# Calculating center of mass and moment of inertia using integrals.

1. Dec 1, 2008

### m00npirate

1. The problem statement, all variables and given/known data
I am very fuzzy about how to find the center of mass of an object and, similarly, the moment of inertia for an object using integrals. Here are the formulas as I remember them.

Center of mass: $$(1/M) \int \vec{r} dm$$
Moment of Inertia: $$\int R^{2} dm$$

What I was wondering was whether anyone knew of any resources with practice problems of this type. Even better would be full solutions.

Types of questions have been to find the CoM for a rod with non-uniform density (with the equation for linear density given) or to find the moment of inertia for various normal shapes (by derivation, not memorization.)

Any help would be greatly appreciated, sorry if this is the wrong forum for this!

2. Dec 1, 2008

3. Dec 1, 2008

### m00npirate

EXACTLY what I was looking for! Thank you so much!

Any more would be helpful as well =]

4. Jan 23, 2009