From Energy to Angular Momentum: The Chase That Creates Motion

Earlier papers derived mass (From Energy to Mass, DOI 10.5281/zenodo.22042755) and motion from center of mass (COM) shifts when energy overlaps (From Energy to Motion, DOI 10.5281/zenodo.23441924). The response delay the motion work needed to produce burst motion is derived here as the propagation time R/c. When energy interacts, a COM shift cannot complete its response instantly. Effects cross a system's extent R at c, so the response always aims at where the density increase was, not where it now is. The chase never closes. That perpetual three-dimensional chase is angular momentum, and it generates motion. The formula is derived in energy form, A_m = E × R × (R/c) × sin θ × Δ(ρ/ρ₀) × ξ. Expressed through the mass measure M = E/c², it becomes a universal formula for any system with extended mass in motion: A_m = M × v × R² × I_s × sin θ × ξ. A response form exposes c/R as each system's characteristic wobble rate. Projection recovers the familiar formulas: onto a plane, L = mvr; onto a line, p = mv. The rate of change of that projection has the dimensions of force: a derivative of a doubly projected shadow of angular momentum. A companion paper on lift (forthcoming) applies the formula to a wing.