introductory physics--ch 2--reference frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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    ] ex lo} o eamoph pbh {ez` *zhdopmsmp}* {mpb lopbhlopmaod l} phz}of` amhfpmcma ael~dhrmp} }hp pbh jo ma aefah~p {bmab {h {mdd pz} phr~domf mf pbh h ~okh m ml~dh& Pbh lopphz ec aefahzf mf zhdopmsozh pbh ~e mpmef "deaopmef- of` lepmef ec ejghap & Pbh jo ma aefah~p mpbop ~e mpmef of` lepmef ec of ejghap aof efd} jh ~hzahmsh` `h azmjh`of` zhaekfmwh` {mpb zhchzhfah pe "pbop m *zhdopmsh* pe- epbhz ejghap[bhf }ex o} *Pbh ~b} ma jeei ozh op pbh dhcp zhoz ec pbh jeei

    pezh * }ex zhchz pbh ~e mpmef ec pbh jeei pe pbh hfpzofah of` expdmfh ec pbh pezh& Ejghap xab o pbh pezh hfpzofah pe {bmab ~e mpmef ez lepmef ozh zhdoph` ozh aoddh`zhchzhfah ejghap & Qhshzod zhchzhfah ejghapx h` mf aeljmfopmef pe `h azmjh ~e mpmef ozh om` pe cezl ozhchzhfah

    czolh " ez czolh ec zhchzhfah- of` {h ~hoi ec pbh ~e mpmef ez lepmefec pbh ezmkmfod ejghap zhdopmsh pe pbh zhchzhfah czolh&

    Mc {h ife{ pbh ~e mpmef of` lepmef ec of ejghap zhdopmsh pe efh zhchz,hfah czolh {h lmkbp o i ojexp pbh ~e mpmef of` lepmef zhdopmsh pe o

    haef` zhchzhfah czolh& Pbm m pbh zeep ec pbh pbhez} ec zhdopmsmp}7 `shde~lhfp ec ~hamcma lopbhlopmaod le`hd cez zhdopmfk ~e mpmef of`lepmef o ej hzsh` zhdopmsh pe efh zhchzhfah czolh pe ~e mpmef of` le,pmef o ej hzsh` zhdopmsh pe ofepbhz zhchzhfah czolh& Hmf phmf+ pbheec zhdopmsmp} m pbh le p ael~dhph pbhez} ec pbh h zhdopmef bm~ & [h {`h azmjh elh o ~hap ec Hmf phmf+ {ezi mf Qhapmef ;&1 jxp {h {mdd feke mfpe pbh lopbhlopmaod `hpomd mf pbm phrp&

    :&? Zhdopmsh ~e mpmefDeei op pbh kmzd mf pbh cmhd` ec `om mh "Cmk& :&?-& Be{ {exd` }ex pelhefh {bhzh bh m 5 Le p `mzhapd} }ex aexd` ke pe pbh h`kh ec pbh

    cmhd` of` ~emfp op bhz o}mfk *Pbh kmzd m pbhzh&* J} pbm oapmefmf`maoph pbh ~e mpmef ec pbh kmzd zhdopmsh pe }exz exp pzhpabh` ozl o

    cmfkhz&Mc }ex bo` pe `h azmjh pbh kmzd+ ~e mpmef pe elhefh {be {o fep{opabmfk }ex aexd` o} *Qbh m o dmppdh {o} mf czel pbh expb h`kh ecpbh cmhd` fhoz pbh expbho p aezfhz&* Pbm pophlhfp mf`maoph bhz ~pmef zhdopmsh pe pbh h`kh of` aezfhz ec pbh cmhd`& Mf epbhz {ez` mpml~e mjdh pe `h azmjh pbh ~e mpmef ec pbh kmzd "ez ec of}pbmfk hd{mpbexp zhchzzmfk pe efh ez lezh epbhz ejghap & Hshf mc }ex {hzh pe`zo{ o lo~ ec pbh kmzd+ ~e mpmef }ex {exd` bosh pe mfadx`h ef mp elhejghap pbop aexd` jh x h` pe odmkf mp {mpb pbh oapxod cmhd`& Zhchzhfah ejghap of` zhchzhfah czolh & Cez ~zoapmaod ~xz~e h pbh

    zhchzhfah ejghap lx p jh ho } pe deaoph of` m`hfpmc} ez pbh} aoffep jhx h` o kxm`h mf cmf`mfk pbh ejghap {be h ~e mpmef m jhmfk `h azmjhMp {exd` jh be~hdh cez hrol~dh pe pz} pe cmf` pbh kmzd mf pbh `omcmhd` mc bhz ~e mpmef {hzh `h azmjh` j} o}mfk *Pbh kmzd m jhp{hhf p`om } jde el &* Qelhpbmfk lezh `m pmfapmsh m fhh`h`7 pbh h`kh of`aelhz ec pbh cmhd` o x h` hozdmhz ez ~e mjd} o aozhaze{ op pbh ahfpec pbh cmhd`&

    Pbh x h ec zhchzhfah ejghap mf hshz}`o} dmch m bmkbd} sozmh` of`o`o~ph` pe lof} ~hamod amzaxl pofah & O ~mhah ec cxzfmpxzh aezfhz ec

    Pbh {ez` ~e mpmef bohshzod lhofmfk $ p{e ec

    {bmab$ *~e pxzh ez oppm,

    px`h* of` * mph ez deao,pmef$* ozh ho md} aef,

    cx h`& [h {mdd x h pbh{ez` ~e mpmef od{o}{mpb pbh dopphz lhofmfk&

    Mf ~b} ma $ pbh phzl*zhdopmsh ~e mpmef* of` *zhdopmsh lepmef* zhchz pepbh coap pbop ~e mpmef of` lepmef lx p jh `hcmfh` *zhdopmsh pe* ez *mf zhdo,pmef pe* elhpbmfk epbhz pbof pbh ejghap mp hdc&

    Mf aellef ~hhab$ {hecphf ml~d} x h exz,

    hdsh ez pbh hozpb o pbhzhchzhfah ejghap {mpbexp

    o}mfk e& Cez hrol~dh${h o}$ *Pbh leef m coz o{o}$* ez *Pbh pzomf mlesmfk&* Mp x xodd} hhlxffhah oz} pe o} *Pbhleef m coz o{o} czellh&* ez *Pbh pzomf mlesmfk {mpb zh ~hap pepbh popmef&* Be{hshz$ mf

    ~b} ma {h ecphf lx p `h azmjh lepmef czelsozmex zhchzhfah czolh $mfadx`mfk h ~hamodd}pbe h mf {bmab {h ozh fep op pbh ezmkmf of`%ez mf{bmab {h ozh fep op zh p&Pbhzhcezh$ {bhfhshz pbhzh m of} ~e mjmdmp} ec aefcx mef$ {h {mdd hr~dm,ampd} folh pbh zhchzhfah

    czolh$ of` }ex bexd` `epbh olh&

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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    1:

    o zeel pzhhp mfphz hapmef ez o podd jxmd`mfk aof jh x h` o o zhchzhfahczolh cez pbh ael~dhph `h azm~pmef ec pbh deaopmef ec o zh m`hfah zh ,poxzofp ez lomdjer& Hrol~dh & Of mlokmfoz} aefshz opmef m zhaexfph` mf Cmk& :&:& [bop

    bo~~hfh` mf pbm aefshz opmef5 [bop cmfodd} odde{h` ^hza} pe aellx,fmaoph pbh deaopmef ec pbh bo{i {mpbexp aefcx mef oljmkxmp} ez oj xz,`mp}5 Cmz p bh h pojdm bh` o zhchzhfah czolh j} hdhapmfk o dozkh ho md}m`hfpmcmojdh jzofab ef pbh pzhh of` ~emfpmfk mf pbh `mzhapmef ec pbh pzhh&Ad}`h aexd` kzo ~ pbm zhchzhfah czolh& Fhrp ^hza} ~hamcmh` pbh `mzha,pmef "*ojesh mp*- of` `m pofah "*pbh haef` jzofab*- czel pbh jzofab pepbh bo{i&

    Pbh zhchzhfah czolh cmz p x h` j} ^hza} aef m ph` ec o zhchzhfah ~emfp "^hza}+ je`}- of` o zhchzhfah `mzhapmef"odefk ^hza}+ ~emfpmfk cmfkhz-&Pbh h p{e ael~efhfp ozh fhah oz} ~ozp ec o zhchzhfah czolh of` ozh`hcmfh` pbzexkb lezh ez dh ho md} m`hfpmcmh` zhchzhfah ejghap ezhozpb,jo h` `mzhapmef xab o fezpb of` x~& ^hza}+ mfmpmod opphl~p pex h pbh pzhh o zhchzhfah ~emfp comdh` jhaox h pbhzh {hzh hshzod pzhh &

    Efh ec pbh le p `mccmaxdp aellxfmaopmef ~zejdhl m pe kmsh mf,pzxapmef cez deaopmfk o jeei pe o ~hz ef {be m fep oaqxomfph` {mpb

    pbh zeel mf {bmab pbh jeei m ih~p& Mf xab o ao h mp m le p bhd~cxd pex h pbh ~hz ef+ je`} o pbh zhchzhfah czolh j} phddmfk bml pe pof` mfpbh `eez pe pbh zeel deei cez pbh jeeiao h ef bm dhcp of` pbhf aofpbh lm``dh ec pbh haef` bhdc ec pbop jeeiao h& Pbm hrol~dh mddx ,pzoph be{ }ex lmkbp x h dozkh hdhlhfp ec pbh hfsmzeflhfp "pbh zeel-pe deaoph loddhz efh "pbh ~hz ef of` `mzhapmef `hcmfh` j} pbh je`}-of` pbhf pmdd loddhz efh "pbh jeeiao h xdpmlophd} pbh jeei- j} o foz,ze{mfk e{f ~zeah &

    @h azmjmfk ~e mpmef m lezh `mccmaxdp {bhf }ex `e fep bosh of} zhchz,hfah ejghap pe x h cez o fozze{mfk `e{f ~zeah & Cez hrol~dh o ~o ,

    hfkhz ef o bm~ {be ej hzsh elhpbmfk mf pbh eahof coah pbm ~zej,dhl& Mf pbh h amzaxl pofah }ex {exd` bosh pe pozp {mpb pbh bm~ }ex

    Cmkxzh :&? Aof }ex cmf` 1 abmd`zhf bm`mfk olefk pbh `om h 5 @h azmjh pbhmz zhdopmsh ~e mpmef &

    Of eshz`e h ec zhdopmsmp}& Lz& Gefh {o kemfk pe o

    `eapez+ eccmah of` bo` fhshz jhhf pbhzh jhcezh& Bhaoddh` pbh `eapez+ eccmah peo i cez `mzhapmef & Ocphz pbhzhah~pmefm p ped` bml be{pe khp pbhzh$ bh o ih` {bhpbhz mp {o ef pbh fezpbez expb m`h ec pbh pzhhp&

    Pbh zh ~ef h7 *Mp `h, ~hf` {bmab {o} }ex+zh{odimfk&*

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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    Abo~phz : , Zhchzhfah czolh 11

    ozh ef of` {ezi exp{oz`& ]ex lo} mkbp o cd}mfk cm b *8>> }oz` ecc pbhpozjeoz` je{* "obho` of` pe pbh zmkbp- x mfk pbh bm~ o zhchzhfah

    czolh& ]ex aexd` o} mf pho` pbop pbh cm b m *8>> }oz` fezpb{h p * xmfk pbh bm~ o zhchzhfah ~emfp of` ael~o `mzhapmef pe ael~dhph pbhzhchzhfah czolh&

    Efh,~ozpmadh le`hd& Qe coz {h bosh jhhf aefphfp {mpb `h azmjmfk pbh~e mpmef ec o shz} lodd ejghap pbop m deaoph` op o ahzpomf ~emfp mf ~oZhod ejghap ec aexz h oapxodd} eaax~} of hfpmzh zhkmef ec ~oah{bmab lo} jh lodd ez dozkh zexf` ez pbmf x~zmkbp ez dofph`& Cez oael~dhph `h azm~pmef ec of ejghap }ex pbhzhcezh bexd` poih mfpe oa,aexfp mp bo~h of` ezmhfpopmef o {hdd o mp deaopmef& O x hcxd o~~zpbop osem` lxab xffhah oz} `hpomd m pe loih oefh,~ozpmadh le`hd cezhoab ejghap ec mfphzh p& O ~ozpmadh m o shz} lodd ejgha

    Cmkxzh :&: ^hza} of` Ad}`h peei o defk {odi pbzexkb pbh aexfp} ec La@exkodd&^hza}7 Ad}`h$ `e }ex hh pbh codaef mppmfk mf pbop pzhh eshz pbhzh5Ad}`h7 [bop codaef5 Mf {bmab pzhh5 [bhzh5^hza}7 Mf pbop jmk$ jzeihf pzhh eshz pbhzh "~emfpmfk bm cmfkhz-&Ad}`h7 Eb$ pbop pzhh mf czefp ec x / M hh mp$ jxp M `ef+p hh pbh codaef&^hza}7 Mp+ ef pbh jzofab&Ad}`h7 Pbhzh ozh pee lof} jzofabh & M kmsh x~& Dhp+ cezkhp mp&^hza}7 Fe$ dhp+ pozp eshz okomf& @e }ex hh pbop jzeihf jzofab ojexp bodc{o}

    x~ pbh pzxfi ef pbh zmkbp m`h5Ad}`h7 ]h $ M `e&^hza}7 Cmfh& Fe{ deei op pbh haef` jzofab ojesh mp$ ef pbh olh m`h ec pbh

    pzhh& Fe{ lesh pe pbh zmkbp of` }ex gx p bosh pe hh pbh codaef&Ad}`h7 Eb xzh$ jxp pbop+ o bo{i&

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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    10

    pbop m deaoph` op pbh ahfphz ez lm`~emfp ec pbh zhkmef eaax~mh` j} pbhzhod ejghap "Cmk& :&1-& Pbm {ezimfk le`hd kzhopd} eshz ml~dmcmh le pejghap jxp m fhshzpbhdh oaaxzoph hfexkb cez le p ~xz~e h mf pbmphrp&

    Aeez`mfoph czolh &Pbh dojezopez} amhfpm p {be pzmh pe `h azmjhfopxzod ~bhfelhfo mf o shz} khfhzod {o} osem` x mfk mfam`hfpod ej,

    ghap xab o pbh dojezopez} {odd ez pojdh xzcoah o zhchzhfah ejghap &Mf pho` o amhfpm p czhqxhfpd} x h o ael~dhphd} ozpmcmamod zhchzhfaczolh aef m pmfk ec of ozjmpzozmd} abe hf zhchzhfah ~emfp of` zhchzhfah`mzhapmef& Pbh efd} zhqxmzhlhfp m pe jh ojdh pe `h azmjh pbh ~e mpmef ec ejghap j} x mfk fxljhz & Pbh fxlhzmaod lho xzh ozh aoddh`aeez`m,foph 9pbh zhchzhfah czolh m aoddh` oaeez`mfoph czolh& P{e aeez`mfophczolh mf aellef x h ozh `hkzhh ec dopmpx`h of` defkmpx`h pe `hcmfh~e mpmef ef pbh hozpb zhdopmsh pe pbh hqxopez of` pbh Kzhhf{mab lhzm,`mof zh ~hapmshd} of` `m pofah lho xzh` mf }oz` czel pbh hf` wefhof` pbh m`hdmfh ef o ceepjodd kzm`mzef&

    edoz aeez`mfoph &Pbh ~zeah`xzh ec kmsmfk pbh `m pofah czel pbh zhc,hzhfah ~emfp of` pbh `mzhapmef zhdopmsh pe pbh zhchzhfah `mzhapmef kmshzm h pe p{e fxljhz aoddh` ~edoz aeez`mfoph &Pbh `m pofah lo} jhlho xzh` mf of} xfmp le p aellefd} mf lhphz ahfpmlhphz ez lmddm,lhphz & Pbh zhdopmsh `mzhapmef m x xodd} lho xzh` mf ofkxdoz `hkzhh &Be{ pbm {ezi m be{f mf Cmk& :&0& Pbh fhah oz} peed ozh o zxdhz pelho xzh `m pofah of` o ~zepzoapez pe lho xzh ofkdh & ^edoz aeez`mfoph~zesm`h of e~hzopmefod `h azm~pmef ec pbh zhdopmsh ~e mpmef ec o ~emfp&

    O ~edoz aeez`mfoph kzm` czel {bmab }ex lo} zho` pbh ~edoz

    Cmkxzh :&1 P{e o~~dmaopmef ec o efh,~ozpmadh le`hd&"o- Of R zh~zh hfp hoab ceepjodd ~do}hz& Hdhshf * ~ozpmadh * zh~zh hfp pbh phol&"j- O {ezimfk le`hd cez pbh jopef m pbh ~ozpmadh op mp ahfphz&

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    5/23

    Abo~phz : , Zhchzhfah czolh 18

    aeez`mfoph ec o ~emfp `mzhapd} m be{f mf Cmk& :&8& [h bodd mf`mpbh zhdopmsh ~e mpmef ec pbh ~emfp ^ j} of ozze{ mf pbh `mokzol of` j}pbh jed`coah }ljed q mf pbh phrp& Pbh ~edoz aeez`mfoph {mdd jh mf`m,aoph` j} pbh dhfkpb ec pbh ozze{ z "z cez zo`mx - of` pbh `mzhapmef ec pbhozze{ "Kzhhi $ pbhpo cez ofkdh- o mf`maoph` mf pbh cmkxzh& Ofkdozh ax pelozmd} lho xzh` aexfphzadeai{m h czel pbh zhchzhfah `mzha,pmef& Hrol~dh & Of hrol~dh ec pbh o~~dmaopmef ec ~edoz aeez`mfoph mbe{f mf Cmk& :&3& Pbh xzsh}ez m x mfk pbh `mzhapmef ec pbh zeo` o p

    zhchzhfah `mzhapmef of` pbh deaopmef ec bm pzm~e` o pbh zhchzhfah ~emfQelh ec pbh lho xzhlhfp bh bo lo`h ozh kmshf mf pbh cmkxzh& Pbh hlho xzhlhfp lo} jh x h` pe loih o lo~ j} deaopmfk pbh ejghap ef o~edoz aeez`mfoph kzm` o mf Cmk& :&;& ^edoz aeez`mfoph bosh pbh mfpxmo`sofpokh pbop pbh} zh~zh hfp zhdopmsh ~e mpmef mf pbh {o} o ~hz ef~hzahmsh pbhl folhd} {mpb pbh ejghap op sozmex `m pofah mf sozmex`mzhapmef czel pbh ej hzshz op pbh ahfphz&

    ^edoz aeez`mfoph ozh x h` pe `mzhap omzazocp pe omz~ezp {mpb pbh pzed pe{hz o zhchzhfah ~emfp of` fezpb o pbh zhchzhfah `mzhapmef o{hdd o mf epbhz mpxopmef {bhzh o xfmqxh ahfpzod ~emfp hrm p "h&kzo`oz xzshmddofah {mpb pbh pzof lmpphz oapmfk o zhchzhfah ~emfp-&

    Cmkxzh :&0 ^edoz aeez`mfoph ec pbh ~emfp ^ zhdopmsh pe pbh zhchzhfah ~emfp > of` pbh zhchzhfah `mzhapmef mf`maoph` j} pbh ozze{&

    Cmkxzh :&8 ^edoz aeez`mfoph ec pbh ~emfp ^ {bmab bo zhdopmsh ~e mpmefq < " z - < "1 al 2>-&

    Pbh zhchzhfah ~emfp mf ~edoz aeez`mfoph m aoddh` o ~edhjhaox h pbh kzm` dmfh aef,shzkh ef mp$ o `e pbh lhzm,`mof op pbh ~edh ec pbhhozpb&

    z of` ozh hrol~dh ec so,zmojdh {mpb xj azm~p & Pbh

    xj azm~p "z of` - mf`maophpbop pbh lomf sozmojdh " - bop{e "ez lezh- `m pmfap sodxh &Pbh xj azm~p aof od e jhfxljhz $ cez hrol~dh ? $ : $

    1 of` e ef&

    ]ex bexd` od e jh o{ozh ec pbh `mcchzhfah jhp{hhf pbhlhofmfk ec xj azm~p "`h,

    azmjh` ojesh- of` x~hz,azm~p $ cez hrol~dh 1 $ {bmab

    lhof &

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    6/23

    13

    Cmkxzh :&3 ^edoz aeez`mfoph &

    `mzhapmef `m pofah

    pzhh O 2> ?> lpzhh J :;> 3 lpzhh A ?> 1? l{mf`lmdd 0> 12 l

    Cmkxzh :&; Pbh ~e mpmef ec pbh ejghap mf Cmk& :&3 m lo~~h` ef o ~edoz aeez`mfoph kzm`&

    Pbmq qhdhapmef of` ozzofkhlhfp ec aefphfp mq dmahfqh` xf`hz pbh Azhopmsh Aellefq Oppzmjxpmef,FefAellhzamo,Fe@hzmsq 1&>Dmahfqh7 bpp~7%%azhopmshaellefq&ezk%dmahfqhq%j},fa,f`%1&>%

  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    7/23

    Abo~phz : , Zhchzhfah czolh 1;

    : : $ qhh Hr& :&?$ jhde{&z r }q q q

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    15/23

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    16/23

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    17/23

    Abo~phz : , Zhchzhfah czolh 0;

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    18/23

    02

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    19/23

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    21/23

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

    22/23

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  • 8/9/2019 Introductory Physics--Ch 2--Reference Frames

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