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3.3.2: Aproximate Center of Area

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    645
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    thinCM.png

    Fig. 3.3 Thin body center of mass/are schematic.

    In the previous case, the body was a three dimensional shape. There are cases where the body can be approximated as a two-dimensional shape because the body is with a thin with uniform density. Consider a uniform thin body with constant thickness shown in Figure 3.3 which has density, \(\rho\). Thus, equation 9 can be transferred into \[\bar{x} = \frac{1}{tA\rho}\int_{V} x \rho t dA \] The density, \(\rho\) and the thickness, \(t\), are constant and can be canceled. Thus equation 11 can be transferred into

    Approximate \(x_i\) of Center Mass

    \[\bar{x_{i}} = \frac{1}{A}\int_{A} x_{i} dA \]

    when the integral now over only the area as oppose over the volume. Finding the centroid location should be done in the most convenient coordinate system since the location is coordinate independent.

    Contributors and Attributions

    • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.


    This page titled 3.3.2: Aproximate Center of Area is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


    This page titled 3.3.2: Aproximate Center of Area is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Genick Bar-Meir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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