Calculating the Polar Second Moment of Area

Figure 1: Polar second moment of area

There is a lot of confusion when it comes to the polar second moment of area (also known as the polar moment of inertia), but the summary diagram at the end of this page is essentially all one will practically need to know about it. It can, however, be helpful to have an idea of how we got there.

The following video explains it nicely:

Figure 2: Polar Second Moment of Area(SnugglyHappyMathTime, 2015)

If you prefer to read:

The polar second moment of area of an object can be calculated using the following equation:

In other words, the polar second moment of area for symmetrical objects is equal to:

J = 2I

Using that, the equations for the polar second moment of inertia of specific shapes can be derived:

Figure 3: Polar moment equation summary for common cross-sections (Engineersedge.com, 2019)

References

Engineersedge.com. (2019). Polar Moment of Inertia, Polar Section Modulus Properties of Common Shapes - Engineers Edge. [online] Available at: https://www.engineersedge.com/polar-moment-inertia.htm [Accessed 6 May 2019].

SnugglyHappyMathTime (2015). Polar Moment of Inertia for Area. [video] Available at: https://www.youtube.com/watch?v=-V-qjog6t94 [Accessed 7 May 2019].