calculate the centroid for an object use combination principle

Jun 24th, 2016
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As the figure above extended y = 2L and x = 2L line so they form a square of 2Lx2L, Then we can assume that the body is made of a perfect 2Lx2L square plus a quarter circle and the triangle of the upper right corner of the square with negative mass density as the square.

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As the figure above extanded y = 2L and x = 2L line so they form a square of 2Lx2L,Then we can assume that the body is made of a perfect 2Lx2L square plus a quarter circle and thetriangle of the upper right corner of the square with negative mass density as the square.The centroid of quarter circle locates atxc /2 L r cos rdrd00L2434 LL2 34L34yc L3The centroid of the right triangle locates atXc =yc = 3/2L + L/2*1/3 = 3L/2 +L/6 = 5/3LThe area of the triangle is L^2/2The centroid of 2Lx2L square is of cause at (L

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