The Rigid Rotor

There is a theory in elementary physics that you might have seen. It says that it is possible to study the dynamics of a "dumbbell" rotor, of the type shown in Figure 1, by a simple transformation. The two masses rotating about their centre of gravity can be replaced by a single mass, called the "reduced mass", rotating on a circle with a radius equal to the distance between the original masses as shown in Figure 2. The reduced mass is given by the equation:

M = m1.m2/(m1 + m2) .......(1)

Now why would we wish to do such a thing? The answer as follows: We can think of Figure 1 as representing a diatomic molecule; the values of m1 and m2 are the weights of the two atoms and r is the distance between them: a total of 3 parameters. After the transformation we have one less parameter, so any calculations on the physics of the system become somewhat simpler.