A pendulum is made of a uniform slender rod (0.5 kg, 1 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.05 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 130 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1700 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.
An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19.5 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 angular acceleration α of the pulley.
A flywheel with a moment of inertia of 1.5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 80 N·m. How long t does it take to stop?
A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 60 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A uniform slender rod of mass 7.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 220 m/s hits the rod 0.38 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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