What is the formula for the first moment?

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Discussion Overview

The discussion revolves around the concept of the first moment of mass, its relationship to the center of mass, and the distinction between the first moment and the moment of inertia. Participants explore definitions and mathematical formulations related to these concepts.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states that the first moment divided by the total mass yields the center of mass, questioning what constitutes the first moment.
  • Another participant asserts that the first moment of mass is defined as mass times distance.
  • A question is raised about whether the second moment of mass is equivalent to the moment of inertia, which is confirmed by another participant.
  • Concerns are expressed regarding the interpretation of the first moment and its relation to the center of mass, specifically questioning how dividing the first moment by total mass results in distance rather than the center of mass.
  • A clarification is provided that the distance obtained from the first moment calculation refers to the center of mass from a reference point, emphasizing the need for position vectors in the calculation.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the definitions of the first moment and its relationship to the center of mass, but there remains uncertainty and debate regarding the interpretation and implications of these concepts.

Contextual Notes

Participants discuss the need for clarity on the definitions of terms such as "first moment" and "center of mass," as well as the importance of using position vectors in calculations. There are unresolved questions about the distinctions between the first moment and the center of mass.

avito009
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The first moment divided by the total mass is the center of mass. Now I know that a moment is a combination of a physical quantity and distance. So what is the First moment made up of? I know that moment of inertia is made up of mass times the radius (distance) squared.
 
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The first moment of mass is just mass times distance.
 
So is the second moment of mass "Moment of Inertia"?
 
avito009 said:
So is the second moment of mass "Moment of Inertia"?
Indeed it is.
 
According to Wikipedia, the first moment divided by the total mass is the center of mass. But as per what you say the first moment is mass times distance so if we divide that by the total mass we get the answer as distance. m*r/m=r. But distance is not the same as centre of mass. How?
 
avito009 said:
According to Wikipedia, the first moment divided by the total mass is the center of mass. But as per what you say the first moment is mass times distance so if we divide that by the total mass we get the answer as distance. m*r/m=r. But distance is not the same as centre of mass. How?
That will give you the distance of the center of mass from some reference point (where the distances were measured from).

More precisely, those distances really should be position vectors. To get the position vector of the center of mass, you would add up all the first moment elements (##\Sigma m_i \vec{r}_i##) and then divide by the total mass.
 

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