degrees of freedom (physics and chemistry)

Degrees of freedom are basically all the ways a thing can move without violating any constraint imposed on it. Imagine a square bead on a taught string. It can slide all along that string, that's one degree of freedom. It can also spin on its axis, that's another. So that bead on a string has 2 degrees of freedom.

Now, every individual gas molecule can translate in any spatial direction (basically freedom of movement through space), like sliding on a string, and then there's freedom in terms of rotation like spinning on an axis. But rotational degrees only apply if the movement makes a meaningful change in orientation. A monoatomic gas has only 3 degrees of freedom. While it can both move freely through space \[(x,y,z)\] and rotate, since it's symmetrical (being only a single atom, more or less a sphere), its rotations doesn't really make a difference.

A diatomic gas has an extra atom. It can move through space, but the extra atom means it does make a difference if it rotates. Spinning on its axis doesn't change anything, but rotating it up or to the side changes its orientation. It can also have intermolecular vibrational motion stretch along its axis, like a bungee cord. So it has three spatial degrees of freedom, two rotational degrees, and one longitudinal degree, for a total of six.