  We use TESS full-frame imaging data to investigate the angular momentum
evolution of young stars in Orion Complex. We confirm recent findings that
stars with rotation periods faster than 2 d are overwhelmingly binaries, with
typical separations of tens of AU; such binaries quickly clear their disks,
leading to a tendency for rapid rotators to be diskless. Among (nominally
single) stars with rotation periods slower than 2 d, we observe the familiar,
gyrochronological horseshoe-shaped relationship of rotation period versus
$T_{\rm eff}$, indicating that the processes which govern the universal
evolution of stellar rotation on Gyr timescales are already in place within the
first few Myr. Using spectroscopic $v\sin i$ we determine the distribution of
$\sin i$, revealing that the youngest stars are biased toward more pole-on
orientations, which may be responsible for the systematics between stellar mass
and age observed in star-forming regions. We are also able for the first time
to make empirical, quantitative measurements of angular momenta and their time
derivative as functions of stellar mass and age, finding these relationships to
be much simpler and monotonic as compared to the complex relationships
involving rotation period alone; evidently, the relationship between rotation
period and $T_{\rm eff}$ is largely a reflection of mass-dependent stellar
structure and not of angular momentum per se. Our measurements show that the
stars experience spin-down torques in the range ~$10^{37}$ erg at ~1 Myr to
~$10^{35}$ erg at ~10 Myr, which provide a crucial empirical touchstone for
theoretical mechanisms of angular momentum loss in young stars.
