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anonymousphys
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1. Why is 2(pie)rh multiplied by the dr (change in r) equal to the change in volume?
This is in the case of deriving the moment of inertia of a cylinder; the equation is (change in mass)=2(pie)(radius)(height)(change in radius)(density).
I don't quite understand how 2(pie)(radius)(volume)(change in radius) equals change in volume? Is there a proof for this? I can imagine this working mathematically but not conceptually.2(pie)(radius)(height) is just the surface area for each layer, but how does the change in radius come in? I know it has something to do with accounting for the thickness of each hollow cylinder?
All replies are much appreciated. thanks.
This is in the case of deriving the moment of inertia of a cylinder; the equation is (change in mass)=2(pie)(radius)(height)(change in radius)(density).
Homework Equations
The Attempt at a Solution
I don't quite understand how 2(pie)(radius)(volume)(change in radius) equals change in volume? Is there a proof for this? I can imagine this working mathematically but not conceptually.2(pie)(radius)(height) is just the surface area for each layer, but how does the change in radius come in? I know it has something to do with accounting for the thickness of each hollow cylinder?
All replies are much appreciated. thanks.