Angular momentum preservation problem

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SUMMARY

The discussion centers on the angular momentum preservation problem involving a rod (A-B) of length L that falls vertically and strikes the ground at an angle O. Upon impact, end A of the rod hits a step, preventing further sliding. The calculations reveal that the angular velocity (w) immediately after the collision can be determined using the formulas for moment of inertia (I = (mL^2)/3) and angular momentum (LsinO*m*v = Iw). The derived angular velocity is w = 3v/L, and the relationship between kinetic and potential energy leads to w^2 = 3gsinO/L.

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1. A rod (A-B) with the length L falls straight down with only translational velocity. The angle between the ground and the rod is O. When the rod hits the ground, the end A hits a step which stops A from sliding. Determine the angular velocity right after it hits the ground. http://oi43.tinypic.com/2a7zxpz.jpg



2.
I = moment of inertia
v = velocity
m = mass
w = angular velocity

I = (mL^2)/3

Angular momentum:
LsinO*m*v = Iw = m*L^2*w/3

w = 3v/L


OR


T = kinetic energy = Iw^2/2 becomes
V = potential energy = mgLsinO

Put them equal and you get

w^2 = 3gsinO/L

==========================
I know I am not getting this 100% just don't know how to combine it.
I have used the following as help:
http://www.mech.kth.se/~hanno/LosnTent5C1140Mar05.pdf
 
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I'm not sure momentum is conserved (unless you include momentum of the earth). In the case where the rod is vertical, the rod just stops at the time of collision. The collision is inelastic, so energy is not conserved either.
 

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