A pendulum is made of a uniform slender rod (2.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 1 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 60 kg and radius 0.25 m. It spins at 2500 rpm. Find its kinetic energy Ek in kJ.
A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19 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 motor brings a flywheel with a moment of inertia of 13.5 kg·m² from rest up to 700 rpm in 6 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A uniform slender rod of mass 2 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 160 m/s hits the rod 0.68 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.