  We show that the classical equations of motion for a particle on three
dimensional fuzzy space and on the fuzzy sphere are underpinned by a natural
Lorentz geometry. From this geometric perspective, the equations of motion
generally correspond to forced geodesic motion, but for an appropriate choice
of noncommutative dynamics, the force is purely noncommutative in origin and
the underpinning Lorentz geometry some standard space-time with, in general,
non-commutatuve corrections to the metric. For these choices of the
noncommutative dynamics the commutative limit therefore corresponds to geodesic
motion on this standard space-time. We identify these Lorentz geometries to be
a Minkowski metric on $\mathbb{R}^4$ and $\mathbb{R} \times S ^2$ in the cases
of a free particle on three dimensional fuzzy space ($\mathbb{R}^3_\star$) and
the fuzzy sphere ($S^2_\star$), respectively. We also demonstrate the
equivalence of the on-shell dynamics of $S^2_\star$ and a relativistic charged
particle on the commutative sphere coupled to the background magnetic field of
a Dirac monopole.
