Feb 3rd, 2012
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The document demonstrates how to use the principle of superposition to calculate the centroid and 2nd moment of a 2D object with "holes". The calculation of 2nd moment involving using the parallel axis theorem. The skills are explained in great detail and very easy to follow and apply to other objects.

Word Count: 540
Showing Page: 1/3
Set up the coordinate system as show, because the object is symmetric about y axis, so the centroid (center of mass) must locate on the y axis. We only need to consider y coordinate of the centroid. By definition the y coordinate of the centroid can be calculated by the integrationThat will take a lot of work. The better approach is to divide the object in 2 parts: top rectangle with 2 holes and bottom rectangle with one hole. From the symmetry, the centroid of top part is at the center of the object, the coordinates is X =0, y =10 mm. For the bottom part we can think that it is consist of a complete rectangle plus a hole with "negative" areal mass density, the centroid of complete bottom rectangle locate at (0,20+15) = (0,35mm), and the hole's centroid locate at its center (0, 42.5), assume the area density of the board is ?, then the mass of the bottom board wit

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