A pendulum is made of a uniform slender rod (0.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 50 kg with a radius of gyration of 0.5 m is accelerated uniformly from 700 rpm to 2200 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.
A flywheel with a moment of inertia of 17.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 165 N·m. How many revolutions N does the flywheel make before it stops?
A motor brings a flywheel with a moment of inertia of 23 kg·m² from rest up to 1200 rpm in 16 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A thin hoop starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 5.5 m along the slope.
A uniform solid disc (mass 38 kg, radius 0.3 m) spins freely at 800 rpm about a vertical frictionless shaft. A thin ring of mass 19 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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