I am having a bit of trouble deriving the moment of inertia for a disk with uniform density:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]I=\int r^{2}\,dm=\int \rho r^{2}\,dV[/tex]

For a disk, I just used dA instead of dV. Now, to calculate the density:

[tex]\rho = \frac{\text{mass}}{\text{volume}}=\frac{m}{\pi r^{2}}[/tex]

So now we have:

[tex]I=\int \rho r^{2}\,dA=\frac{m}{\pi}\int \,dA=\boxed{mr^{2}}[/tex]

However, I know that the moment of inertia for a disk is [itex]\frac{1}{2}mr^{2}[/itex]. Where did I go wrong?

Thank you.

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# Moment of Inertia of a Disk

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