Center of mass and center of area

AI Thread Summary
The center of mass and center of area are equivalent for bodies with constant density because their mass distribution is uniform, making the geometric center align with the mass center. For non-constant density bodies, the center of mass shifts towards denser regions, while the center of area remains at the geometric center. This difference arises because the center of mass accounts for variations in mass distribution, whereas the center of area does not. An example is a pencil, where the heavier ends cause the center of mass to be off-center from the geometric midpoint. Understanding these concepts is crucial for applications in physics and engineering.
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what is the difference between center of mass and center of area ??

i know that they are the same for an constant density body but why ?and why they are different for nonconst density body??

thank u ,,​
 
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The center is a geometric center, the center of mass is where the mass is balanced. Think about your pencil or pen, usually the eraser and that metal on the end is a little bit heavier, so if you want to balance it you need to have your finger slightly towards it and not in the geometric center, hence its center of mass is where its balanced.
 
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I have Mass A being pulled vertically. I have Mass B on an incline that is pulling Mass A. There is a 2:1 pulley between them. The math I'm using is: FA = MA / 2 = ? t-force MB * SIN(of the incline degree) = ? If MB is greater then FA, it pulls FA up as MB moves down the incline. BUT... If I reverse the 2:1 pulley. Then the math changes to... FA = MA * 2 = ? t-force MB * SIN(of the incline degree) = ? If FA is greater then MB, it pulls MB up the incline as FA moves down. It's confusing...
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