The principal axes are the axes about which the product of inertia is zero.

The product of inertia (I_{xy}) of plane area A with respect to x and y axes is given by equation (4.17), as

The above result shows that by rotating the axes through 90^{0}, the product of inertia has become negative. This means that the product of inertia which was positive previously has now become negative by rotating the axes through 90^{0}.

Hence product of inertia has changed as sign.

It is also possible that by rotating the axes through certain angle, the product of inertia will become zero. The axes about which product of inertia is zero, are known as **principal axes.**

**Note.**

(i) The product of inertia is zero about principal axes

(ii) As the product of inertia is zero about symmetrical axis, hence symmetrical axis is the principal axis of inertia for the area.

(iii) The product of inertia depends upon the orientation of the axes.

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