A pendulum is made of a uniform slender rod (1 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 120 kg with a radius of gyration of 0.4 m is accelerated uniformly from 600 rpm to 2500 rpm. The driving torque is a constant 220 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 4.5 kg·m² spins at 1700 rpm. A brake applies a constant friction torque of 185 N·m. How long t does it take to stop?
A motor brings a flywheel with a moment of inertia of 3 kg·m² from rest up to 2700 rpm in 16 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A thin hoop rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 7.5 m down the slope?
A thin hoop rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?
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