Proposed Exercise - Mass Center of a Composite Body Determine the coordinates (x, y) of the center of mass of the body illustrated in the picture below

x = 3.76 cm

y = 3.76 cm

Explanation:

This composite shape can be modeled as a square (7.2 cm × 7.2 cm) minus a quarter circle in the lower left corner (3.6 cm radius) and a right triangle in the upper right corner (3.6 cm × 3.6 cm).

The centroid of a square (or any rectangle) is at x = b/2 and y = h/2.

The centroid of a quarter circle is at x = y = 4r/(3π).

The centroid of a right triangle is at x = b/3 and y = h/3.

Build a table listing each shape, the coordinates of its centroid (x and y), and its area (A).  Use negative areas for the shapes that are being subtracted.

Next, multiply each coordinate by the area (Ax and Ay), sum the results (∑Ax and ∑Ay), then divide by the total area (∑Ax / ∑A and ∑Ay / ∑A).  The result will be the x and y coordinates of the center of mass.

See attached image.