(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive the moment of inertia for a solid sphere with a uniform mass

2. Relevant equations

[Tex]I= \sum mr^{2}[/tex]

3. The attempt at a solution

I decided to change everything to polar coordinates. Since the polar coordinate substitution is

[tex]\int\int\int_{v} Fr^{2}sin(\phi)drd\phi d\theta[/tex]

I figured that all you should do is plug in the moment of inertia equation into the integral giving you:

[tex]m\int^{2\pi}_{0}\int^{\pi}_{0}\int^{R}_{0} r^{4}sin(\phi)drd\phid\theta =\frac{4\pi R^{5}}{5}[/tex]

however this does not seem to be the correct answer. Can anyone tell me what I'm doing wrong? Thanks in advance for your time and any help.

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# Deriving the moment of inertia for a sphere

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