Does Center of Mass make sense in more than three dimensions? In the definition of the Center of Mass we have $dV$. Isn't the volume a three dimensional property? Or it is not and to define the center of mass for, say $4$ dimensions, we just have to calculate a four iterated integral instead of three?
2026-02-23 04:56:34.1771822594
Center of Mass in $N$ dimensions
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It makes sense in any number of dimensions. You are correct that for a continuous distribution you need one integral per dimension. Volume is sometimes referred to as $4-$volume in $4$ dimensions. $dV$ has the dimensionality of the space.