Rigid-body rotation worksheet with answers

A flywheel of mass 250 kg has a radius of gyration of 0.3 m about its axis. It spins at 2000 rpm. Find its kinetic energy E_k in kJ.

A pendulum is made of a uniform slender rod (2 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.5 m below O. Find the mass moment of inertia I_O of the pendulum about O.

A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6 kg and radius 0.1 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 uniform slender rod of mass 8 kg and length 1.2 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 uniform solid disc (mass 2 kg, radius 0.35 m) spins freely at 400 rpm about a vertical frictionless shaft. A thin ring of mass 11 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n₂ in rpm.

A hollow sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.