Two masses $m$ and $2m$ are connected by a light string passing over a pulley (disc) of mass $M = 30m$ and radius $r = 0.1 \ m$. The pulley is mounted in a vertical plane and is free to rotate about its axis. The $2m$ mass is released from rest. Find its speed when it has descended through a height of $h = 3.6 \ m$. (Assume the string does not slip and $g = 10 \ m/s^2$)

$A$ 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 cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

$A$ uniform cylinder of mass $m$ can rotate freely about its own axis,which is horizontal. $A$ particle of mass $m_0$ hangs from the end of a light string wound around the cylinder,which does not slip over it. When the system is allowed to move,the acceleration of the descending mass will be

What are the characteristics of rotational motion?

Consider two masses with $m_1 > m_2$ connected by a light inextensible string that passes over a pulley of radius $R$ and moment of inertia $I$ about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance $2h$. When the two masses pass each other,the speed of the masses is proportional to

$A$ spool of mass $M$ and radius $R$ is unwinding under gravity as a string is pulled. What is the acceleration of the spool?