A pendulum is made of a uniform slender rod (1.5 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 90 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 400 rpm. The driving torque is a constant 3.9 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 13 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 195 N·m. How long t does it take to stop?
A uniform slender rod of mass 13 kg and length 2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A thin hoop rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A person stands on a frictionless turntable and holds a 3 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 2.5 kg·m² about the axis. They turn at 55 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
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