A pendulum is made of a uniform slender rod (4 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.5 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 130 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 200 rpm. The driving torque is a constant 270 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 11.5 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 vertical force R that the pin exerts on the rod just after release.
A flywheel with a moment of inertia of 11 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 140 N·m. How long t does it take to stop?
A uniform solid disc (mass 35 kg, radius 0.25 m) spins freely at 1100 rpm about a vertical frictionless shaft. A thin ring of mass 17 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 uniform solid disc (mass 31 kg, radius 0.15 m) spins freely at 1000 rpm about a vertical frictionless shaft. A thin ring of mass 5 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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