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 10 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 90 kg has a radius of gyration of 0.55 m about its axis. It spins at 2500 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 8 kg and length 0.7 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 speed v of the free end as the rod swings through the vertical position.
A motor brings a flywheel with a moment of inertia of 30 kg·m² from rest up to 1700 rpm in 42 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A solid sphere of mass 2.5 kg rolls without slipping at 2.5 m/s. Find its rotational kinetic energy Erot.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° 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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