Re: Center of mass within a two dimentional system

The centre of mass of a system of particles m1,m2,m3 is defined
to be at

Xcm = m1x1+m2x2+m3x3/m1+m2+m3

Ycm = m1y1+m2y2+m3y3/m1+m2+m3

where the coordinates xj, yj are measured from some fixed reference.

Let us take  the origin of a rectangular coordinate system to be centred 
at the O atom, the x axis to be horizontal and positive to the right and
the y axis to be vertical and positive upwards.

 H             H  _
  \           /    |
   \   105¤  /     |
    \-------/      | D = .96A
     \     /       |
      \   /        |
       \ /         |
        O-----------------------------------------> x axis         -


 then

Xo=0
Xh1= Dcot(37.5)=1.3032D=1.2511A
Xh2=                   -1.2511A


Yo=0
Yh1=D=.96A
Yh2=D=.96A

I call h1 to be the h atom on the right and h2 to be the one on the left.

Xcm = Xo*Mo + Xh1*Mh1+ Xh2*Mh2 / Mo + Mh1 +Mh2
    = 0 

Ycm =Yo*Mo + Yh1*Mh1+ Yh2*Mh2 / Mo + Mh1 +Mh2
   
    = 0 + D + D / 16 + 1 +1

    =  D/9

    =  .1067A


So, the centre of mass is located .1067 A exactly above the O atom.