A pendulum is made of a uniform slender rod (1.5 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 4 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.4 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (3.5 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 4.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A 5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.2 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 9 kg and length 1.5 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 hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2.5 m down the slope?
A hollow sphere 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 9.5 m along the slope.
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