Find the center of mass of the lamina which occupies the portion of the circle x^2 + y^2 <= 1, which is in the first quadrant and has density of rho(x,y)= x*y.
first, i calculated the mass: m= [0,1]int [0,1]int x*y dxdy
the mass i got was (1/4).
second i calculated x-bar (x coordinate):
4*[0,1]int[0,1]int x*x*y dxdy = x coordinate
x-coordinate = (4/6)=(2/3)
third, i calculated the y bar ( y coordinate):
4*[0,1]int[0,1]int y*x*y dxdy = y coordinate
y-coordinate = (4/6)=(2/3)
so the center of mass is (2/3,2/3). Is that correct? I just feel awkward seeing both coordinates equal. Is that what should happen in a circle or is it because the density function was just too simple and perfect?
2007-12-18
13:00:01
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2 answers
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asked by
Kala J
3
in
Mathematics