A flywheel of mass 70 kg with a radius of gyration of 0.45 m is accelerated uniformly from 400 rpm to 1500 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.
A pendulum is made of a uniform slender rod (2.5 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 9.5 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A motor delivers a torque of 1490 N·m at 1900 rpm. Find its power output P in kW.
A 0.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 16.5 kg and radius 0.25 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 of mass 19 kg rolls without slipping at 8 m/s. Find its rotational kinetic energy Erot.
A person stands on a frictionless turntable and holds a 1.5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 4.5 kg·m² about the axis. They turn at 60 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
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