**Moment of Inertia**

Moment of inertia, also called the second moment of area, is the product of area and the square of its moment arm about a reference axis.

Moment of inertia about the x-axis:

Moment of inertia about the y-axis:

**Polar Moment of Inertia**:

Polar moment of inertia is the moment of inertia about about the z-axis.

**Radius of Gyration**

**Transfer Formula for Moment of Inertia**

= centroidal axis

= any axis parallel to the centroidal axis

= moment of inertia about the x-axis

= centroidal moment of inertia

= area of the section

= distance between x and x’

In the same manner, the transfer formula for polar moment of inertia and the radii of gyration are respectively

**Product of Inertia**

**Moment of Inertia of Common Shapes**

Shape |
Moment of Inertia |
Radius of Gyration |

Rectangle | ||

Triangle | ||

Circle | ||

Semicircle | ||

Quarter circle | ||

Ellipse |

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