Non Uniform Center of Gravity

[crowajordan]

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.

 

[zhermes]

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.

 

[crowajordan]

Thanks for responding. Do you have any thoughts on a program that would be able to do that? Would Solidworks do?

 

[zhermes]

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.

 

[rwisz]

Sure, I would be happy to assist you in calculating the center of mass for your non-uniform object. The center of mass is the point at which an object's mass is evenly distributed in all directions. For a non-uniform object, the center of mass can be found by dividing the object into smaller, uniform sections and calculating the center of mass for each section. Then, the overall center of mass can be determined by considering the mass and position of each section.

To calculate the center of mass for your "shell" object, you will need to first determine the mass and position of each section. This can be done by measuring the dimensions of each section and multiplying them by the density of the material to find the mass. Next, you will need to determine the position of each section by measuring the distance from a known reference point. Once you have the mass and position for each section, you can use the formula:

Center of mass = (Σm x) / Σm

Where Σm is the sum of the masses of each section and x is the position of each section. This will give you the overall center of mass for your non-uniform object.

It is important to note that the center of mass may vary depending on the orientation of the object. So, if your solar car is in motion, the center of mass may shift. It is important to take this into consideration when designing and building your solar car.

I hope this helps you in calculating the center of mass for your non-uniform object. If you have any further questions, please let me know.