- #1

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## Main Question or Discussion Point

Sorry to bring this question up again.

@aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as:

$$

I=\sum_{n=1}^{N}\frac{\rho}{12}||\vec{P}_{n+1}\times\vec{P}_{n}||(\vec{P}_{n+1}^{2}+\vec{P}_{n+1}\cdot\vec{P}_{n}+\vec{P}_{n}^{2})

$$

in https://www.physicsforums.com/threads/moment-of-inertia-of-a-polygon.43071/ , @chris23 provides a link for the derivation, but the link is dead.

So, can someone give me a hint on how to derive this equation?

@aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as:

$$

I=\sum_{n=1}^{N}\frac{\rho}{12}||\vec{P}_{n+1}\times\vec{P}_{n}||(\vec{P}_{n+1}^{2}+\vec{P}_{n+1}\cdot\vec{P}_{n}+\vec{P}_{n}^{2})

$$

in https://www.physicsforums.com/threads/moment-of-inertia-of-a-polygon.43071/ , @chris23 provides a link for the derivation, but the link is dead.

So, can someone give me a hint on how to derive this equation?