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 7.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (1.5 kg, 0.9 m long) pivoted at its top end O, with a thin solid disc of mass 4 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 3 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 3 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 3.5 m.
A flywheel with a moment of inertia of 5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 40 N·m. How many revolutions N does the flywheel make before it stops?
A solid sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A uniform slender rod of mass 9.5 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 280 m/s hits the rod 0.72 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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