Where can I find the centre of mass in a 3D co-ordinate system?

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Homework Help Overview

The discussion revolves around finding the center of mass (CM) of an object within a 3D coordinate system, specifically addressing both discrete and continuous mass distributions.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks assistance in determining the center of mass in a 3D context. One participant provides a formula for calculating the CM in Cartesian coordinates and extends it to continuous distributions using integrals. Another participant questions the meaning of the variable 'r' used in the explanation.

Discussion Status

The discussion is ongoing, with participants exploring the definitions and implications of the variables involved in the center of mass calculations. Clarifications regarding the notation and concepts are being addressed.

Contextual Notes

There is a focus on the mathematical representation of the center of mass, including the distinction between discrete and continuous systems. The original poster's request indicates a need for foundational understanding in this area.

smriti
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hi,
Can anyone please help me to find the centre of mass of an object in a 3D co-ordinate system.
Thanks in advance
 
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In cartesian co-ordinates, the CM of of a system of particles is [sigma miri]/total mass. Simply put, multiply the mass at a point by its posn vector, add all of these, and divide by the total mass.

If it's a continuous distribution, it will become triple integral [r*rho(r)dV]/total mass, where rho(r) is the density at r.

EDIT: This is the general form, not limited to Cartesian co-ordinates.
 
Last edited:
can u please wht does the r stands for?
 
r denotes the position vector of a point wrt the origin. For example, if the Cartesian co-ordinates of a point is (x,y,z), then r = xi + yj + zk.
 

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