A pendulum is made of a uniform slender rod (5 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 200 kg has a radius of gyration of 0.3 m about its axis. It spins at 500 rpm. Find its kinetic energy Ek in kJ.
A 12 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12 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 tension T in the cord.
A flywheel with a moment of inertia of 18.5 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 90 N·m. How long t does it take to stop?
A person stands on a frictionless turntable and holds a 6 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 35 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.
A uniform solid disc (mass 19 kg, radius 0.2 m) spins freely at 900 rpm about a vertical frictionless shaft. A thin ring of mass 6 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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