We use TESS full-frame imaging data to investigate the angular momentum evolution of young stars in Orion Complex. We find that sources 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. Using spectroscopic vsini 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 Teff is largely a reflection of mass-dependent stellar structure and not of angular momentum per se. Our direct empirical measurements of the spin-down torque provide a crucial empirical touchstone for theoretical mechanisms of angular momentum loss in young stars.