# Homework Help: Finding the center of mass of an incomplete circle

1. May 21, 2013

### Jbray

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

Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 .

The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.

2. Relevant equations

x=rcosθ, y=rsinθ, dL=r*dθ

3. The attempt at a solution

I found "M" by integrating "170 dθ" from (-5/6)pi to (5/6)pi. This gave me 890.12mm.

I found "My" by integrating "170 (cosθ) 170 dθ" from (-5/6)pi to (5/6)pi. This gave me 170^2 or 28900mm.

I used My/M to find the x coordinate of the center of mass as 28900/890.12 or 32.468mm. However this is incorrect.

Last edited: May 22, 2013
2. May 21, 2013

### ehild

The solution looks good, but you miss the unit, and try to give the result with three significant digits.

ehild

3. May 22, 2013

### Jbray

I updated the units. I also found out that the answer is supposed to be 70.3mm but I still can't figure out how to get that.

4. May 22, 2013

### ehild

Are the limits -5/6 and 5/6pi, or -5/6pi and 5/6pi? But even then, the result is different from that 70 mm. The given results happen to be wrong quite often.

ehild

5. May 22, 2013

### haruspex

That would be the answer if the angle were -2π/3 to +2π/3.

6. May 22, 2013

### ehild

You are a genius! So they took over the solution from an old version of the problem, while changing the limits in the problem text.

ehild