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How can I find final velocity of a metal rod that is hanging by one end...

How can I find final velocity of a metal rod that is hanging by one end when I am only given its total length?

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Answer #1

L = length of rod

h = height of center of mass of rod when rod is in upright position = L/2

m = mass of rod

w = angular speed of rod as rod falls down about one end

I = moment of inertia of rod = mL2/3

using conservation of energy

Rotational Kinetic energy at bottom = initial potential energy

(0.5) I w2 = mgh

(0.5) (mL2/3) (v/L)2 = mg(L/2)                        v = linear speed

(1/6) m v2 = mgL/2

v = sqrt(3gL)

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