A pendulum is made of a uniform slender rod (5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 5.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (0.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 2 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel with a moment of inertia of 19 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 25 N·m. How many revolutions N does the flywheel make before it stops?
An 8.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 18 kg and radius 0.3 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 hollow sphere of mass 14 kg rolls without slipping at 8 m/s. Find its rotational kinetic energy Erot.
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. Find its speed v after it has rolled 4.5 m along the slope.
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