This work presents high-precision measurements of the specific baryon angular momentum j b contained in stars, atomic gas, and molecular gas, out to ≳ 10 scale radii, in 16 nearby spiral galaxies of the THINGS sample. The accuracy of these measurements improves on existing studies by an order of magnitude, leading to the discovery of a strong correlation between the baryon mass M b, j b, and the bulge mass fraction β, fitted by on the full sample range of 0 ≤ β ≲ 0.3 and 10 9 M <M b <1011 M. The corresponding relation for the stellar quantities M * and j * is identical within the uncertainties. These M-j-β relations likely originate from the proportionality between jM -1 and the surface density of the disk that dictates its stability against (pseudo-)bulge formation. Using a cold dark matter model, we can approximately explain classical scaling relations, such as the fundamental plane of spiral galaxies, the Tully-Fisher relation, and the mass-size relation, in terms of the M-j(-β) relation. These results advocate the use of mass and angular momentum as the most fundamental quantities of spiral galaxies. © 2014. The American Astronomical Society. All rights reserved..