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

Two rotating bodies A and B of masses m and 2m with moments of inertia $${I_A}$$ and $${I_B}$$ ($${I_B}$$ > $${I_A}$$) have equal kinetic energy of rotation. If L_A and L_B be their angular momenta respectively, then

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (E_sphere / E_cylinder) will be