Rigid-body rotation worksheet with answers

A uniform slender rod of mass 7.5 kg and length 3 m rotates about an axis O perpendicular to the rod, 1.35 m from its centre G. Find its mass moment of inertia I_O about that axis.

A pendulum is made of a uniform slender rod (3.5 kg, 0.6 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia I_O of the pendulum about O.

A uniform slender rod of mass 2 kg and length 1.7 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

A 4 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17 kg and radius 0.35 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

A solid sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 6 m along the slope.

A uniform slender rod of mass 6.5 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 140 m/s hits the rod 0.66 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.