  The radiative energy loss of a quark jet traversing a finite size QCD medium
with dynamical constituents is calculated to first order in opacity. Although
finite size corrections reduce the energy loss relative to an infinite
dynamical QCD medium, under realistic conditions it remains significantly
larger than in a static medium. Quantitative predictions of jet suppression in
relativistic heavy ion collisions must therefore account for the dynamics of
the medium's constituents. Finite size effects are shown to induce a non-linear
path length dependence of the energy loss. Our results suggest a simple general
mapping between energy loss expressions for static and dynamical QCD media.
