A pendulum is made of a uniform slender rod (2 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 8 kg and length 1.2 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 10 kg and length 1.8 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 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 uniform slender rod of mass 4.5 kg and length 2.1 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.85 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 20 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 person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 55 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
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