How to Derive the Reduced Mass Formula for Inertia between Two Atoms?

[Jex]

Does anyone know how to actually derive the reduced mass formula? I have to prove the formula: inertia = (reduced mass)r^2 and am having some difficulties.

To be more specific I'm working with the inertia between to atoms where r is the bond length.

Any help with this is much appreciated, really.

 

[Hootenanny]

This may be of some use http://farside.ph.utexas.edu/teaching/336k/lectures/node54.html

 

[tim_lou]

are you talking about the 2 body problem or the moment of inertial? if you are talking about the moment, then around which axis is it calculated? the axis orthogonal to the plane of rotation and at the center of mass of the system?

 

[tim_lou]

if it is what i think it is, then:
let a=r1, b=r2, a+b=r, m be the mass of the first body, M be the mass of the second body, and r be the bond length:
$I=ma^2+Mb^2$
relative to the center of mass:
$ma=Mb$
$I=(ma)a+(Mb)b$
$I=ma(a+b)=mar$
$a=r-b=r-ma/M$
$a(1+m/M)=r$
$I=mar={m\over{(1+m/M)}}r^2$
so
I=reduced mass*r^2