The figure below shows a uniform square plate of edge length 6d = 6.0 m from which a square piece of edge length 2d has been removed. Find the coordinates of the center of mass of the remaining piece.

( , ) m

One way: Replace each visible rectangle with a particle-like concentration of its mass at its center. Then you have a three-particle system as in Sample Problem 9-1. Using only x coordinates, solve for the x coordinate of the com. Repeat using only y coordinates. Another way: Treat the missing section as a particle located at its center, as in Sample Problem 9-2. The com of the whole piece is at the coordinate system origin. You want the com of the remaining piece. The ratio of the mass of piece to the whole mass is equal to the ratio of the area of the piece to the whole area.

HINT: Replace each rod with a particle-like concentration of its mass at its center. Then you have a three-particle system as in Sample Problem 9-1. Using only x coordinates, solve for the x coordinate of the com. Repeat using only y coordinates.

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