A flywheel of mass 50 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1200 rpm. The driving torque is a constant 6.3 N·m and friction can be ignored. How long t does this take?
A pendulum is made of a uniform slender rod (3 kg, 0.6 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 17 kg and length 1.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A uniform slender rod of mass 7.5 kg and length 1.9 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 person stands on a frictionless turntable and holds a 4.5 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 45 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A uniform solid disc (mass 39 kg, radius 0.4 m) spins freely at 700 rpm about a vertical frictionless shaft. A thin ring of mass 9 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
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