For a proton, when its magnetic dipole spin flips in an external magnetic field from the highest energy state to its lowest energy state, to conserve energy, a photon with an energy that equals the difference between these energy states is emitted.$$ Conversely, photons with an energy that precisely equal the energy difference between these spin states is absorbed when the proton's magnetic dipole moment flips from its lowest energy to highest energy state.$$ In our experiment looking at a macroscopic magnetic dipole, as the dipole $($starting from rest$)$ flips from its highest energy state to its lowest energy state, however, its potential energy is converted to kinetic energy, like a ball rolling down a hill.$$ To be more precise, this potential energy is converted to rotational kinetic energy, Krot$=12$I$2($analogous to linear kinetic energy, Klin$=12$mv$2)$ where I is the "moment of inertia" of the dipole, which is the rotational analog of mass $($in other words, the moment of inertia of an object tells us how hard it is to change the object's rotational motion just as mass tells us how hard it is to change$$ an object's linear motion$)$ and is the angular speed of the dipole, which is the rotational analog of linear speed $($in other words, it tells us how much angle $--$ in radians $--$ an object spins through per unit time instead of how much distance is covered per unit time for linear speed$).$

If a dipole, starting from rest and initially pointing opposite to an external magnetic field, is slightly perturbed, it will rotate in order to point in the same direction of the external magnetic field $($its lowest potential energy state$),$ with its potential energy changing to kinetic energy $($just like a ball given a slight push at the top of a hill rolling into a valley$).$ Considering this energy conversion, what is the angular speed of the dipole moment as it passes through its lowest potential energy state $($when it points in the same direction as the external magnetic field$)?$

Group of answer choices

$4$BI