A pendulum is made of a uniform slender rod (2 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 290 kg and radius 0.25 m. It spins at 900 rpm. Find its kinetic energy Ek in kJ.
A motor brings a flywheel with a moment of inertia of 20.5 kg·m² from rest up to 1600 rpm in 30 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform slender rod of mass 3 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 thin hoop starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 7 m along the slope.
A uniform slender rod of mass 4.5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 260 m/s hits the rod 0.45 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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