A pendulum is made of a uniform slender rod (3.5 kg, 1.1 m long) pivoted at its top end O, with a solid sphere of mass 6.5 kg and radius 0.25 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 flywheel of mass 10 kg with a radius of gyration of 0.25 m is accelerated uniformly from 700 rpm to 2600 rpm. The driving torque is a constant 9.6 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 14.5 kg·m² spins at 2500 rpm. A brake applies a constant friction torque of 65 N·m. How long t does it take to stop?
A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.35 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 5 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 380 m/s hits the rod 0.73 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 solid cylinder of mass 3 kg rolls without slipping at 7.5 m/s. What percentage p of its total kinetic energy is rotational?
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