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Applications of Integrals: Moments and Centers of Mass: Example 2: Semi-Circle

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First published at 02:23 UTC on March 27th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over the example of determining the center of mass of a semi-circular plate using the formulas for centers of mass that I determined in my last video. To simplify this problem, I use the fact that a semi-circle is symmetric about the y-axis, thus its center of mass must lie on the y-axis. Thus we only need to solve for the center of mass y-variable. And in that integral I also show how we can simplify the integral by first noticing that the integrand is in fact an even function. This is a very useful video for not only showing how to apply the formulas of centers of mass but also on how to implement integral and symmetry properties to greatly simplify the integral, so make sure to watch this video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104606&authkey=!ACbH4sbFg10MR54&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-moments-and-centers-of-mass-example-2-semi-circle

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