A pendulum is made of a uniform slender rod (0.5 kg, 1.3 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 190 kg has a radius of gyration of 0.35 m about its axis. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 5 kg and length 1.7 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 motor delivers a torque of 140 N·m at 2700 rpm. Find its power output P in kW.
A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 6 m down the slope?
A uniform slender rod of mass 6.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 220 m/s hits the rod 0.34 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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