Angular momentum preservation problem

AI Thread Summary
The discussion focuses on calculating the angular velocity of a rod that falls and hits the ground at an angle O, with one end stopping upon impact. The moment of inertia is defined as I = (mL^2)/3, and angular momentum is expressed as LsinO*m*v = Iw. The derived angular velocity after impact is w = 3v/L, while an alternative approach equates kinetic and potential energy to yield w^2 = 3gsinO/L. There is uncertainty about the conservation of momentum due to the inelastic nature of the collision, which complicates energy conservation considerations. The discussion highlights the challenges in combining these principles to reach a clear solution.
Guille_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

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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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