A pendulum is made of a uniform slender rod (1 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (2.5 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 2 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 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 speed v of the block after it has fallen 1 m.
A 5.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 kg and radius 0.4 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 solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 10 m along the slope.
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