A pendulum is made of a uniform slender rod (3 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 7 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 100 kg and radius 0.45 m. It spins at 600 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 17.5 kg and length 0.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A uniform slender rod of mass 6 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 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 solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
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