A pendulum is made of a uniform slender rod (5 kg, 0.6 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.65 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, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A motor brings a flywheel with a moment of inertia of 9.5 kg·m² from rest up to 1100 rpm in 23 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A 13 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 kg and radius 0.15 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 1.5 m.
A solid sphere of mass 10 kg rolls without slipping at 8.5 m/s. What percentage p of its total kinetic energy is rotational?
A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8.5 m along the slope.
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