  The spin force operator on a non-relativistic Dirac oscillator ( in the
non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic
oscillator with strong spin-orbit interaction) is derived using the Heisenberg
equations of motion and is seen to be formally similar to the force by the
electromagnetic field on a moving charged particle . When confined to a sphere
of radius R, it is shown that the Hamiltonian of this non-relativistic
oscillator can be expressed as a mere kinetic energy operator with an anomalous
part. As a result, the power by the spin force and torque operators in this
case are seen to vanish. The spin force operator on the sphere is calculated
explicitly and its torque is shown to be equal to the rate of change of the
kinetic orbital angular momentum operator, again with an anomalous part. This,
along with the conservation of the total angular momentum, suggest that the
spin force exerts a spin-dependent torque on the kinetic orbital angular
momentum operator in order to conserve total angular momentum. The presence of
an anomalous spin part in the kinetic orbital angular momentum operator gives
rise to an oscillatory behavior similar to the \textit{Zitterbewegung}. It is
suggested that the underlying physics that gives rise to the spin force and the
\textit{Zitterbewegung} is one and the same in NRDO and in systems that
manifest spin Hall effect.
