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 7.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.2 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 70 kg with a radius of gyration of 0.5 m is accelerated uniformly from 300 rpm to 2300 rpm. The driving torque is a constant 370 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 18.5 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 65 N·m. How many revolutions N does the flywheel make before it stops?
A flywheel with a moment of inertia of 15 kg·m² spins at 400 rpm. A brake applies a constant friction torque of 185 N·m. How long t does it take to stop?
A solid sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 7 m along the slope.
A person stands on a frictionless turntable and holds a 3 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
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