A pendulum is made of a uniform slender rod (1.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 8.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.4 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 7.5 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.35 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 16.5 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 speed v of the block after it has fallen 2.5 m.
A uniform slender rod of mass 4 kg and length 1.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A solid sphere of mass 17 kg rolls without slipping at 4 m/s. Find its rotational kinetic energy Erot.
A uniform slender rod of mass 8 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 500 m/s hits the rod 0.87 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
Full step-by-step solutions: practise this topic on examproblems.com.