Learning Goal:

To be able to use the parallel$-$axis theorem to calculate the moment of inertia for an area.

The parallel$-$axis theorem can be used to find an area's moment of inertia about any axis that is parallel to an axis that passes through the centroid and whose moment of inertia is known. If $x^{\text{'}}$ and $y^{\text{'}}$ are the axes that pass through an area's centroid, the parallel$-$axis theorem for the moment about the $x$ axis, moment about the $y$ axis, and the polar moment of inertia is expressed by the following equations:

$I_x\frac{?}{b}=ar(I{)}_{x^{\text{'}}}+A{d}_y^2$

$I_y\frac{?}{b}=ar(I{)}_{y^{\text{'}}}+A{d}_x^2$

$J_O\frac{?}{b}=ar(J{)}_{C^{\text{'}}}+A{d}^2$

Figure

$2$ of $3$

$$