A pendulum is made of a uniform slender rod (3.5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (3.5 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 0.95 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 4 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 kg and radius 0.1 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
A motor brings a flywheel with a moment of inertia of 36 kg·m² from rest up to 2200 rpm in 26 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform solid disc (mass 27 kg, radius 0.2 m) spins freely at 100 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. How much kinetic energy ΔE is lost in the process?
A solid cylinder of mass 10.5 kg rolls without slipping at 2 m/s. What percentage p of its total kinetic energy is rotational?
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