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Math Help - Finding a Common centre of gravity

  1. #1
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    Finding a Common centre of gravity

    Hi there, i have a problem that needs solving. Put simply it goes like this:
    I have lots of objects all referenced from there own centres of gravity to a point in 3D space and i need to know the common centre of gravity of all these objects combined.

    I dont know if i am just not seeing the easy solution to this or whether it is genuinely a complicated problem...

    Any ideas on an explanation or a formula, that Excel could handle to do this, would be awesome.

    All the points have an X,Y,Z position on Right hand coordinate system.

    Cheers, Nad.
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  2. #2
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    Are all these constituent centers of gravity referencing the same point in 3D space? If so, let \mathbf{r}_{j} be the vector from the common reference point O to mass m_{j}. Then the vector \mathbf{R} from point O to the overall center of gravity is given by

    \displaystyle \mathbf{R}=\frac{\sum_{j}\mathbf{r}_{j}m_{j}}{\sum  _{j}m_{j}}.
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  3. #3
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    Yes after doing a bit of research i came up with the same formula, thanks for confirming it.

    But now im struggling in putting that into an excel format to deal with the list of co-ordinates i have!
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  4. #4
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    You can do everything component-wise with the sumproduct and sum functions in Excel. Look at the help (hit F1 in Windows, anyway) to look up the syntax. The vector equation I gave is valid if you only look at one component at a time. Make sense?
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  5. #5
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    Yeh that makes sense, i take it you dont have to take the mass as a vector too, as that would surely give errors (well, zeros) as it only acts in one direction? you just leave it as kg.. yeh i think i get it :P ill crack on with it tomorrow, thanks very much.
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  6. #6
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    Right. Mass is not a vector quantity, at least not in your context. Let me know how it goes.
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  7. #7
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    Worked a treat, Thankyou!
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  8. #8
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    You're welcome. Have a good one!
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