A flywheel of mass 90 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1100 rpm. The driving torque is a constant 10 N·m and friction can be ignored. How long t does this take?
A pendulum is made of a uniform slender rod (1.5 kg, 1.1 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 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 10 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 18.5 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
A uniform slender rod of mass 2 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 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.
A thin hoop starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 2 m along the slope.
A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 55 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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