A pendulum is made of a uniform slender rod (0.5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 10.5 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.
A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 18 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 angular acceleration α of the pulley.
A 3 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 2 kg and radius 0.2 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 0.5 m.
A uniform slender rod of mass 8 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 100 m/s hits the rod 1.33 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform solid disc (mass 10 kg, radius 0.45 m) spins freely at 150 rpm about a vertical frictionless shaft. A thin ring of mass 6 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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