Rigid-body rotation worksheet with answers

A uniform slender rod of mass 11.5 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.4 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 (0.5 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 2 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia I_O of the pendulum about O.

A motor delivers a torque of 810 N·m at 300 rpm. Find its power output P in kW.

A 9.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.3 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

A solid sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 1 m along the slope.

A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 55 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n₂ in rpm.