A pendulum is made of a uniform slender rod (0.5 kg, 0.9 m long) pivoted at its top end O, with a thin solid disc of mass 2.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 120 kg with a radius of gyration of 0.6 m is accelerated uniformly from 500 rpm to 1200 rpm. The driving torque is a constant 450 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 30 kg·m² spins at 900 rpm. A brake applies a constant friction torque of 50 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 1 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.
A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 55 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.
A solid cylinder rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2 m down the slope?
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