A flywheel of mass 110 kg with a radius of gyration of 0.4 m is accelerated uniformly from 100 rpm to 1100 rpm. The driving torque is a constant 77 N·m and friction can be ignored. How long t does this take?
A flywheel of mass 250 kg has a radius of gyration of 0.5 m about its axis. It spins at 900 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 3 kg and length 1.7 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 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 4 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.45 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 solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 5.5 m along the slope.
A uniform slender rod of mass 2.5 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 240 m/s hits the rod 0.52 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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