How to Calculate Moment of Inertia for Polygons in a 2D System?

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Calculating the moment of inertia for a polygon in a 2D system can be achieved using a double integral without the need for triangulation, provided the polygon has a continuous mass distribution. The moment of inertia should be calculated relative to the polygon's centroid, and the axis of rotation is critical for accurate results. While triangulating the polygon simplifies calculations, it is not strictly necessary; however, the polygon must be "star-shaped" for certain formulas to apply. The discussion also highlights the importance of density in calculations, as discrepancies can arise from using different mass or density units. Overall, understanding the relationship between mass, density, and the geometry of the polygon is essential for accurate moment of inertia calculations.
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GINGERBEER said:
Sorry to comment on an old thread but i was just wondering why the ||\vec{P}_{n+1}\times\vec{P}_{n}|| is not canceled out in the equation seeing as it is in the numerator and denominator.

You can only cancel common factors in the numerator and denominator.

Just because a given term in the numerator happens to include a factor that is identical to a term in the numerator does not make this into a common factor.
 

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