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PRINCIPAL MOMENTS Of INERTIA

Fig. 4.40 (a) shows a body of area A with respect to old axes (x, y) and new axes (x1, y1), The new axes x1 and y1 have been rotated through an angle O in anticlockwise direction. Consider a small area dA. The co-ordinates of the small area with respect to old axes is (x, y) whereas with respect to new axes, the co-ordinates are x’ and y’. The new co-ordinates (x’,y’) are expressed in terms of old co-ordinates (x, y) and angle S as [Refer to Figs. 4.40 (b) and 4.40 (c)]