Understanding Moment of Inertia in a Ball-Rod System

AI Thread Summary
The discussion centers on calculating the moment of inertia for a system consisting of a uniform steel rod and two attached balls. The relevant equations for moment of inertia are provided, specifically I = (1/12)ML^2 for the rod and I = MR^2 for the balls. The user initially struggles with understanding why the radius (R) for the balls is considered half the length of the rod. Upon reviewing notes, it is clarified that R represents the perpendicular distance from the rotation axis to the balls, which is indeed L/2. This realization helps in correctly applying the moment of inertia formulas for the entire system.
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Homework Statement


"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."

Homework Equations


I = (1/12)ML^2
I = MR^2

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.
 
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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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