A pendulum is made of a uniform slender rod (4.5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 5.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.2 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 120 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1000 rpm. The driving torque is a constant 120 N·m and friction can be ignored. How long t does this take?
A 15 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.4 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 1.5 kg and length 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 uniform slender rod of mass 7 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 340 m/s hits the rod 0.24 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.
A uniform slender rod of mass 9 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 500 m/s hits the rod 0.88 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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