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Mechanics volume of revolution question

Image 10-06-2023 at 16.42.jpg
Can anyone explain why they have multiplied y^2 by x in the volume of revolution and why they have multiplied the mass by x bar.
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Original post by Joshholloway3
Image 10-06-2023 at 16.42.jpg
Can anyone explain why they have multiplied y^2 by x in the volume of revolution and why they have multiplied the mass by x bar.

xbar is the position of the com so all the mass acts as through its through that point. Hence mass*xbar gives the moment (/g). Its similar on the right pi*y^2*rho*dx gives the mass of the disc and x is the distance from the plane face so the moment (/g) is the product of the two. So the equation defines the com.
(edited 10 months ago)

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