A pendulum is made of a uniform slender rod (5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.5 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 2.5 kg and length 1.6 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 8.5 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 kg and radius 0.3 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 solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 7 m down the slope?
A uniform solid disc (mass 25 kg, radius 0.2 m) spins freely at 1050 rpm about a vertical frictionless shaft. A thin ring of mass 1 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?
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