How to find moments and center of mass for a given shape using integration?

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SUMMARY

The discussion centers on calculating the moments Mx and My, as well as the center of mass for a lamina with a density of ρ = 4, using integration techniques. The calculated values are Mx = 2, My = 12, and the center of mass coordinates are (x, y) = (2, 1/3). The formula utilized for these calculations is referenced from a specific educational resource. The shape in question is defined by the function f(x) = 1/3x.

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  • Understanding of integration techniques in calculus
  • Familiarity with the concepts of moments in physics
  • Knowledge of density functions in relation to mass
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  • Study the derivation of moments using integration techniques
  • Explore the application of density functions in calculating center of mass
  • Learn about different shapes and their respective moment calculations
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Students in calculus, physics enthusiasts, and anyone interested in understanding the application of integration to find moments and centers of mass for various shapes.

tnutty
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Not really a homework problem but related. In one of my homework problem, it says ,
Calculate the moments Mx and My and the center of mass of a lamina with density ρ = 4 and the given shape.
Mx = 2
My = 12
(x, y) = (2,1/3 )

I got the answer. YOUR WELCOME.


But, I only got it because I looked up the formula to find Mx,My and (x,y).
the formula is given in this site near the intro http://www.math.utep.edu/Faculty/javila/Calculus%20II/Math%201312%20problems%20for%20section%207.6.pdf

But I was hoping one of you could prove this, since my book didn't.
 
Last edited by a moderator:
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What is the given shape?
 
it is a function of f(x) = 1/3x.
 

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