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General Centre of mass derivation

  1. Mar 23, 2015 #1
    Hello,
    It's my first question here. So I'll try to give as much as information as I know

    Actually I am stuck with a problem of centre of mass derivation of a triangle with its base on the X axis and symmetric about it.
    The base is b and height is H

    As far as I know I have to imagine it as a couple of 1d bodies and integrate them.

    Thanks
    SAGNIK
     
  2. jcsd
  3. Mar 23, 2015 #2
    Since its symmetric about the X axis the y coordinate needs to be found only.
     
  4. Mar 23, 2015 #3

    HallsofIvy

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    The y- coordinate of the center of gravity of an object with density function [itex]\delta(x,y)[/itex] is
    [tex]\frac{\int y \delta(x,y) dxdy}{\int \delta(x, y) dxdy}[/tex]
    In particular, if [tex]\delta[/tex] is a constant, it can be factored out of the two integrals and cancelled- that is the "center of gravity" is just the
    geometrical "centroid". Here, we can set up a coordinate system so that the origin is at the center of the base of the isosceles triangle, base
    along the x- axis, height along the y-axis. The equations of the two slant sides can easily be determined.
     
    Last edited by a moderator: Mar 23, 2015
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