A pendulum is made of a uniform slender rod (4 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 7 kg and length 1.2 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.
An 11 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.
A motor delivers a torque of 1100 N·m at 2200 rpm. Find its power output P in kW.
A solid cylinder 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 0.1 m. Find its angular velocity ω after it has rolled 1 m along the slope.
A solid sphere of mass 4.5 kg rolls without slipping at 9 m/s. What percentage p of its total kinetic energy is rotational?
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