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Cone omas Cewainvoaluonw or-Anaan momintum VaruiablL MAMAHatem dm- dv N oaAyshm a numb o parkels, Ao a pan Cw...

Cone omas Cewainvoaluonw or-Anaan momintum VaruiablL MAMAHatem dm- dv N oaAyshm a numb o parkels, Ao a pan Cwantng u entve has whue bekavi as s tha prnt and SHptem tentenbralnd a o tm m mouov mottn t UT dunubld Awms of u motun o- syatm Can ki Core o man Aysttm N baukoles o manis mas t Cemide aw1HK 0huvess YYY N An figo shnen ti o shnn Fig0) nive atiud aigm o T r Coubrond suptem otarrole o u The ThL Cehe o that ot mam Cavin hration vuew duine a bru w T t Y,t N  N M frtal ma) o a sptem ThThu expema w lhe gtun veav oUa Censye omam (c.M) o astom porheles to venh N m Yi - roAn abo duhunihw, we draw two Cnelumms Ci) all t N hrhelun Rave a sane 4nas m N N N M=Nm N CN Conedw Ths npiyhak D e né enve Kpttm enre otm (i) weak huw or nk Attm N Th w u um ok h mauenb mami yphtm ab n Chre omax b uo. s condinalis o 9e ew a s Kawr N L 2 2 arhel. Cnhr oAA o arid bodu bodus ne a ung numb o SCaA 14d parked,madium hahen N ) a tight A mmakun bw hhnawn amd i onst nuas oLeen tnterahun ie torkt nuruy Ca h ekangad vetkw ou oparhele, u bcntun Asm n t e n an wnten An o mas wre o wh dm a,duhalFy may elm ( w n in hg) hunk o d n an nteyod, visualig Ahai ovome dv Jstated nan elmn Dhmam mam donm at r. aohtuw H n dm = dv ad elomint i , Tdv. Y mtyral enlnd a voum ib Tw tegrad Tw an a m r ad uin raollsy s o-e.H of-C.H and om ) Va dw dm d dn 7 dm dm 2 d = dm dm ervdinaln o &teuhal ma elumim dm ad Xem +Yo +2 Ycm  Cenhre oa vuw daen i enbruman tv \hu pmtu Astew o badkelen M hae Rittounkahng t 0.r.t. tmu N H i Ve =P mininkun MM Vw As Cnhr otma and A velru ot Thn Hu vtn 1 bavtrel, velru h wapMtm h velsih oR-asyple»dot-pedrhelks lhi t t l h hi e M Onent Ve h.S. e g 2 ) i l tral inan mgmintun Th oenwtnalr u abstnti Jw Yenatnß lonat mOmUntum P 2 m 0; tor n k ensiof. srt u VYunaus and n e e H as ha ua eM b an Imhelm punr A absnes oerlnal absnel o eltnal Tw T h unthard n u vuluty Tenalns Konaradio atttve u l e p ub fd enanpA dos v eonan vebu, move tn ditfeu moviny A91 patkele phel, A bu he velou umb i&ipteaunt veiu its ma n a n m e diyuks Aeir Conbe o gpANtpdsg- stav_ Thetts k M G wp R k Imlonal tovee bueon a New ton A izd aw batttel oha syaem dhiy u fovUo ir TMatual Inlinthas bMotm Etk eultans e a t l behw TWin erlbnal 1e attung n ln Apkem, t ave a Vem F o a C.H sspm e bartelus mo ves Thu u erlot nal yanlrat a total mam and sena abplied a thu pn ve te F o n ), No wtung eirnad = d th CBskrn reaultnt enlornal tar hws hun Aave a m patreles Yemalnd etantF ie. n uomAntuN AhT e N ethu a Cemalnved n meh a a Mort L8h Cotant velsTih Cm O mn pli dephklvotun Tws kmth n Cnhre eGrav qrailakiend bauieles na ni owm aAsun o CaUlP Lhe Cerre a A AOmd emty idd, Core o ra  (10) Calewdalcb eahye o mam (CH- Conhe o ma o wo bolhiolw P X- a s d omass MA Cenaielu a s4ptem oAO burcles d aMd M, Alpandted ey d antl eN. o u systen We Aave elullz 1uz and lk x -am als omqpn 0 a m, a nu 10nhg nd m and m an_gevenb ane_gvn Udimalus o Th Th (0,0,0), (d,0,o) pwvelz mt2 mam N The tt AiU bt a hm lhi C.H. dne O 2 en CAM two pantt ols u l n oun  (IO Conre o mam oa wtYm sou gkt-so o A B X-ans lgu MandL l Aq mam and i uM Osiqtn a a L end o Yod akl k rod X-ann aling i longbk ohz od o d ana rod lautwten Ue elannt (dm) o- i an Conadev O n d ntdx 0 h on o f i Tod M long The mas 2 n unt d = M dx emen-b (,0,0). ohi &uT rod londindis e utCN o nd X-Lndinal The d == Xn d M i e.M e. M e nmdd nnaa lltt ot o 2 T s n d. Ond Y, 0,2-0) vod u at(X at(Xe T h eH oU  0 Cemhre omas oawnmtam Smi irtnlan wire M lo lh M a and R h -Rdo r a d i u o u Unsorm R6mo semicAra r e ORus X ive a A eLnhre o nds a X-a 0UnungJu two amd hu u aun ve md u Y-an n X-1 Xant heM. mus Rdt o aire ak an dnint o y& b oh m lnyh e d i n a l u n me) ( = Rer,, 7 R eire nu ntk o TR Th mam dm= M(RdA) Rdo) elonn JTR AL o =Hdg JT aCH nu Tu Cdinal Hd CRe) 0 d m JT M JT (R h t ) Mdo 2R JT JT oie at0, 2R ) AL C.N. h  (101) 4 Conre s ma t a unem inieirtwla pla R 0 a sinieirenlonpadi , a A eCahre o a and iY-aww shaighF edga X-0 alg shauy ma and R u vaduuo of-ki KM b drad a n d n i id o Yodiwr and Yodiw d Y Cenidn l oTods aKd YHdr smieirnlM hi h) Can treaed rgion h a d a d ryion shodsd mh m his u Riknun dr dr No tye o elemnhol ALeirla Non oe fov lu aAki eH. o ARNUYulan| ah  (105 NA nloa o h adsd yuiom e JTrr 2 2M T mas JTR TR T mas o smd nm Ye b MTdr dr, 2 m ITY JTR R b d t CH. We kwno kT nderulm i r hrd vegim 2 R 2H rdr dn R eeM M dr AR.4 3T M JTR Y 0 m Ound Xex = AUmitirwm pil b at Tw CH. o A ( 4  (oG) 55 onre o ma oaa1Uom Aolyd gomishonu aduus a D 0h 2-a no omipusu nb divid Ah radius r O als 'o sud eirtwan O hnn n que AbepA an ueh KuGn b h i t k n e be d h Onre oA otane ki ha Conve ot om d rcudan blali 0 G1= 24-a thiekun eirtnlan blut othieknun eirulan pluti ot voum o-IU N JTYd2=F ila )de dz omisskn omis4hnu t UI denila eirenlanXA L u g b eirm 'Tue maM d o0(a-z)d2 and 20 Xoz0 Ye t hae Thu  2d 2 T(a2)dz 2 20 2/5 Ta w Codrdinalus Conre omas Condre 0 man oRhnene alarhei t revgeu tHh aa bod bod. tyam tyam polurebs ot CH. a mo a piilim NAutu b stve Ru b Vey T h u) COAL a foo ^arhiels ilsbalin Byskom to1K uninal Condina t n ane eated AkT parhfeln and Har cH, and H a r eH -Y-2, and Y' a a r t mY2 wt 22 C o h omav We no w oadnal Mam O eere maN  sadiral (108 osiens mR uskm ane supanakd Csvdinali Mm and old a veuw R b0nton vess ao o and W,r.tUnt mew tw0 in and m, 0ma&darala e Conhre ane Cve 0 OundY Y- R Y - R Cundinal h n he ma/o Jr Conbre e mas a tval l dm a 1% Cen 5nee o um Fwlkamae untrm mov cdn wn S w H esodumal Atem, Atem, o Csrdunalk 0 M CH m,Y=O m r+ divaety bonttk hrtiraT divuty trll3 So o b fiore oka AL mot o  syakrn dvuablL man Motu o-a vuckeh hne, aw Cwla yms WhosL manA do ns bu vau remaln nandwuA Har motm wilk um Amaluaen ln betemn en n wiek n a' of ma tyrap Nuwto's laos blindl T mst dramati enaxplu et sa A Yotke povidis u pepelld b We kni Hat a rotkel- a Mm wiueh eaualy ttrud anan a t h n g bwntud aLilwaluy divwasn as Ah yotkeF Yoek Mot a vrke- u m Mrnlokung A rotke M o vvanuab a u a L l na uay a tt bas o u i baus ena b enblamed &n lhi Shmouw an Ahe prineuAlu marun and Nuom's Anvarun 3ra lao m o m i n t u m ekambr a embustuy tnkans owwwt. h L otkh yAlFAtgaal As a windn ni hawem Qa- oil Evdh an a u n teye er diveihn 0oeek Nh yoekel baek0 md 4a-1 n U tovu on IN turo a venttum @nd k panju axc dirtton When UTYoeket un UtW  m a triwand ytkeF auduatug n U Rup tntn h a ane h n ahal duvesrm tkut+ q 1e) Astcen J OlbsenkLU aenlutnak kovtu hu trtal s R i n (rorket a-jet) mbment umm ewsnved yocket m dlaul, A wotum o nalyze a eanal Annal V momentum Vt4V+ N M V4V Tn tt4t t. bitwcen e nkntcal atm rocker, dm CPwidnw u (EF4E a may o f u l velsi lh n t t and an Aas-je Qnd npallud The erhawa bwnl relaiye a vtke. hu natm dliamimad b u Vlou i rotlung Ahe wplants tAvuluy ofreh , iy ndtptrdt ehens er. bu  (16 above shw Suem a la and a tnt ttAt) T ayhm towavb O pus renan ma o K rotke H.Jene Mt4mn A veleeily Yotker a ime t i V Cnd a ns (t +4t), Vt4V The nittal Amowomfum (t) Mtm)v u) P(ttt) = MV4V)+4wVt4V+ Vt4V+b vedauy h ZaN -jet rlahve han n monUntwm T 4P P(th4t)-P(t HWsAV 4m4V + 4mu - M+M4V + 4m/v 4 O a limit s t o =M4v 4 (4m)u metnenun hue - () dP d 4t0 poaitve oslttve dumd u Ne thar m have 4 tonvenk mednvenmta hgarve, opoulk w V eanaBum. M Ln hT yolk m nd o-Ua mad. erkanst maM. AaNe oUu enkanst d L valiounUlAA yscket, rocke, mas Comis m n ie M d  1 aung th eae) m e aud equatng t edna t v t dP, oblaun Jatndaminad Tocke eanatm JN i ehhyAi all h veloidies Kowe blD nbresad Aber an mental trame U Yenent, nat a rin atehed oeke F aF YTckeh, takun a i veatn lasrm n e ma* he H dv F W dUuVA ohen O uT ina velau nal o Yke hare (ii yTcket ina yOaket n tye 9 tauun  (11 ( i Rotke n Frce Spat 9A nA l n na tne en tm otkel aMA mottm vn ly M dM dv dM genual Qu ehaut veluy u must nm RehCaA b wy 0ntegrali enarum s moftm dv dt dM dv H V a l velouity v,=o -u n ab0ve UMAN Ay n velre TL mdepedut et lt, velaask o qnanhthi an tind veou Only mporlat an 4 An1e The Hu vo, ofi tal erhau -je veki u od maM  (14 T Autuakun m oii dinunt a qwavr tarional ield An runt a houn hlku mt ename, (ti) Roke m a Ghalsi tahi bral Rdd a a reeke takes o CBaen geunatunal wd eaC) bLLms en dy d Hd M dv -u ae h and g diyted drAw and n anA owan dv wt te e get Smtegratvy t V M Vo h ( ) + 7 ) M ad V= t=o velsul w e k d Ku in tiad po five bwnd, 4ake velseu you