A pendulum is made of a uniform slender rod (2.5 kg, 1.3 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 9 kg and length 1.4 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia IO about that axis.
A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.
A uniform slender rod of mass 2.5 kg and length 0.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A person stands on a frictionless turntable and holds a 3 kg dumbbell in each hand, 0.75 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 20 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 25 kg, radius 0.3 m) spins freely at 850 rpm about a vertical frictionless shaft. A thin ring of mass 10 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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