![]() ![]() The moment of inertia about any axis can be easily determined for common shapes using a look-up table or other reference. The parallel axis theorem is useful when an object’s cross-section is a composite of several common cross-sections. Therefore, the moment of inertia of an arbitrary shape about any axis can be determined by adding Ad 2 to the parallel centroidal moment of inertia. ![]() The above equation can be generalized to any axis. The second equation is the first moment of area about the x’-axis:īecause the x’-axis passes through the centroid of the body, Q x’ is equal to 0. The third equation is the total area of the shape A. The first equation is the first centroidal moment of inertia of I x’. ![]() Through the parallel axis theorem, the moment of inertia of the shape can be equated as follows: ![]() Dividing the area of the shape A into differential elements dA, the distance from the x-axis to an element is y and the distance from the x’-axis is y’. In general, the moment of inertia of an arbitrary shape about the x-axis can be calculated as follows:įor the shape shown in the figure below, the x’-axis parallel to the x-axis passes through the centroid C of the shape. Derivation of the Parallel Axis Theorem. ![]()
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