  As fundamental parameters of the Sun, the Alfv\'en radius and angular
momentum loss determine how the solar wind changes from sub-Alfv\'enic to
super-Alfv\'enic and how the Sun spins down. We present an approach to
determining the solar wind angular momentum flux based on observations from
Parker Solar Probe (PSP). A flux of about $0.15\times10^{30}$ dyn cm sr$^{-1}$
near the ecliptic plane and 0.7:1 partition of that flux between the particles
and magnetic field are obtained by averaging data from the first four
encounters within 0.3 au from the Sun. The angular momentum flux and its
particle component decrease with the solar wind speed, while the flux in the
field is remarkably constant. A speed dependence in the Alfv\'en radius is also
observed, which suggests a "rugged" Alfv\'en surface around the Sun.
Substantial diving below the Alfv\'en surface seems plausible only for
relatively slow solar wind given the orbital design of PSP. Uncertainties are
evaluated based on the acceleration profiles of the same solar wind streams
observed at PSP and a radially aligned spacecraft near 1 au. We illustrate that
the "angular momentum paradox" raised by R\'eville et al. can be removed by
taking into account the contribution of the alpha particles. The large proton
transverse velocity observed by PSP is perhaps inherent in the solar wind
acceleration process, where an opposite transverse velocity is produced for the
alphas with the angular momentum conserved. Preliminary analysis of some
recovered alpha parameters tends to agree with the results.
