l23 - rl ‘l[a l l l l l l l 15.80 bammlcb 0‘ CU:9...

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Unformatted text preview: rl ‘l ! [a l l l l l l l- 15.80 bammlcb 0‘? CU :9 namics '0‘; RC —->: mm: 0% at ‘(N {A loo <——-> o} (Ang‘yar qCCe\€Y‘0J(‘(Ol/\3 ._~., F l ——1 {A 0:1 .244 P:‘C\‘\ (\e I: = mm (Meiokms Q'Mb LCM—0) lofzoeb -\MQ\U\ cu {Force is leaedj ngZL‘cJ "to on 4314 d i Conslévr «lime aciiwi On 0., PY¥K {\fl Q‘CLUHfl cu f0 MAME Nb‘\€4 alomi’ cm «unis ‘l UM“ v WAQVKJ-fi 0‘?‘ cu looka‘lo rb‘hjre hi ‘FN‘C: I5 meam‘cci ‘3 CL iioqu‘Jta cat/Meier q‘igrfrg ive \(Y‘ 79‘ 7—? U ‘ics in Cu QIC‘reci‘toh 0°th 043er VQBVQC1> +0 4&2 V q TCQN‘CMCQ axis '13? ._>? a ruxF rqu'i‘AG {‘i‘ow kfgue V‘Uklh ‘15 direction perpendicular to the a ”‘3 +0 422 Educ (1e BMW! The torque vector 1' lies in a “”8 ‘xi'aml plane formed by the position vector r and the applied force F. 44-10 (a) Here r sine is the (b) Here F sinB is the Z Z x F perpendicular distance , component of F / \ F I i I I I i / between the line of / \ perpendicular to r. action of the force and the origin of coordinates. ii Momevx+ 4““ (w \em an“) 053 firtce . 1* i$ Wm F“? ML (CO‘QY 46M: Rom )YRt vb\‘ofl‘i°\n clott'S +0 +6! II‘IM —0Q’ «(Skew 09 F. Twice (or {human = Momevxi’ mm x che, firefld I? in 7’6va 0? componenj‘s: Ii: EL ) comPonevi' prin‘lit0\<vr +0 7? E“:- I¥sin 9 5, = Fcose , (wromefil’ Famflc‘ ~11: :3 Toy“ 0L : Rqéid {aka/“(Q x Tmsuevse Fovtfi = ‘V\ \F-E\ I F Recs no Qovai‘ouHOh ‘\-o +0 M or voti‘fons. {Sam M) W +134 av widow. [7,] ;. N . m = j (“0* used) :1pr 1:0 T=Rf F=2f F=f (Lfo Q¢O iEKmmgk 1 Net Twice on cu CHE ‘i’nJev 914-“ E} ii EEFovces ET act vultus is: EEc'uuL a (A‘ VQAikS 7?). EEexexA‘ ‘i-ov 0e; on +Q~Q it mm 0:: at '3“? Lortufloetl. quOn$ +2? tic-kiimLe‘r. A solid cylinder is pivoted about the z axis through 0. The moment arm of F1 is R, and the moment arm of F2 is R2 1 i i 1 fl) ' giFofce R 9‘45 cu mcmcn'f qvm R, qwl (mark a EEC‘OC‘duuibe tovbue ov mom-M17 Call +£fo neaJwe ‘8‘ z - F‘ R. Towaoe 40¢ +0 F1 3*. coodtvclocltufis: (Fosfijriuc), ' ta: +4313; ‘1 M Jr *0»: U! i; L ‘6.” mi W235 ‘ERH— FaRa. :0; firSM R\: Wm B: 4,” in: 0-Sm. Bud»: ~(53xL\3+(ux(o-§) 2 “RN-imi- TN oz {3 MEAN“ CWE‘NLW WM VOW do Lkmgge .Anaukur MomeN‘oM ccné Tovioe FIN Ck '5wa e facd‘ick I an: Fm q szyxem 0‘? f\)qx-'¥ x c‘es/ 9‘ ~-——7 *9 L - i’ “1% PA __5 7 Homo Ages L Cawaq Lode +\W\€.- ‘A ~ —> —-—7 ~—..9 .9 ELL: L $331?sz ax 43 .gl * QR ‘ ” ’ 4+ _..~% —-> _—§ '3? ’LVU‘W‘X hing“: B 20 -§ ~ _.—'> El}: :Lfij-XE 1' Z. 2;. CPU ‘ x cm M99 of Cam 9 0&2 I" e We +0 we “WM +0701. 7 1 :Fonces ~ 15o1cd19t\ Slum 1.111409ch 1 . 13'n4 Lang) -' th‘kom “remake“ it , {vs . Zi‘ E 0a} <1va or 1'4 owe E£01035 -1 05( C F116 QIOME lime 8%“ 13m‘1ic1es "*7 €1le F123 RiftI sin 91 (mag) 71% ‘5 - . ‘91; x E94 - 57‘9"“ 9; (Ma) The forces that two particles exert on one another are of ‘ : ' equal magnitude and of ‘1 \C‘ s W\ 9‘ (‘9‘ 3‘ M 93‘ opposite direction. Further— [L Q1 {5-1 . Q‘COW o \(x\‘ ‘\y\ +0 more, we assume that the 1 forces act along the line 1 hue — 01: - CL C110 \A 0 ‘YCNC 63] joining the particles. l I '-T0\f€60€$ CQWCC( ‘m‘h‘onallkk - _SQW\W\0§€3 A __ J? :5 ixfi'im‘1 Z Z‘ijd’ J—E ’ L o :3: : “C1, use cowimom ow’ in 21+RQY J'é ‘m cw\ inev'th '1: 6W“? 91 011” Igu CM - 7? E CWQLMVP Law 013 Comevhjxfir‘xom otp’ Afiu‘afl‘ Meme UM- Tow$je 0V\ R CovxCCQ.( ?€N\AO(OW\ ‘O‘CKCgW Q‘\’ A : :¥0\f<€$ ovx EOE 1 Tcosd— M3 - 0 . _>, - A K flflflflflfl ‘ 1; = “\scv‘ rt xx“ _¢ un- -___,. 1 :' O . (1 HA x Fa: __> smce rtfi // F .9 a L - = C ms‘hvd' LA ' 0 Ln/ 0 cl lcosa Ofligm 43‘? B ”J7 ——> “I? /”’M OE) ” NB X \\“‘~..._E__.. Touch! = mg. _.7 .88 (51LowmeJF +0 km 043 mo‘kom 0-8? M a z m Lsmd 3 81% wk] WM“ 08 W V ‘mnl z Ln(€+afc\ — an A; [ALR‘ 1 Ln A6 As (Vt—’20 44L - L 3:; _ “3(th : LHCO 4141 Mb? 1 : .— : (0 -df wed (sow = ”W Q1 ‘ loo/30L = mg, 43L]: : MEL 5mg llComsiJev cu Fav'lrcle moi/{ma in ct llqivcle 09 meats v “Jew {Re m llxo'l‘ion 0‘9 q’lflflyn‘wd fovcc E: . lePv‘s govcfi fro ores q MWCJ i llaccelewi‘iovx alt, CUM"! ;! ‘l l ,l ‘l 3.; FL = m q”: A particle rotating in a circle under lflk 40¢ UK 0% F 5 0+ +e\e (NC in the influence of a tangential force ‘1; ‘ ' Ft. A centripetal force Fr (not lL-th\&\ is «its 013 Y°+°~£L°W shown) must also be present to i; w _. maintain the circular motion, ;l b = FLY ‘ (“A (MAY :TKL Mm‘l‘iki QCCJCWJQWK {s wldcé 110 ‘lRe avg/Jar llqccetvwl‘ion at, [ma Ore zrok t: (“Y1)O( :l 9"! lfi< 4‘»sz «(,le OV\ Ri {oar—'MCIQ l5 Propor‘lt'ontvl "’13 ll?“ om \qv accelcvoA‘lovx. llRo¥c3rioum\ amlokoe og‘ Nun‘km‘s 3km Labo- l i; ll .. n ‘l i; ll ti éRiaté B045 Igoawcwxics 2‘Ro2c0‘nom Q0002 6\ EXCA c2125. ('30ch ConSiS'E 0232\nC'mi‘2f 7“)ka 2%o-Q mass _e2emev\}ts chm. 7che mass elemevd \(‘O+q)“€3 in q 22 6rd: 0120002 Rt Oviaxin «“4 945 22 2 . . A rigid body pivoted about an a: q 22“ 0‘2““2 (‘4 CC€2 {WVJC 2°“ QT: axis through 0. Each mass 22 ~ element dm rotates about 0 22 rvbAOQc 203 R +6UA64AC1‘HJ ENE? with the same angular 22 F acceleration or, and the net 3* '2: ' torque on the body is =2 *— M endlmvds 3 2ND La LO ‘COV‘ ma 85 proportional to or. i 2 demehk‘ “hi. : 6"“) Cit 2Assoc2dul 20v 0? ‘23 W2“ L AT, : $321: REY“) (be? \Nc 22qu (Lt = T02 AT: : QFAW)\C01 = Q’qum)ol 2152 Edcvxf O2w\+§ Qavz QUQQCV(V\'2 (l \3U+ Savinfi 0/. 2 2p +1 2‘ IVGVCQ‘T‘JW‘K ‘- 1 1 ‘ EMPSKV 4‘94 = °‘SV 4*“ a __) that = I ok IE xcwn$\t ij A '5‘\-\~{Y\tb Rs qu‘apetl QV‘OUHJ “ r m c \‘mA-w 0‘: mass M and TQAHIS R. Wm cuskml-w 3's QR: 4b rd‘td‘e abouf ,(k cons. ' : {Tet 8““ is u“ 211‘ 1L “aha. U I f “U“ OK Q“ Q Wmainkl n K mg q E‘fc onsk‘ig’ 1A-ensiovx I. ‘1 masks ’; R: (3% l T 2 2” t: Iok «(3sz = (comm : omum \ I: gum": ikrghfiko 0Q ‘ Q7oxl0 o<= 1:31. = 2:1 = 3:3. : i I Vlmka‘ MK ISXOB 0“ air-«s E I H H :5 H :1 H l 3E tam \€ 4446 E———P—-E jEAroPe is covcufloecl qmuncl q E , gh‘nétr O‘C ma$$ Mam! V‘qtlu'us K. r every is POHQA La amass m. ENQaA’ q‘t(.‘\’9\€ acce‘e‘raj‘iohs 01‘3 +29 E4100 mxés e s ? 1 5 MR2 1‘ i Q...” E iE “mg. I = moo (Eamg) SE 1:: ;; R|:Io{=_nma°‘o{ (Lula) i; a i‘ H @EE CL: Rd (Geome‘h‘hk) 5s”; ®fi¥o® Tzimw @ I :1 ; a~ E a: 4—— - (i=3 : i/K l+ Mlam R H mlam 51$ M: o T: o 'E $5 0;: 68 Ea E} ii ii E: E E H 24‘ I7 em \ 0M "\Q‘uu'\ ffKUk‘CmA NV“\ 3‘ J8) Ulle‘é U‘C‘chefl I Q r3 a ROYQEOACAQW A m HIS R \V\ «(Q33 2‘ S R S‘M‘ka QH‘ ‘cml (‘6; \U \oHQoui‘ m Pu“: m. +. ms 1 HfF \ - :: TR: mama 1‘ Mack—- 21 I» ‘R : Io<=KmR)o( {QR-n k ] C W S ‘0 409$ n6!“ s+ve'\’ ‘Q\ h Rd [Skina GJ| : q} : (L Ta le \‘ {wit T‘ an 7; : “MC“ 94$ *0 awn " — “0qu :fmyyh— . %D\VC_ Qof (12‘ T1‘ |\ _£E$._ a" - m\+Ma+M m\ M; j T : (My? “Mi “\ma 1 "\\+W\3~ __ = M ‘ mrHVbJ- ‘ ‘ooé 0" i r4 MODS M minim qLo at 4 1 #Re R164:- Z—qst \S. i i i i I :i . «Aid com‘govxevd‘ 053 UM' g; (ma. momf ii ' %’C0W\Y)O_V\ev{t De QhTJIflM. i -2:*cow\f)0vvw& 09 'qmta‘w‘qv momwfuwx influences Jtexe 3' ad‘cAWOMJ mosh'on 0% We o‘oa‘ccii cJooo+ (3(er 11(3- -g——covr\(.>omev{* is associca‘u-l \oi+R kvces +€d +3? cuis t1€T¥$ on *Q9 suflaovi‘ Leavings. ‘ FOY q $ mme+rCC vi (4 (ad Kt matte} comment (80$ f’A‘Q Wmistfih %“ComPovxew7(‘S (14:1 ° Forces on Leqv‘wx}; \lccvflSQ‘. A rigid body rotating about its axis of symmetry. 24—4 i“ FOV “‘435 elemevfly elm 49 =§Loclm 7&2 401ml ¥~C0vnwcmud g 01; +11,a cm W i'mbmwxxum cg ‘Kw o‘okcti” IS. o'o‘Lcu'ngJ L18 9 mass e lemeN‘s. :31W‘c (M “a oue‘r a“ SAQQT: bog €141“ L1,: I90 OY L0: L3. (:1. 7014 KUmA-ic E‘MNX‘X 'Towaoe clue 40 GM“)? .BOAX 05: mass M rovixm qu A . ',COV\b‘\t\ti‘(‘ ‘MaSS r‘kic‘? .. WV 001“: ms‘rkou Ucd‘ox' 12. \3 :3) A, Q? o. = TLX mg 3 A Q .j, 7‘ .__2, _~., :Z : n. - .0 t3 2 AXME 11%}? A (“0 W8 {5ch ME; = M? 5R1“? A fO'Vhow Uec¥of 0? CM t? = MEX—i) “3 —>; :RXMOQ 5%? To (balm? cum O‘o‘ed‘ (44.350) +G£ Puojf‘ musflc (>9 a CM. égExchPE: Ro+ajtm§ R03 a4-I8’ LIA UMQQVVW 1‘04 O-C pewfa L, w } +0 LIMA mass m {3 Ewe giveknLe gkodk Pwo‘k d @434 ‘ fevxtl 1'fimes a} HR Pme cavx Produce vw ‘Hvzues a‘oou‘i‘ +RQ Tan/0+- I: 1 ML)” {M‘bgf ($00" tfli ogvoil ‘5 Iok: M _L_ '3 a o( = m2; {L133 3%. J. ml." a L4 :VT‘RQ lihtawr QCCJEWJE'DM {36¢ PO‘IW‘S (HA 1& NJ ‘K AmLa/Ne \r 9mm 1% Pix/0* is azvdv‘ 3 Y‘ 3% IQFO‘C \~>%\, ma Row: M “5% I" EE Xmmfle Two 101$“de 09* mass W i} +2\€ enés 0? OK “BRA— r04. ERot nukes cm mate 9 Lotta file—cons (mus 0‘3 mutation}. i "i i! R: Ysin G «r: 00R: to‘CS'mQ ,i A“ . mumwx‘kom 90¢ echx Parka)“ Qqs mari'kul-P. Si mlfix?\ 1‘ ‘mY’U‘ = mm‘f sing :Ith‘méUoJ L's ar£ in same ééireC/‘k‘iovy To‘iwt mag. momeW‘Um = i L: QMUOVD‘ sin 9 i? ,r Two particles of mass m at the ends of a rod that makes an angle 6 with the axis of rotation. At the instant shown here the angular momentum vectors L1 and L2 of the two particles are both in the y-z plane. It makes 4‘“ anak (6163—6) UDYJC é—afxig qnql ff€C€SSCS a‘ooo‘\‘ GUJLCS QS ‘MX‘kC/‘eS MOVE. L} = Loos (700-93: amto‘f L2: = QMUQRD‘ L}.: 1w 1 SW39 —-> L213 444:? ‘AvxcEEm/Eqv mom-NOEUM «mwe3 1n PVOEDOY'E’E'OH +Q .6— ;E VOE'JeYJV 0E3 Eew 04 CLvi meqsoveb "E‘Rt IE resanwvme 0E2 +e\€ EDOEE ‘E'u cQamacs ivx 1J6 EE may/lav memewEum. E E Q GM cu veEOci‘Enk L0. 1'15 mm \yxr-gx-‘kca/E fiw: VA? . ' Momevdmwm Vaw‘es ivx Ewe ovE‘iQn +0 ‘EKQ V€E0CElr :33 T2“ WMSS m meaSvaS . +£€ EE MSESE’mce 0‘9 4% E9041 ‘Eo m CQ e in HS VeEoci‘Et. «M3 1 EE K 1 E? K: 429: 1‘: 90m E SUVVOR 1—,} 2 comE’aWE’ EE I; $~\3‘\t\m towEWoLchs omA 1 Jecreasesl'KE EE‘mus'E \vxweosse. RE( E6“ +9, EM ”same, +29“ EEVMBEV \oe 0k sowme 0E1 {\A-erckxEY. E: E ' ng CQEEGKJSLNES Jame) ' 0V SAFQYSI “14.3 SOUTCf’ is HAWK. GaavE'ZfA/E-{omd PE is he QJECW (1M4 Become's move “QaadE‘ivf q<_. 0L3 ech’ con‘E‘Y‘aC/ES. .3E3mwsz‘ \MMQYEWK Dir {Cc-SEimx-{Y QEOPS HOOVE— <1$ oomrvs 0mg ENE? owe ‘ZDUEIQJ inwaYcE. &L 'C’ Rah 0e CQOU‘MC 0% cm . mom- a 3 Texe ‘bei’wxcwx (or mammflom (‘2 2.3 OflL‘KM re: 0M5€ E cum {I‘LU‘hJ +0f7 we %0 Cancun/6 \mltcvndlufi (arctluceé 40(5065 (Fez/‘76 +Q€ Mfr/“(QM MSW-QM “ Tag *o‘kd mayday meme/“740m 5g OUY\ i30iq£ei svyzkth i$ consev U014 ‘FOV OK \F\t& (L [064* Y‘Olfai’w‘x «LOQ£ q 43(er CL‘JU‘S (42% ¥- (wuss§ u3\JrQ\ 2";—0 @4q COKSQVV '0V\ (3‘? 0Mqu mmmi‘um V‘fJUCeS +0 (“.4 : O '::‘> N =0 33; L% 3 CQRS‘LQIA-k :7 L; 3 L1“; Lug _, tanglm/vo’r 11w; 2 1:“: mi ...
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