- #1
Tomas Carvalho
- 3
- 0
Homework Statement
We have a circle of radius 4 with center at the origin of a referential, and a circle hole in it of radius 1 and center at (-2,0). We're supposed to calculate the center of mass.
2.MY QUESTION.
I know, by the usual formulas for calculating center of mass I get 2/15 as the x of the center of mass, however I don't know why this other approach doesn't seem to work:
I'm assuming that any line passing through the center of mass divides the body into two equal mass parts. As such, if we draw a vertical line through the center of mass we're looking for, the area inside the cricle between that line and the one passing through the center has an area of pi/2 (simple calculations so that area to the left is equal to ares to the right of line), so calling b the x of the center of mass:
The indefinite integral from 0 to b of sqrt(16-x^2) should be equal to (pi/2)/2)=pi/4, but once I input this on wolfram alpha I get an approximate value of 0.196 which doesn't seem correct.
How so?