# Definition
> The [[Polar Moment of Inertia|polar moment of inertia]] of an object is given by:
>$
J=I_x+I_y
$
# Derivation
Given the radius $\rho$ from the origin to a 2D element $dA$
$
J=\int_A\rho^2\,dA
$
$
\rho^2=x^2+y^2
$
$
\begin{align}
J&=\int_A\left(x^2+y^2\right)\,dA\\
&=\int_ax^2\,dA+\int_Ay^2\,dA
\end{align}
$
$
J=I_x+I_y
$