Find the moment of inertia of a thin wire of mass

AI Thread Summary
The discussion focuses on calculating the moment of inertia for a thin wire bent into a square shape without a top. The moment of inertia for the two vertical uprights is established as (m/3)b^2. There is debate regarding the contribution of the horizontal part, with some arguing it should not be zero due to its center of mass. The importance of using the parallel axis theorem and correctly defining the rotation axis is emphasized. Overall, the conversation highlights the complexities involved in accurately determining the moment of inertia for this configuration.
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[SOLVED] Moment of inertia

Homework Statement


Find the moment of inertia of a thin wire of mass, m, bent into a square without a top, with each side being of length, b, about its axis of symmetry. (looks like field goal uprights)


Homework Equations



I = I1 + I2 + I3

The Attempt at a Solution



I know the two uprights I are (m/3)b^2. I found a solution on the net that shows the moment of inertia of the horizontal part being 0 because its center of mass is at the origin. I think that there should still be a 1/12(m/3)b^2 contribution from the horizontal part.
 
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Hmm, I don't know if I necessarily agree with your statement for the uprights. Did you try to superpose two rods? You have to remember that the mass given to you is for the whole square thing. The rod equations you are using are not accounting for that. You should also consider that the equation you are using uses the bottom of the rod as the rotation axis. Hint: you may want to consider the parallel axis theorem.

Sorry I can't be much more help, but I don't know what you mean by solution on the net. Where is your origin defined?
 

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