Question

What is the general definition of the center of mass? I've already found the integral of the function given radiuses and x values.

Answer 1

I guess to clarify, I need the equation that calculates the center of mass of any object. I can solve the rest for myself, I just don't have a clear idea of how to find the center of mass.

Answer 2

the equation depends on the type or obect you are trying to find the Center of Mass for. is it a square? pyramid? a bus? a plane? anything else?

Answer 3

It's a rod with an increasing radius of constant density.

Answer 4

I've seen elsewhere that it's the integral of the function divided by two, but that doesn't seem right to me.

Answer 5

he centre of mass of a body or a system of particles is the resultant of the weights of the individual particles making up the body or system.
Remember, from the definition of the centre of mass, it is the resultant of the weights of the individual particles making up the body. So we can take moments about any point and:

Moment of the total = the total of moments

In other words, (distance of centre of mass from O) × (weight of body) = the sum of: (the mass of each particle) × (the distance of each particle from O).

The "sum of" part can be replaced by an integral.

This might sound a bit confusing at first, but with practise it becomes second nature.

Another useful equation is: mass = density × volume

Answer 6

this might help too:
http://www.physicsforums.com/showthread.php?t=423162

another guy has a similar problem
:)