A pendulum is made of a uniform slender rod (4.5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 2.5 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (0.5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 8.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 13.5 kg and length 1.4 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 uniform slender rod of mass 7 kg and length 2.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 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 uniform slender rod of mass 7 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 340 m/s hits the rod 0.2 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.
A solid cylinder 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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