Example :①F=R+1=V(t)R2福J=rxm=(R+I)xv(t)RmR= mv(t)I × k= mv(t)lk7didRdRdldrdlv(t)kdtdtdtdtdtdtdldRdli=-0 Ro(-i)+i=0RO=福dtdtdtdt
R r L V0 V Example : r R l = + v = v(t) R J r mv = mv t lk mv t l k R l v t R m ( ) ( ) ( ) ( ) = = = + = = + = + + l dt dl l dt d l dt dR dt dl dt dR dt dr v t k ( ) + = 0 l dt dl dt dR (− ) + = 0 • l dt dl R l dt dl R = •
dedld(-l)DklTdtdtdt1 d?1 dlVoR=Vok dt2 dt水[2 = 2v.Rl3(t)=v(t)k→=ok1 dlAdl④Vokdtdt
k l dt d l dt d l l dt d l v = − = = ( ) kl l = dt dl k v 1 0 = dt dl v R 2 0 21 = l v Rl 0 2 = 2 v(t) = v(t) k → v = v 0 k l dt d l v = l dt dl k v 1 0 = R r L V0 V
1-3 Center of mass framedjM=available in inertia systemdt=+r=r+ricM=ErxFexr:C=E(r +r)xFr=ErxF" +rx(EF")C0=M"+rxFJ-Erxmy=E(r+r)xm(yxv)
i ic c r r r = + i ic c v v v = + 1-3 Center of mass frame ex i i M ri F = = + i ex ic c F i r r ( ) dt dJ M = available in inertia system. r r r c o i ic = + c i i ex c i ex r ic F i r ( F ) ex c ex M c r F = + = i i i i J r mv = + i ic c i ic v (r r ) m (v v )
=(r xVm+r xym +mrxy +mrx))=E(rxm)+rxJ=J.+mr,xy1 Orbital angular momentumProper angular momentumspin :intrinsic spinAtom:↑electronJ=S+LDiracStorynuclearHesienberg
= + + + i ic ic i ic c i i c ic i c c (r v m r v m m r v m r v ) = + i ic ic i c c r v m r v ( ) c c c J J mr v = + Orbital angular momentum. Proper angular momentum J S L = + electron nuclear Atom: spin : intrinsic spin Story Dirac Hesienberg
[J=J.+r.xm)djdjdmv+r x-CdtdtdtM= M.+r,xFexdpdPr.xFex=r.xFer -dtdtdjavailable in non-inertia system= MexrthenWhy? How about M inertia ?dtMimer-ErxFiner =Eriem,ainer =(Eriexm,)a, =0
dt dmv r dt dJ dt dJ c c c = + = + = + ex c c c c c M M r F J J r m v dt dP F ex c = dt dP r F rc ex c = ex c c M dt dJ = →M iner i i i ic iner i i Miner ric F r m a = = = ( i) i = 0 i ric m a then available in non -inertia system. Why? How about inertia ?