A pendulum is made of a uniform slender rod (0.5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (3 kg, 1.1 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.3 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel with a moment of inertia of 16.5 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 55 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 3.5 kg and length 0.9 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 solid disc (mass 30 kg, radius 0.3 m) spins freely at 250 rpm about a vertical frictionless shaft. A thin ring of mass 13 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 10 kg, radius 0.2 m) spins freely at 450 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.
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