ROTATIONAL- SHOCK(S) Impulse-Jerk(I-J) [VS. T=I$\alpha $] Plasticity/Fracture Burst Acoustic-Emission(BAE) NON: ``1''/[f=$\omega $]-``Noise''; Power-Law Power-Spectrum is T=I$\alpha $ DERIVATIVE I-J Time-Series Integral-Transform

ROTATIONAL-[``spin-up''/``spin-down'']-SHOCK(S)-plasticity/fracture BAE[E.S.:MSE 8,310(71); PSS:(a)5,601 /607(71); Xl..-Latt. Defects 5,277(74);Scripta Met.:6,785(72);8,587/617(74);3$^{rd}$ Tokyo A.-E. Symp.(76);Acta Met. 25,383(77);JMMM 7,312(78)] NON: ``1''/$\omega $ noise''; Zipf-(Pareto); power-law universality power-spectrum; is manifestly-demonstrated in two distinct ways to be nothing but ROTATIONAL(in 2 OR 3-dimensions)ANGULAR-momentum Newton's 3$^{rd}$ Law of Motion T=I$\alpha $=dJ/dt REdiscovery!!! A/Siegel PHYSICS derivation FAILS!!! "PURE"-MATHS: dT(t)/dt=(dJ(t)/dt)$^{2}$=[I(t)d$\alpha $(t)/dt+$\alpha $(t)(t)dI(t)/dt TRIPLE-integral VS. T=I$\alpha $ DOUBLE-integral time-series(T-S) Dichotomy: $\theta $(t)=[$\varpi _{0}$t+$\alpha $(t)t$^{2}$/2+EXTRA-TERM(S)] VS. $\theta $(t)=[$\varpi _{0}$t+$\alpha $(t)t$^{2}$/2] integral-transform formally defines power-spectrum Dichotomy: P($\omega )$=?$\theta $(t)e$^{-i\omega t}$dt=?[$\varpi _{0}$t+$\alpha $t$^{2}$/2]e$^{-i\omega t}$dt=$\varpi _{0}$?te$^{-i\omega t}$dt+?{\{}[$\alpha \ne \alpha $(t)]/2{\}}t$^{2}$e$^{i\omega t}$dt= $\varpi _{0}$ ($\omega )$/d$\omega $+{\{}[a$\ne $a(t)]/2{\}}d$^{2}\delta (\omega )$/d$\omega ^{2}=\varpi _{0}$/$\omega ^{0}$+{\{}[$\alpha \ne \alpha $(t)]/2{\}}/$\omega ^{1.000\ldots }$: if $\alpha $=0, then P($\omega )\sim $1/$\omega ^{0}$, VS. if $\alpha \ne \alpha $(t)$\ne $0, then P($\omega )\sim $1/$\omega \sim $1/$\omega ^{1.000\ldots }$