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I General formula for centre of mass of polygons

  1. Jul 15, 2016 #1
    The position vector of the center of mass of a triangle is ##\frac{1}{3}(\mathbf{a}+\mathbf{b}+\mathbf{c})##.

    Screen Shot 2016-07-16 at 4.08.19 am.png

    Is the position vector of the center of mass of a planar four-sided figure ABCD ##\frac{1}{4}(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d})##? Does this generalise to n-sided figure?

    How about a 3D figure ABCD in the form of an arbitrary triangular pyramid (whose faces need not be equilateral)? Is the center of mass also ##\frac{1}{4}(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d})##? Does this generalise to n-dimensonal figure?
     
  2. jcsd
  3. Jul 15, 2016 #2

    mfb

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    Yes to all.
     
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