![]() There is perpendicular axis theorem for the area. The moment of inertia is minimal when the rotation axis passes through the center-of-mass and increases as the rotation axis is moved further from the center-of. ![]() The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. This holds true for all regular polygons. Moment of Inertia is the integration of the square of the distance of the centroid and the del area along the whole area of the structure. Parallel Axis Theorem: The moment of inertia of an area with respect to any given axis is equal to the moment of inertia with respect to the centroidal axis plus the product of the area and the square of the distance between the 2 axes. The following is a list of second moments of area of some shapes. The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin. Mechanics Map (Moore et al.) 17: Appendix 2 - Moment Integrals. ![]()
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