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Two rigid bodies combined center of gravity

  1. Jan 23, 2009 #1
    Hello all. I'm trying to find the equation for combined Center of Gravity (CoG) when you combine two objects with different weight.

    I know how to find the centroid, which is what the CoG would be if both objects were the same weight.

    But what about two objects with different weight? For an example, I have two square with the area of x^2. Square A weights 40lbs and square B weights 600lbs. If I combined both squares, where would the CoG be?

    I'm assuming the equation has something to do with density, distance of CoG at a specific point, and area invovled. Thanks for the help!
  2. jcsd
  3. Jan 23, 2009 #2


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    Gold Member

    Consider the straight line connecting the CoG's of the 2 items. Find a point on the line where mass times distance (from the individual CoG to that point) is the same for both weights.
  4. Jan 23, 2009 #3


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    Staff: Mentor

    Is this related to the tipping forklift issue at work?

    It would help if you could show us a diagram of what you are asking, but I'll take a try at some hints to help you out. Think of a teeter-totter -- it's balanced when the two weights at the ends are equal, right? Now what if the fulcrum were moved closer to the left weight? How would the two end weights have to be related in order to still balance?

    The concept you use in the above question is "balancing the torques" or balancing the moments. Torque is force X distance. Do you see how balancing the two torques will make the teeter-totter balance? Can you see how this applies to your COG question?

    BTW, I appreciate you mentioning in your other forklift thread that it's okay to move the thread to the Homework Help forums. The threads may still get moved, but I'll leave this here for now.
  5. Jan 23, 2009 #4
    Thanks mathman and berkeman. I see how it's related. I'm not sure why I didn't think of that. Must be late in the day!

    BTW, good memory berkeman! I'm in transition in putting theory into practice and seeing how everything works out. I've already obtained my answer so hopefully someone else may learn something useful out of these scenarios.

    I'm trying to be as broad as I can so I don't leak out anything I'm working on directly. Hope you undrestand! Thanks again.
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