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THEOREM OF THE PERPENDICULAR AXIS

Theorem of the perpendicular axis states that if IXX and IYY be the moment of intertia of a plane section about two mutually perpendicular axis X-X and Y-Y in the plane of the section, then the moment of intertia of the section IZZ about the axis Z-Z, perpendicular to the plane and passing through the intersection of X-X and Y-Y is given by

IZZ = IXX + IYY.

The moment of intertia IZZ is also known as polar moment of intertia.

THEOREM OF THE PERPENDICULAR AXIS

Proof. A plane section of area A and lying in plane x-y is shown in Fig. 4.20. Let OX and OY be the two mutually perpendicular axes, and OZ be the perpendicular axis. Consider a small area dA.

Let x = Distance of dA from the axis OY

y = Distance of dA from axis OX

r = Distance of dA from axis OZ

THEOREM OF THE PERPENDICULAR AXIS

The above equation shows that the moment of intertia of an area about an axis at origin normal to x, y plane is the sum of moments of intertia about the corresponding x and y-axis.