Radius of Gyration for Generic Polygons

AI Thread Summary
To calculate the radius of gyration for a generic convex polygon with a known centroid and constant density, an equation does exist. The suggested method involves triangulating the polygon into smaller parts and calculating the moment of inertia for each triangle around the centroid. This approach allows for accurate computation of the total moment of inertia, which is essential for determining the radius of gyration. Resources such as Wikipedia and specific lab articles provide further insights into the calculations involved. Understanding these methods is crucial for applications in mechanics involving polygonal shapes.
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I need to calculate the radius of gyration for a generic, convex polygon, where the density is constant, the axis of rotation is the centroid (which is known), and the positions of the vertices are known. Does such an equation exist?
 
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