Center of Mass

  • Thread starter Thread starter Gerhard
  • Start date Start date
G

Gerhard

Hello together,
i have a 20*10 matrix with positive integer-values and I have to calculate
the center of mass of this "volume". Should be easy in Excel...but what's the
easiest way of doing it?
Best Regards
Gerhard
 
Gerhard,

What do the integer values represent, and what does the matrix represent?

HTH,
Bernie
MS Excel MVP
 
I can solve this problem with these assumptions:
1) the integers represent mass and
2) the first mass is in located at point (1, 1) on Cartesian plane.
I will demonstrate with a 2 by 3 matrix
1 1
2 2
1 1

I located this in A2:B4 but it can be anywhere provided you adjust the
formulas
In A6:B* I compute the X coordinate of each mass; in A6 use
=ROW(A2)-ROW($A$2)+1 and copy down and across
1 1
2 2
3 3

Likewise in A10:B12 find the Y coordinates; in A10 use
=COLUMN(A6)-COLUMN($A$2)+1
1 2
1 2
1 2

The inner term in these allows you to move the data on the worksheet

The X coordinate of the centre of mass is give by
=SUMPRODUCT(A2:B4,A6:B8)/SUM(A2:B4)
The Y coordinate of the centre of mass is give by
=SUMPRODUCT(A2:B4,A10:B12)/SUM(A2:B4)
The result (2, 1.5) agrees with other ways of computing this example.
Clearly if the first mass is on the origin, we need to subtract 1 from the x
and y values.
Email me (remove TRUENORTH.) and I will send you a file
best wishes
 
Depending on how you look at the matrix, you may wish toe reverse X and Y in
my demo
 
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