A pendulum is made of a uniform slender rod (3 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 170 kg and radius 0.45 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 19.5 kg and length 2.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A uniform slender rod of mass 7 kg and length 1.6 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 thin hoop rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
A person stands on a frictionless turntable and holds a 3.5 kg dumbbell in each hand, 0.9 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.
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