A Biology textbook stated that, "single bonds allow the atoms they join to rotate freely about the bond axis".
This definition is not clear enough for me to answer the question, "do two atoms 'participating' in a single covalent bond rotate in only one direction, without rotating the entire molecule?", like this:
I think I have read that single bonds permit rotation, because the overlap between two atoms' orbitals, participating in a single bond, does not change with rotation in one direction, whereas, in double bonds, another pair of orbitals is shared between the two atoms, therefore, rotation of one atom, in any direction, independent of the other, would cause one of these orbital pairs to cease overlap.
So, I take it this is the reason why atoms participating in single bonds, rotate independently of one another, in a specific direction, whereas, atoms participating in double bonds rotate with one another, unitedly, regardless of the direction of rotation.
Moving on, let us say we have an atom single covalently bonded to two atoms, such as our good old friend H2O, let us assume it is linear (which it is not in reality):
H — O — H
If we rotate the single oxygen atom 'sideways' (in line with the hydrogen atoms), I would assume the single bonds between the hydrogen atoms and oxygen atom, would rotate with the oxygen atom to maintain the overlap between the two hydrogens' orbitals and the oxygen's orbitals.
In reality H2O looks more like this:
Therefore, I would assume that rotating the oxygen atom in any direction (up, down, left and right), would result in the orbitals of the hydrogen and oxygen atoms losing their overlap with one another and to maintain overlap, the single bonds would rotate with the oxygen atom.
Thus, why I think atoms in a single covalent bond can only rotate in one direction, without rotating the entire molecule.