Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $$\omega $$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $${\omega _1}$$ and $${\omega _2}$$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

A light rod of length $$l$$ has two masses m₁ and m₂ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is