Moments, Centers of Mass, & Centroids - Calculus 2

Another application of definite integrals is the ability to find the center of mass for planar lamina, or thin pieces of material with a negligible thickness. However, before we can look at the calculus of finding the center of mass for these planar lamina, we need to discuss what a center of mass even is.

In the most basic case (being in one-dimension), you can think of the center of mass as the balancing point for a see-saw from a playground, where each side contains a particular amount of mass. This concept seems simple enough in one-dimension, but it becomes a bit more complicated when we extend it to two-dimensions. And that will be the focus of this lesson in Calculus 2. Once again, there is a lot to cover here, so let's get started!

In this lesson, you will learn:

• What the center of mass is for a system of masses
• How to calculate the center of mass in one-dimensional and two-dimensional systems
• What a planar lamina is, and how to calculate its center of mass, which is sometimes called the centroid

I hope you find this video to be helpful!

-Josh