A pendulum is made of a uniform slender rod (4.5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 5.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 70 kg has a radius of gyration of 0.6 m about its axis. It spins at 2600 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 8 kg and length 1.5 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 motor delivers a torque of 1440 N·m at 2300 rpm. Find its power output P in kW.
A person stands on a frictionless turntable and holds a 6 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 35 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 thin hoop of mass 6.5 kg rolls without slipping at 5 m/s. Find its rotational kinetic energy Erot.
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