Calculating Volume With Center of Mass

Click For Summary

Discussion Overview

The discussion revolves around calculating volume using concepts related to the center of mass and centroid, particularly in the context of rotating a function around the x-axis. Participants explore the relationship between these concepts and seek clarification on the appropriate methods and equations to use.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests material or proof related to calculating volume with center of mass.
  • Another participant points out the ambiguity in the request, asking whether the focus is on the centroid of a volume or the center of gravity of a mass, noting that these may not be the same.
  • A later reply clarifies the original request, specifying interest in finding the volume of a function rotated around the x-axis and questioning the equivalence of centroid and center of mass.
  • One participant suggests looking up the Theorems of Pappus as a relevant resource.
  • Another participant provides the equation 2πA\bar{x}, where A represents the area between two curves and \bar{x} is the center of mass.
  • It is noted that \bar{x} is the centroid of the area being revolved, measured with respect to the axis of revolution.

Areas of Agreement / Disagreement

Participants express some agreement on the relevance of the centroid in calculating volume, but there remains ambiguity regarding the distinction between centroid and center of gravity, as well as the specific methods to be used.

Contextual Notes

The discussion highlights potential limitations in understanding the relationship between centroid and center of gravity, as well as the need for clarity in the definitions and contexts being used.

iRaid
Messages
558
Reaction score
8
I remember seeing a way to do this, can someone link me to some relevant material or post a proof and equation?

Thanks
 
Physics news on Phys.org
Your request is a little ambiguous. Do you want to calculate the centroid of a volume or do you want to calculate the center of gravity of a mass? The two may not necessarily be the same.
 
SteamKing said:
Your request is a little ambiguous. Do you want to calculate the centroid of a volume or do you want to calculate the center of gravity of a mass? The two may not necessarily be the same.

I'm sorry. I mean: given a function, f(x) and rotating it around the x-axis. Can you find the volume of this function using the centroid/center of mass (I was told these are the same...)?
 
You want to look up the Theorems of Pappus.
 
So it is:
[tex]2\pi A\bar{x}[/tex]
Where A is the area between 2 curves and x bar is the center of mass.
 
x-bar is the centroid of the area being revolved, measured with respect to the axis of revolution.
 

Similar threads

Undergrad Visualizing the Fourier transform using the center of mass concept
  • · Replies 2 ·
Replies
2
Views
7K
High School Mass estimate only through mass rate of change
  • · Replies 4 ·
Replies
4
Views
2K
MHB Mass and Center of Mass for a Lamina with Variable Density and Given Points
  • · Replies 9 ·
Replies
9
Views
2K
High School Question about volume of a sphere
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
4K
MHB Where is the Center of Mass of a Thin Plate with Given Boundaries?
  • · Replies 4 ·
Replies
4
Views
3K
MHB How to Find Mass and Center of Mass of a Lamina Bounded by Curves?
  • · Replies 5 ·
Replies
5
Views
2K
High School How to calculate a hollow cylinder's volume without the hollow center?
  • · Replies 7 ·
Replies
7
Views
2K
MHB How to Find Mass and Center of Mass for a Triangle with Variable Vertices?
  • · Replies 26 ·
Replies
26
Views
4K
Undergrad Conservation of Mass for Compressible Flow
  • · Replies 33 ·
2
Replies
33
Views
4K