A pendulum is made of a uniform slender rod (1.5 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.05 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (0.5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 5.5 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 IO of the pendulum about O.
A flywheel with a moment of inertia of 35.5 kg·m² spins at 2000 rpm. A brake applies a constant friction torque of 140 N·m. How many revolutions N does the flywheel make before it stops?
A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 4.5 m.
A uniform solid disc (mass 20 kg, radius 0.45 m) spins freely at 700 rpm about a vertical frictionless shaft. A thin ring of mass 9 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 person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 35 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
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