A pendulum is made of a uniform slender rod (5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.65 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 0.25 m about its axis. It spins at 1200 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 7.5 kg and length 0.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A uniform slender rod of mass 5 kg and length 1.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 9.5 m along the slope.
A uniform slender rod of mass 9 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 300 m/s hits the rod 0.42 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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