A pendulum is made of a uniform slender rod (3 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 7 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 200 kg with a radius of gyration of 0.25 m is accelerated uniformly from rest to 1600 rpm. The driving torque is a constant 210 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 5.5 kg and length 3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A flywheel with a moment of inertia of 31.5 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 35 N·m. How many revolutions N does the flywheel make before it stops?
A solid cylinder of mass 3 kg rolls without slipping at 4 m/s. Find its rotational kinetic energy Erot.
A uniform solid disc (mass 27 kg, radius 0.2 m) spins freely at 300 rpm about a vertical frictionless shaft. A thin ring of mass 11 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
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