A pendulum is made of a uniform slender rod (4.5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 20 kg and radius 0.25 m. It spins at 2300 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 3.5 kg and length 0.9 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 slender rod of mass 3.5 kg and length 0.8 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 solid cylinder rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A solid cylinder rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 8 m down the slope?
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