I'm just trying to review for an exam and the only thing I don't really get is how to calculate centers of mass. I'll just use two problems I had in my homework that I didn't know how to do. I feel like these two problems should be really easy but I have idea how to do them.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

1. Find the center of mass of a uniform wire that subtends an arc θ if the radius of the arc is a. My terrible MSPaint picture to give you an idea:

2. Find the center of mass of this isoceles triangle:

2. Relevant equations

1/M [Integral] rdm

3. The attempt at a solution

In the first one I tried to use polar coordinates and substitute dm for density*dθ. Density would be M/θ. But when you get to the integral it's 1/θ so you would get the natural log of zero or a negative number depending on how you want to do it.

For the second one, I have no idea where to begin even. Would you have to do a double integral and find the equation of the line that forms the triangle or is there an easier way?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding Centers of Mass

**Physics Forums | Science Articles, Homework Help, Discussion**