Calculating Volume With Center of Mass

[iRaid]

I remember seeing a way to do this, can someone link me to some relevant material or post a proof and equation?

Thanks

 

[SteamKing]

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.

 

[iRaid]

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...)?

 

[SteamKing]

You want to look up the Theorems of Pappus.

 

[iRaid]

So it is:
2\pi A\bar{x}
Where A is the area between 2 curves and x bar is the center of mass.

 

[SteamKing]

x-bar is the centroid of the area being revolved, measured with respect to the axis of revolution.