A pendulum is made of a uniform slender rod (4.5 kg, 1.3 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 3 kg and length 1.2 m rotates about an axis O perpendicular to the rod, 0.6 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 11 kg and length 0.5 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 11.5 kg and length 1.7 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 solid disc (mass 31 kg, radius 0.2 m) spins freely at 900 rpm about a vertical frictionless shaft. A thin ring of mass 6 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.
A hollow sphere 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.
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