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In the equation above for the MI for a rod, why are we taking the limits from -l/2 to l/2?

And why doesn't the integral doesn't include the centre of mass?


The limits run where they are because you're taking the moment about the center of the rod, which means that the center (x=0) of your coordinate system is the middle of the rod.

As for your second question, it doesn't make a ton of sense to me -- the integral runs through the center of mass, but moment of inertia and center of mass are two different concepts.


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