No, the nucleus of an atom does not freely rotate with respect to the orbitals. In the quantum mechanical description of atoms, the nucleus is much more massive compared to the electrons, and it is held in place by the strong nuclear forces that bind the protons and neutrons together.
The behavior of electrons in an atom is determined by the electrostatic attraction between the negatively charged electrons and the positively charged nucleus. The distribution of electrons around the nucleus forms the electron cloud or orbitals. However, the motion of the nucleus itself is governed by a different set of forces.
The nucleus experiences its own interactions, primarily the strong nuclear force that binds the protons and neutrons together. This force is much stronger than the electromagnetic forces that govern the behavior of electrons. As a result, the nucleus remains relatively stationary within the atom.
While there can be small oscillations or vibrations of the nucleus within the atom due to thermal motion or external influences, these motions are typically negligible compared to the much larger scale of electronic motion and are often treated as stationary for most purposes in atomic physics.
In summary, the nucleus of an atom does not freely rotate with respect to the orbitals. It remains relatively stationary due to the strong nuclear forces that hold it together.