  This paper provides an analytical examination of non-radial geodesics within
the context of the spatially flat Friedmann Lema\^itre Robertson Walker (FLRW)
spacetime. Using the symmetry properties of the system, two constants of motion
related to this dynamical system are derived. This treatment enables us to
explicitly compute the radial and angular peculiar velocities, as well as the
evolution of the comoving radial distance and angle over time. The study
introduces three distinct methods to characterize geodesic solutions, and
additionally examines the radial geodesic limit, the null geodesic limit, and
the comoving geodesic limit. Additionally, the paper investigates both
non-radial and radial free geodesics within the Lambda Cold Dark Matter
({\Lambda}CDM) model, presenting detailed results and discussions. Lastly, we
explore the total angle swept by a free particle from the initial singularity
to infinity as measured by a comoving observer, offering insights into the
dynamics of free particles in FLRW spacetime.
