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The dynamics of the spin-orbit interaction in atomic hydrogen are studied ina classical electrodynamics-like setting. A Rutherfordian atomic model is usedassuming a circular electron orbit, without the quantum principle as imposedarbitrarily in the Bohr model, but with an ad hoc incorporation in the electronof intrinsic spin and associated magnetic dipole moment. Analyzing the motionsof the electron spin and orbital angular momenta, it is found that in thepresence of Thomas precession, the total angular momentum averaged over theorbit is not generally a constant of the motion. It is noted this differs fromthe finding of Thomas in a similar assessment of 1927, and the reason for thisdifference is provided. It is found that although the total orbit-averagedangular momentum is not a constant of the motion, it precesses around a fixedaxis similarly to the precession of the total angular momentum vector seen inspin-orbit coupling in quantum theory. The magnitude of the angular velocity ofthe total orbit-averaged angular momentum is seen to vanish only when the spinand orbital angular momenta are antiparallel and their mutual precessionfrequencies equate. It is then found, there is a unique radius where the mutualprecession frequencies equate. Assuming the electron magnetic moment is theBohr magneton, and an electron g-factor of two, this radius corresponds towhere the orbital angular momentum is the reduced Planck's constant. The orbitradius for stationary total angular momentum for the circular orbit model withnonzero orbital angular momentum is thus the ground-state radius of the Bohrmodel.

On the Bohr radius relationship to spin-orbit interaction, spin magnitude, and Thomas precession