A pendulum is made of a uniform slender rod (2 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.7 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 40 kg with a radius of gyration of 0.35 m is accelerated uniformly from 100 rpm to 1000 rpm. This takes 24 s. Ignoring friction, find the constant torque T needed.
A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 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 angular acceleration α of the pulley.
A motor delivers a torque of 560 N·m at 3000 rpm. Find its power output P in kW.
A thin hoop starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 6.5 m along the slope.
A uniform slender rod of mass 9.5 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 300 m/s hits the rod 0.88 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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