A pendulum is made of a uniform slender rod (1 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 280 kg has a radius of gyration of 0.35 m about its axis. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.
A flywheel with a moment of inertia of 18.5 kg·m² spins at 1700 rpm. A brake applies a constant friction torque of 200 N·m. How long t does it take to stop?
A motor delivers a torque of 830 N·m at 1100 rpm. Find its power output P in kW.
A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.75 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 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A uniform solid disc (mass 10 kg, radius 0.25 m) spins freely at 1050 rpm about a vertical frictionless shaft. A thin ring of mass 15 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.
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