A pendulum is made of a uniform slender rod (5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 7.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 6.5 kg and length 0.4 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 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 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 acceleration a of the block.
A uniform slender rod of mass 4.5 kg and length 2.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A uniform slender rod of mass 4.5 kg and length 1.8 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 160 m/s hits the rod 1.72 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 5 m down the slope?
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