How Do You Calculate the Center of Mass for a Non-Uniform Object?

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To calculate the center of mass for a non-uniform object, such as a solar car shell, calculus is required to integrate the mass-weighted average position of its components. For uniform shapes, the center of mass aligns with the geometric center, but for non-uniform objects, it shifts towards the denser areas. A practical approach for complex shapes involves using computer software for numerical calculations or creating analytical approximations. SolidWorks is suggested as a potential tool for this purpose, as it includes a motion analysis feature. Accurate determination of the center of mass is crucial for the design and stability of the solar car.
crowajordan
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Could anyone help me figure out a formula to calculate a Center of mass for a non uniform object. In my case it would be a "shell" that would go over a body of a solar car. If anyone could help me that would be great.
 
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Hi crowajordan, welcome to PF!

You just have to use a little calculus to calculate the http://en.wikipedia.org/wiki/Center_of_mass" .

The 'center of mass' is the mass-weighted average position of an object. If you have a uniform, symmetric object: the center of mass is at the geometrical center (e.g. the center of a sphere). If one part was more massive than another (e.g. one hemisphere heavier) then the CoM would be displaced in that direction.

For a complicated object, you have to add up (integrate) over every piece ("differential element") of the object to find the center.

For a complicated real-life object, like a car-shell, you would either need to make a computer-program to calculate it numerically; or make some some sort of analytical approximation to the shape.
 
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Thanks for responding. Do you have any thoughts on a program that would be able to do that? Would Solidworks do?
 
I'm not familiar with programs like that, but I think solidworks should be able to do it. They have some sort of 'motion analysis' macro I believe. Google will know.
 

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