A pendulum is made of a uniform slender rod (3.5 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 8 kg and radius 0.15 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 4 kg and length 2 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 1 kg and length 1.8 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.
A motor delivers a torque of 1840 N·m at 2500 rpm. Find its power output P in kW.
A solid cylinder 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 7.5 m along the slope.
A solid cylinder of mass 16.5 kg rolls without slipping at 5.5 m/s. Find its total kinetic energy Ek.
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