# Homework Help: Center of mass

1. Jun 15, 2012

### Jalo

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

Given a homogenous rectangular surface, sides of length a and b=4*a, with a circular hole in x=a and y=a/2, find the center of mass.

2. Relevant equations

R=1/M*Ʃmi*ri , M= total mass, r= position vector

area of a circle = pi*r2 , r being the radius

3. The attempt at a solution

I determined the center of mass of the surface and circle and tried to subtract one from another, however the result did not agree with the solutions.

Acircle=pi*r2 = pi*a2/4
Arectangle= a*4a = 4a2
Center of mass of the rectangle alone:
Rr=(2a,a/2)
Center of mass of the circle alone:
Rc=(a,a/2)

R=[Rr*Arectangle - Rc*Acircle] / Total area ⇔
⇔R=a*(32-pi)/(16+pi)

The correct center of mass is (2,05,a/2)

Thanks!

D.

2. Jun 15, 2012

### vela

Staff Emeritus
You need to subtract the areas in the denominator because you're considering the circle to have negative mass. Right now, your calculation is for the solid slab plus a positive-mass circle located at (-a, -a/2).

Also, to get the answer you cited, I think you need a different radius for the circle. Is the radius of the circle really equal to a/2? If so, you won't get that answer.