A pendulum is made of a uniform slender rod (3.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (2 kg, 0.6 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 3 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
A uniform slender rod of mass 3.5 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. 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 uniform solid disc (mass 13 kg, radius 0.3 m) spins freely at 1050 rpm about a vertical frictionless shaft. A thin ring of mass 9 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
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