Area Moment of Inertia | Product of Inertia

**Polar Moment of Inertia:**
The polar moment of inertia of area A shown below about point O is
defined as

(3) |

Since x and y form the rectangular components of distance r, we have the equality

Thus, the polar moment of inertia is simply the sum of
I_{x} and I_{y} defined by Eqs. (1) and (2).

**Application:** The polar moment of
inertia is used in finding the shear stress and twist angle in
shafts under torsion.