A pendulum is made of a uniform slender rod (1.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 6.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 20 kg and radius 0.55 m. It spins at 2600 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 17.5 kg and length 1.6 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 uniform slender rod of mass 9 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. 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 solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A uniform solid disc (mass 6 kg, radius 0.4 m) spins freely at 800 rpm about a vertical frictionless shaft. A thin ring of mass 14 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
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