A pendulum is made of a uniform slender rod (3 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 4.5 kg and length 2.5 m rotates about an axis O perpendicular to the rod, 0.9 m from its centre G. Find its mass moment of inertia IO about that axis.
A 13.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
A flywheel with a moment of inertia of 19.5 kg·m² spins at 2000 rpm. A brake applies a constant friction torque of 15 N·m. How many revolutions N does the flywheel make before it stops?
A uniform solid disc (mass 40 kg, radius 0.45 m) spins freely at 600 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. How much kinetic energy ΔE is lost in the process?
A hollow sphere rolls without slipping down a slope inclined at 15° 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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