Integral Formulas for Center of Mass of Uniform Density

AI Thread Summary
The discussion focuses on calculating the center of mass for uniformly dense objects using integral formulas. The textbook suggests using the formula 1/V ∫ x dV, which is confusing for those unfamiliar with multiple variable integrals. A participant proposes an alternative approach for flat objects of uniform thickness by expressing dV as y(x) H dx, allowing the use of single-variable integrals. This method simplifies the problem for students not yet versed in multivariable calculus. The conversation highlights the need for accessible techniques in understanding center of mass calculations.
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Homework Statement



I'm being given problems regarding the center of mass of a uniformly dense object, and I am told by the textbook to use:

\frac{1}{V}\int x dV

I have no idea what to do with that. I'm pretty sure I won't be learning anything about multiple variable integrals for two years. There must be some other way?

Homework Equations





The Attempt at a Solution

 
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In case of a "flat" object of uniform thickness H, dV=y(x) H dx. So you need single-variable integrals.

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