A pendulum is made of a uniform slender rod (3 kg, 1 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.2 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, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 18.5 kg and length 2.2 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 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 16 kg and radius 0.5 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 1.5 m.
A solid sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 7.5 m down the slope?
A uniform slender rod of mass 3.5 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 100 m/s hits the rod 1.68 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.
Full step-by-step solutions: practise this topic on examproblems.com.