A flywheel of mass 40 kg with a radius of gyration of 0.25 m is accelerated uniformly from rest to 800 rpm. The driving torque is a constant 52 N·m and friction can be ignored. How long t does this take?
A flywheel of mass 170 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1200 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.
A uniform slender rod of mass 17.5 kg and length 2.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A uniform slender rod of mass 10 kg and length 1.8 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 angular velocity ω of the rod as it swings through the vertical position.
A uniform slender rod of mass 10 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 280 m/s hits the rod 0.3 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A hollow sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
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