A pendulum is made of a uniform slender rod (5 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 140 kg and radius 0.6 m. It spins at 1100 rpm. Find its kinetic energy Ek in kJ.
A shaft transmits 81.5 kW at 600 rpm. Find the torque T in the shaft.
A uniform slender rod of mass 20 kg and length 1.8 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 7.5 kg and length 0.9 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 140 m/s hits the rod 0.81 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
A uniform solid disc (mass 11 kg, radius 0.5 m) spins freely at 500 rpm about a vertical frictionless shaft. A thin ring of mass 19 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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