Educator

Center of Mass

Main formula:

Hints and tips:

• These formulas are not symmetric. You don’t get from one to the other just by switching x’s and y’s!

• Often you will have to do another integral to find the area, . However, sometimes you can find it just using geometry, such as the standard formulas for areas of rectangles, triangles, and circles.

• If the region has horizontal or vertical symmetry, you can use that to find the corresponding coordinate of the center of mass without integrating.

• When it’s feasible, check that your answers make sense. Graph the region and locate the coordinates of the centroid that you found. Are they inside the region? Are they approximately where it looks like a plate of that shape would balance?

• The centroid of a triangle with a horizontal base is always 1/3 of the way up from the base.