A pendulum is made of a uniform slender rod (2.5 kg, 1.2 m long) pivoted at its top end O, with a thin solid disc of mass 4 kg and radius 0.05 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 uniform slender rod of mass 10 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.95 m from its centre G. Find its mass moment of inertia IO about that axis.
A motor brings a flywheel with a moment of inertia of 16 kg·m² from rest up to 2100 rpm in 4 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A motor delivers a torque of 440 N·m at 2600 rpm. Find its power output P in kW.
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 0.3 m. Find its angular velocity ω after it has rolled 9.5 m along the slope.
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2 m along the slope.
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