What Does 'Moment About a Plane' Mean in the Context of Solids?

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Discussion Overview

The discussion revolves around the concept of "moment about a plane" in the context of solids, exploring its meaning and implications in relation to moments about axes and the center of mass. Participants seek clarification on the definitions and formulas associated with this concept.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the meaning of "moment about a plane," suggesting it may refer to moments about two axes simultaneously.
  • Another participant notes that the integrals related to moments provide a weighted average mass density, which is linked to the determination of the center of mass.
  • A different participant connects the concept of moment about a plane to the center of mass, asking how it relates to balancing the solid.
  • There is a suggestion that the "moment about the xy-plane" could imply the solid's moment about the x and y axes.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definition and implications of "moment about a plane," indicating that multiple interpretations and understandings exist without a clear consensus.

Contextual Notes

Participants have not fully resolved the mathematical definitions or the derivation of the formulas mentioned, leaving some assumptions and steps unclear.

Nikitin
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http://www.math24.net/physical-applications-of-triple-integrals.html

"The static moments of the solid about the coordinate planes Oxy, Oyz, Oxz are given by the formulas"

What exactly does that mean? I understand what a moment about an axis is, but about a plane? what? Do they mean moment about two axis at the same time, or something?

And how did they arrive at the following formulas? http://www.math24.net/images/7tri2.gif
 
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Nikitin said:
Help?

The integrals give you the average mass density weighted value of each coordinate.

One shows that these weighted coordinates determine the center of mass. For a rigid body, its kinematics can be reduced to the motion of its center of mass - I think.
 
If a solid has a moment about a plane, what does this mean? I know that you can find the centre of mass in a solid, and then use this point to balance the solid, but how does this relate to "moment about plane"?

Does the "moment about the xy-plane" simply mean the solid's moment about the x and y axis?
 

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