Quantitative Falsification of the Conservation of Angular Momentum: The 12,000 RPM Paradox in the Standard Ball-on-a-String Demonstration.

The Law of Conservation of Angular Momentum (L) is a foundational principle, routinely demonstrated by reducing the radius of a mass in rotation. A rigorous application of the textbook formula, Li =Lf  (Equation 1), to a typical hand-held demonstration (initial ω=2 rps, rf =0.1ri ) predicts a final rotational speed of approximately 12,000 RPM. This prediction is roughly 10× greater than physically observed, representing a quantitative falsification. While this discrepancy is often qualitatively dismissed as 'friction' or 'non-ideal effects,' the magnitude of the error exceeds the plausible effects of neglected forces. We present a reductio ad absurdum proof demonstrating a flaw in the fundamental mathematical assumption and propose that a different quantity, provisionally termed 'Angular Energy,' is conserved.