A pendulum is made of a uniform slender rod (3 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 2.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.15 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 6 kg and length 0.7 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia IO about that axis.
A motor brings a flywheel with a moment of inertia of 8.5 kg·m² from rest up to 700 rpm in 26 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform slender rod of mass 3.5 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.75 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 55 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 hollow sphere of mass 18.5 kg rolls without slipping at 8.5 m/s. Find its total kinetic energy Ek.
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