Second Moments and Products of Area in the rotated Coordinate System
Second Moments and Products of Area in the rotated Coordinate System: If we know, the second moment and products of area about a reference xy, we can find these quantities relative to a rotated reference x'y' that has the same origin as xy. Let us consider that reference x'y' is rotated at an angle q from xy as shown in figure.
From figure it can be seen that
In the same way,
The product of inertia about the inclined axes is
Thus we can obtain Ix'x' , Iy'y' and Ix'y' in terms of Ixx , Iyy and Ixy.