A pendulum is made of a uniform slender rod (5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 120 kg with a radius of gyration of 0.5 m is accelerated uniformly from 100 rpm to 1900 rpm. The driving torque is a constant 220 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 12 kg and length 1.7 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 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 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 speed v of the block after it has fallen 3.5 m.
A uniform solid disc (mass 10 kg, radius 0.15 m) spins freely at 200 rpm about a vertical frictionless shaft. A thin ring of mass 11 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?
A solid cylinder rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
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