Rigid-body rotation worksheet with answers

A uniform slender rod of mass 5 kg and length 2.9 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 (5 kg, 0.9 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.15 m below O. Find the mass moment of inertia I_O of the pendulum about O.

An 11.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 20 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.5 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 person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n₂ in rpm.

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 60 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n₂ in rpm.