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Transfer of Rectangular Axes

Let us transfer (x, y) coordinate to (x’, y’) coordinate as per Fig. 7.4

the plane area, be represented by IX,  IY, IZ then the moment of inertia of the given plane area about a  parallel axes of the area is given by equations (7.5).

IZ is sometimes written as J i.e., the polar moment of inertia of the area A.