A flywheel of mass 80 kg with a radius of gyration of 0.6 m is accelerated uniformly from 800 rpm to 2200 rpm. The driving torque is a constant 150 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 2.5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 6 kg and length 2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
An 8.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.
A hollow sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 1 m down the slope?
A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 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.
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