the angular velocity of the cord $\omega$ after it has turned through an angle $\theta$ is

$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the system is released from rest,then the acceleration of each mass will be

Write the change in magnitude and direction of angular velocity with respect to time for a body rotating about a fixed axis.

Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.