[Mikez]

what does degree of freedom mean (in the context of the article below)? I just don't intuitively understand what it represents. How can you possibly "subtract" degrees of freedom when they basically represent where molecules move?
Ex. vibrational energy of linear molecules is 3N - 5

If 3N is the total energy of the molecule (so could be measured in something like Joules) how can you possibly subtract something like "degree of freedom" which is unitless to find the vibrational energy?

Thanks in advance (the article I was referring to is from wiki, some of it is pasted below)

"In 3D, there are 6 degrees of freedom associated to the movement of a mechanical particle, 3 for its position, and 3 for its momentum.

Thus, there are a total of 6 degrees of freedom. An equivalent interpretation is that the movement of the molecule is described by the movement of the two mechanical particles representing its two atoms, and 6 degrees of freedom are attached to each particle, as above. In this alternative interpretation, different sets of degrees of freedom can be defined to describe the movement of the molecule. Simply stated, a set of degrees of freedom for a mechanical system is a set of independent axes in the phase space of the system which allows the generation of the whole phase space. For a multidimensional space like phase space, there is more than one possible set of axes.

It is notable that not all degrees of freedom of the hydrogen molecule participate in the above expression of its energy. For example, those degrees of freedom associated to the position of the center of mass of the particle do not weigh in the energy.

In the table below the degrees which are disregarded are like this because of their low effect on total energy, unless they are at very high temperatures or energies. The diatomic rotation is disregarded due to rotation about the molecules axis. Monatomic rotation is disregarded for the same reason as diatomic, but this effect continues into the other 2 directions."