A pendulum is made of a uniform slender rod (2.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 2.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.05 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 2.8 m rotates about an axis O perpendicular to the rod, 0.6 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 10 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 0.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.5 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 thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2 m along the slope.
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 0.25 m. Find its angular velocity ω after it has rolled 8.5 m along the slope.
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