A pendulum is made of a uniform slender rod (3.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 8.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 230 kg and radius 0.3 m. It spins at 2700 rpm. Find its kinetic energy Ek in kJ.
A flywheel with a moment of inertia of 20.5 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 80 N·m. How long t does it take to stop?
A shaft transmits 143.5 kW at 2700 rpm. Find the torque T in the shaft.
A person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.6 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 45 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 thin hoop of mass 16.5 kg rolls without slipping at 7 m/s. Find its total kinetic energy Ek.
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