A thin rod (length = 1.37 m) is oriented vertically, with itsbottom end attached

Question

A thin rod (length = 1.37 m) is oriented vertically, with itsbottom end attached to the floor by means of a frictionless hinge.The mass of the rod may be ignored, compared to the mass of theobject fixed to the top of the rod. The rod, starting from rest,tips over and rotates downward. (a) What is theangular speed of the rod just before it strikes the floor?(Hint: Consider using the principle of conservation ofmechanical energy.)(b) What is the magnitudeof the angular acceleration of the rod just before it strikes thefloor?

Explanation / Answer

(a)    according to the law of conservation ofenergy the initial energy is equal to the fginal energy so    we can write    Eo = Ef    initial energy is the gravitationalpotential energy and the final energy is the kinetic energyonly    m g ho = m gl              = (1 / 2) m v2       v = (2 g l)    we know that    v = r    = vT / r        = v / l        = (2 gl) / l        = (2 g /l)        = ......... rad / s (b)    we know that angular acceleration     = aT / r       = g / l       = 9.80 m / s2 /l       = ......... rad /s2
   initial energy is the gravitationalpotential energy and the final energy is the kinetic energyonly    m g ho = m gl              = (1 / 2) m v2       v = (2 g l)    we know that    v = r    = vT / r        = v / l        = (2 gl) / l        = (2 g /l)        = ......... rad / s (b)    we know that angular acceleration     = aT / r       = g / l       = 9.80 m / s2 /l       = ......... rad /s2
      = 9.80 m / s2 /l       = ......... rad /s2
      = ......... rad /s2

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