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Math Help - Center of Mass

  1. #1
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    Center of Mass

    I have two problems here that i cant figure out

    EDIT find the center of mass given that the mass is constant

    1.)the "triangular" region in the first quadrant between the circle x^2+y^2=9 and the lines x=3 and y =3 (Hint: use geomentry to find the area).


    2.) Find the center of mass of a thin plate covering the region between the x-axis and the curve y= 2/x^2. 1<=x<=2 if the plates density ate the point (x,y)
    is delta(x)=x^2
    Last edited by cyberdx16; December 4th 2006 at 09:22 PM.
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  2. #2
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    (1)You can view the the region as subtracting the rectangle from the quater-circle.

    Now the centroid of the rectangle is trivial (1.5,1.5) und the area is 9.

    The centroid of a quater-circle is located on the line y=x (that is symettry) and is \frac{4r}{3\pi} (a known formula). In this case r=3. Thus the centroid is \frac{4(3)}{3 \pi}=\frac{4}{\pi}=1.27. Thus, (x,y)=(1.27,1.27). And has area \frac{1}{4}\pi (3)^2=7.06.

    Thus, by the composite centroid formula we have,
    \bar x= \frac{(1.5)(9)-(1.27)(7.06)}{9+7.06}

    \bar y=\frac{(1.5)(9)-(1.27)(7.06)}{9+7.06}
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  3. #3
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    hmmm.... my book say's i should get 2/(4-pie).... i think ur #### gives me the c of m of the semicircle... i want to find the c of m of the triangular shape made by the semicircle and x=3 and y=3
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