A flywheel of mass 200 kg with a radius of gyration of 0.15 m is accelerated uniformly from 800 rpm to 1000 rpm. This takes 21 s. Ignoring friction, find the constant torque T needed.
A flywheel of mass 280 kg has a radius of gyration of 0.6 m about its axis. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 8.5 kg and length 0.5 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 speed v of the free end as the rod swings through the vertical position.
A uniform slender rod of mass 6 kg and length 1.6 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 solid disc (mass 26 kg, radius 0.2 m) spins freely at 700 rpm about a vertical frictionless shaft. A thin ring of mass 1 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.9 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 50 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.
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