Just how do you calculate the rotational inertia of a sphere?(adsbygoogle = window.adsbygoogle || []).push({});

Assuming the sphere lies at the center of the xyz coordinate system, I divided the sphere into a series of cross-sections of verticle width dz and area pi*y^2. I then multiplied these together and multiplied this by z^2, and multiplied this by density (M/V, or M/(4/3*pi*R^3)), and then tried to integrate with respect to z from -R to R. I wasn't sure whether or not to include z itself in the integration (z=(R^2-Y^2)^(1/2)). I have a feeling I completely messed the entire problem up; however, I'm not sure where. :yuck: Did I go about doing it in an entirely wrong way? Should I use double integrals (would that be easier)? Do I have to use spherical coordinates or something?

Any help is appreciated.

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# Homework Help: Calculating rotational inertia of a sphere

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