# Rotation-Equation Problem

1. Mar 11, 2008

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Hi! I have a problem here that i got on a practice worksheet. It's all about deriving an equation for the rotation of a rod! :S
1. The problem statement, all variables and given/known data
A thin uniform rod that is L long and M in mass pivots about one end (the rod is hanging from a pivot attached to the ceiling). Suppose a small mass of 2M is attached some distance from the pivot and released horizontally from rest, and allowed to swing downward without any resistance of any kind. What is the equation to determine the speed of its tip when the rod is at vertical position?

The answer given is: vt=$$\sqrt{3gL}$$$$\sqrt{\frac{1+4(d/L)}{1+6(d/L)^{2}}}$$

2. Relevant equations
Ei=Ef
Ei=0.5Iw$$^{2}$$+MgL

Ef=0.5Iw$$^{2}$$+Mg(d/L)

I (for rod rotating by one end)= (1/3)ML$$^{2}$$

vt=wL

I'm using 'w' as omega because I can't get it to stop looking like an exponent for some reason when using latext.

3. The attempt at a solution
I know how to do the question when the center of mass is directly (L/2) for the rod, in which case using the equations above gives me a speed equation of $$\sqrt{3gL}$$. But I'm completely thrown off by the addition of mass as that changes the centre of mass (I'm not sure what to do with that). My attempt so far is starting off with relevant equations.

I really appreciate any pointers to help me out! Thanks!