A pendulum is made of a uniform slender rod (4 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 2 kg and length 1.3 m rotates about an axis O perpendicular to the rod, 0.2 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 10 kg and radius 0.35 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.
A flywheel with a moment of inertia of 12.5 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 170 N·m. How long t does it take to stop?
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3.5 m along the slope.
A hollow sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
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