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Is there any way, perhaps in a different dimension as well, that an object can be constructed to not have a center of mass but a linear center of mass?
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I'm inclined to think not, because if it did, the object could be considered as if it were that line. But then the line itself could be considered as having a point COM, rendering the whole object having that point as a COM.
@brainshot: that is a completely useless answer and I'm sure you know it. Don't it again please.
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