A pendulum is made of a uniform slender rod (3.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 2.5 kg and length 1.1 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.
A 14.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 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 tension T in the cord.
A uniform slender rod of mass 4.5 kg and length 1.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 0.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
A thin hoop 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 2 m down the slope?
A uniform slender rod of mass 7 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 460 m/s hits the rod 0.7 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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