A flywheel of mass 160 kg with a radius of gyration of 0.3 m is accelerated uniformly from 600 rpm to 1700 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.
A pendulum is made of a uniform slender rod (4 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
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. 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 motor delivers a torque of 1230 N·m at 2200 rpm. Find its power output P in kW.
A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 10 m along the slope.
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