  We determine the character of orbits of stars moving in the meridional plane
$(R,z)$ of an axially symmetric time-independent disk galaxy model with a
spherical central nucleus. In particular, we try to reveal the influence of the
value of the angular momentum on the different families of orbits of stars, by
monitoring how the percentage of chaotic orbits, as well as the percentages of
orbits of the main regular resonant families evolve when angular momentum
varies. The smaller alignment index (SALI) was computed by numerically
integrating the equations of motion as well as the variational equations to
extensive samples of orbits in order to distinguish safely between ordered and
chaotic motion. In addition, a method based on the concept of spectral dynamics
that utilizes the Fourier transform of the time series of each coordinate is
used to identify the various families of regular orbits and also to recognize
the secondary resonances that bifurcate from them. Our investigation takes
place both in the physical $(R,z)$ and the phase $(R,\dot{R})$ space for a
better understanding of the orbital properties of the system. Our numerical
computations reveal that low angular momentum stars are most likely to move in
chaotic orbits, while on the other hand, the vast majority of high angular
momentum stars perform regular orbits.
