System of Particles & Rotational Motion

A uniform rod of length 2 m, pivoted at one end, is released from rest in a horizontal position. Find its angular acceleration the instant it becomes vertical. (g = 10 m/s²)

A rod of mass 4 kg, length 3 m, free to rotate about its centre, is struck by a 2 kg particle moving at 6 m/s perpendicular to it, which sticks to one end. Find the angular speed just after impact.

A hollow sphere rolls without slipping down an incline from a height of 3 m. Find its speed at the bottom. (g = 10 m/s²)

A rotating disc has moment of inertia 8 kg·m² and angular speed 2 rad/s. Its moment of inertia changes to 4 kg·m² with no external torque. Find the new angular speed.

Masses of 3 kg and 5 kg hang from a pulley of moment of inertia 0.5 kg·m² and radius 0.25 m. Find the system's acceleration. (g = 10 m/s²)

A solid sphere of mass 4 kg rolls without slipping at 5 m/s. Find its rotational kinetic energy.

A torque of 20 N·m acts on a body of moment of inertia 4 kg·m². Find its angular acceleration.

A ring and a disc have the same mass and radius. Find the ratio of their moments of inertia about the central axis (ring : disc).

A body has moment of inertia 50 kg·m² and mass 8 kg. Find its radius of gyration.

A wheel rotates at 300 revolutions per minute. Find its angular velocity in rad/s.

A constant torque of 15 N·m rotates a body through an angle of 4 rad. Find the work done by the torque.

A 0.5 kg particle moves at 8 m/s along a line that passes at a perpendicular distance of 2 m from a fixed point O. Find its angular momentum about O.