A thin rod (uniform density and thickness) has mass M and length L. It is attach

Question

A thin rod (uniform density and thickness) has mass M and length L. It is attached to the floor at a fixed location by a frictionless hinge. The rod starts at rest, balanced vertically on its hinge end. Use the hinge as the pivot (rotational axis) for ALL of the following questions

Question: What is the Final Angular Veloctiy of the rod just before it hits the floor? Wf = ______?

(Hint: Use conservation of energy) Express final answer in terms of variables L, M, g and mathematical consants and use simplest anlgebraic forms)

Explanation / Answer

conservation of energy.
decrease in potential energy = increase in kinetic energy
=> mgL/2 = 1/2 IWf2.
=> mgL = (mL2/3) Wf2.
=> Wf = sqrt(3g/L)

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