# Moment of Inertia of a System

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1. Mar 30, 2015

### Okazaki

1. The problem statement, all variables and given/known data
"a uniform steel rod of length 1.20 meters and mass 6.40 kg has attached to each end a small ball of mass 1.06 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. Find the moment of inertia of the ball-rod system."

2. Relevant equations
I = (1/12)ML^2
I = MR^2

3. The attempt at a solution
So, my friend was trying to help explain to me the solution to this, but I'm kind of stuck on it. See, what she did was:

I(system) = I(ball) + I(rod)
= MR^2 + (1/12)ML^2
= M(L/2)^2 + (1/12)M(L)^2

My question is why you can assume that the radius of the ball is apparently half of the length of the rod. That doesn't really seem like a logical conclusion to make.

2. Mar 30, 2015

### Okazaki

Wait! Never mind. I just looked through my notes again. "R" (as it is defined here) is actually just the perpendicular distance that a particle (in this case, the ball) is from the given rotation axis. In that case, R should be L/2 here.

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