A pendulum is made of a uniform slender rod (0.5 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 11.5 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.
A 5.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19 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 tension T in the cord.
A uniform slender rod of mass 7.5 kg and length 1.2 m is pinned at one end and released from rest in a horizontal position. 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 of mass 1 kg rolls without slipping at 8 m/s. Find its rotational kinetic energy Erot.
A uniform slender rod of mass 6 kg and length 1.1 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 460 m/s hits the rod 0.69 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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