l23 - mimics 6 Ri{A Mi 2411‘ ‘l[a 0‘ cu...

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Unformatted text preview: mimics 6(- Ri {A Mi 2411‘ ‘l ! [a 0‘? cu PQ‘CSfi‘C‘e M l? = m5? (Memlon‘s Q'Mb Lana) l l l l l , l l ilb‘gflmicis 0% 0L victiA B0318 :4”) 0< (Angular qtcekmx‘mhs l To r; o as . NQVK“ cu (some is fwo‘aev‘j 40 oo rigid 3‘ bog} F'uvaeé alaogi' cum cutiS) *l g w‘i“ Vida-k ‘ ' e 4‘Cva‘QWU-8 o'?‘ Cu look?) ‘l-o ro‘iajre e +3 op ‘FN‘CQ is measure; CL ioqu‘tha CCU‘AQi q 4031042. Cons'iévr «33°th aciivi on 0., Erick Q‘cw'nn Cu 0 (how i FIT ? “e V Tex +‘0‘f of 7 Lei-\Qx tes‘mcf +0 4&2 g V‘hkin 0L5 5 q Reecch «XS 1%? a “‘fixF U: rqu‘imG :2? lid. in Cu clirecjtioh 0°2ch ‘ is A- .“ R2 dame defined The torque VGCtOl'TlleS ma direction perpendicular to the 4 plane formed by the position L} T 0mg F ’ 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. H Momem+ 4W“ (w \ewv an“) 053 firtce . 1* i$ Wm Few? ML (CO‘QY 46M: Rom )YRt vb\‘ofil‘i°\n clott'S +0 +6! II‘IM —0Q’ «(Skew 09 Twice (1N Named”) = Momevxi’ mm x Force, firefld I? in 7’6va 0? componenj‘s: Ii: EL , comPonevi' Forpirulitxfitvr +0 T? E“:- Fsi“ 9 5, = Fcose , (wromefil’ Fmafld ~11: :3 Toy“ 0L : tic-Aid {aka/Ne x Tmsuevse FDYCQ = i"\ F Recs no Qovai‘ouHOh ‘\-o +0 M or V‘o‘hJLfth. {Sam M) +134 av widow. [7,] ;. N . m = j (“0* weal) 2mm» 1;:0 T=Rf F=2f F=f Q¢O iEKmmgk 1 Ne“ Twice on at C3‘ ‘I'nJeV 914-“ i; it 1:tiwces ET Oct vultus is: a (A‘ VQAikS 7‘: ‘i-ov 0e; on +Q~Q 3.}; mm or: at '3“? Lortufloetl. RY‘OOV\& +2? tic-QimLe‘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 mcm¢vif qvm R, qwl (mark at jiciockiuube *ovbue ov mom-M17 Call “as. neaJwe ‘8‘ z - F‘ R. Towaoe 40¢ +0 F1 is coovd‘tv (PosfiJriUc), ' ta: +4313; ‘1 M Jr *0»: U! r; L b” UM: W235 ‘ERH— FaRa. :0; fi=su RV- l-Om pa: 4,” in: 0-Sm. Bmt: ~(53xL\3+(ux(o-§) 2 “RN-imi- TN oz {3 MEAN“ Cj/“Nl‘w WM VOW do Lkmgge .Avgukur MomeN‘oM ccné Tovioe FIN cu '5wa e facd‘ick I Em: Fm q szg‘x‘em 0‘? f\)q\-+ x c‘es/ 9‘ ~-——7 *9 L - i’ “1% PA __5 7 Homo Ages L Cawaq Lode +\W\€.- ‘A ~ —> —-—7 ‘——’9 .9 “ELL: L «Sign? +Z ax 43 .gl * QR ‘ ” ’ 4+ _..~% —-> _—§ '3? ’LVU‘W‘X hing“: B 20 -§ ~ _.—'> El}: 1' Z. AJC ‘ x cm «age of Cam 9 0&2 I" e We +0 we CW)th +0701. 7 ( :Fonces ~ Iso(c«>¢et\ Skew :R‘LN‘WQ . Lang) -' Cickom ~Teqc‘\{ou ii , its . Zi‘ E cal a.va or A owe E"3041135 -l 05( C Flit QIOME lime 8‘m‘mi fm‘ttcles if;\(“>< FLL— F‘AnismB‘ (mag) 7%» ‘5 - . x E94 ' Eianv“ 9.; (WA) The forces that two particles exert on one another are of ‘ : ' equal magnitude and of “ \C‘ smg‘ (ELSW‘ 93‘ opposite direction. Further— [_L_ Q1\‘§-\ . Q‘com 0fo ‘\y\ +0 more, we assume that the {u forces act along the line l‘me — 09 — at io \/\ o ¥o~rc es] joining the particles. '. Tonéoes CQWCC( intro ;iSQW\v\/\a\(‘ -' A i f ‘ - x F = Z Z; _L_ 1‘ A A i 1 94+ ,Jruad’ lec N51 ‘ <3: : out} Use COWWhOIA o‘ci' m zilliw Q} “('- ‘m aw inev'hcu‘ 'C 6W“? 0‘1 actual CM. E CWQLMVP Law 0‘; COMSP‘FVQJKOM otp’ AVQUJCLV‘ Murine UM. .To‘c%u€ 0V\ R CovxCCA.( ?€N\AO(OW\ ‘O‘CKCgW Q‘\’ A : i¢ow<e5 cm EOE 1 Teosd— M3 - 0 _ a, - A [I flflflfl M ‘ 1; = “\sdv‘ *1 xx“ _¢ «- -___,. 1 :' O . on HA x Fa: __> smce rtfi // F s» a L - = C ms‘hvd' LA ' O 0 cl lcosa Ofligm 43‘? B .3? “‘7 ’F? //”’* h OE) r X \xx‘h_E—’ Too/3a! = mg. _.7 ‘38 is +0 km 043 mo‘kom 0-8? M a z m Lsmd 3 81% wk] WM“ ‘8 W v ;an1 z Lq(€1—A‘£\ — an A; [ALR‘ 1 Ln A6 {Vt—’20 44L - L _ “if: : LHCO cum ML‘C 3‘ : .— : (0 -df wed (sow = "W Q1 ‘ loo/30L = mg. 43L]: : MEL 5mg léComsiJeV cu Fav'lrc‘e moi/{ma in Ci llqivde 09 meats v “Jew {Re m ignition 0‘9 affilwt‘d fovcc E: . ngPv‘s fiwcfi fro uces q i liaccelewi‘iovx alt, CUM"! ;! ‘l l ,l =i 3.; FL z m q”: A particle rotating in a circle under real 40“. UK 0% F 0+ +e\e (we in the influence of a tangential force ‘1; ‘ ' Ft. A centripetal force Fr (not is «its 013 Y°+°~£L°W shown) must also be present to i; w _. maintain the circular motion, ;i b = FLY ‘ (“A QCCJCWiI'NK {s wldcé 110 ‘lRe avg/Jar fiqccetvd‘ion at, o:E zrok t: (“Y1)O( :l 9"! 4msz (ac/*1“ OV\ Ri InrA‘icle l5 Propor‘x‘t'ontvl "lb om \qv accc‘cvoj‘iom- glRo¥c3rioum\ amlokoe og‘ Nanak)“: a'ub Labo- l i; ll .. n ‘l i; ll ti éRiaté B045 Igoawccmics «\oooli 6\ Cist c2115. ConSl$+S oQ‘mC'mhlt m)ka 03: m435 elemenks clm. mass: elemevd m'huLes in q Cvfdc q\000{’ 'fo O‘Naxiv‘ and 945 ii _ . A rigid body pivoted about an q +“ BAH“! (‘4 CC€{ {WVJC ‘OV‘ qt axis through 0. Each mass rvbéoqc R +qw t~ d RVce element dm rotates about 0 13 with the same angular F acceleration or, and the net il 'l: ' torque on the body is M (UK) “‘5 Q IND La La ‘Coxr ma 85 proportional to or. A7: : “Avgvcl = Raviool Edcvxf 0MB Qavz ka‘QCV{\/\_¥ (l \3U+ Savinfi l \p +1 1‘ Imkth‘vuhmz ‘- 1 1 ‘ EMPSKV Md = °‘SV 4*“ a __) that = I ok IE xcwn$\t 1 s H A 3““?an R3 ummmoetl QV‘OUWJ “ r c \‘mA-w 0‘: mass M and TQAHIS R. cuskml-w 3's QR: 4b rd‘td‘e abouf cons ‘. ' ETRQ 3““ is u“ 211‘ 1L “aha. * f “M T Q“ Q Wmainkl n K mg q acmd‘ah'k ‘E-Lensiou T " masks R: (30m T :w ‘1 m l l, H t: Iok «6: RT = u)on : om N-m \ it: gum": AUSEPKO 0“ ‘ 370K“) o<= 1:31. = 2:1 = 3:3. : i 1 ylmkl MR BLOB 0-‘1 air-«s 1 z ;E quP\€ 44-16 g-AroPe is covcufloecl qvogmcl q \CHAQV o‘c ma$$ M mml V‘qtlu'us R. X} ', every is foHQA amass m. q‘t(.‘\’9\€ acce‘e‘raj‘iohs 01‘3 +e9 Hum mxés e s 1 5 MR2 1‘ i Q...” E m%- I 3 m1} J H g; R|:Io{=_nma°‘o{ (Lula) :g a L H CL: Rd (Geome‘h‘hk) fsuk ®{A\‘o® T-zirmu @ I 3. ; a~ g (L: i ' (1:53: : l+ mlam R H mlam 51$ M: o T: o 'E $3 0;: 68 %e ,j} 31 H i: ‘ ‘ H 24‘ I7 G; «33*9‘t 1 M1 s‘ic‘e) wiqu'\ frft‘k‘iofi 0M Rovi‘ion*k‘ surfiru‘e. 7R9 {Julie} q Rm c \‘méer o-Q quS M («thus R. S‘H‘ka «H‘M‘Qevl m‘ \oHQoui‘ 4° mass iml Pulls i5\in‘h3 on N1 T }; Wack~ '3‘: mama kmn‘ R = m : W234 0". 3 Ch. 3 R4 [Skiha Joes n6!" s“\‘va‘\’c«9\ hw s\{‘o:\ i =~ "MM 9:“ +0 numb/V411 T‘ «Yul Ta cum! %D\VQ QO‘C a’\_ ; Tg.‘_|\ : m “4 ‘ ‘ooé 0" i t4 MODS M minim qLo 4 1 #Re R164:- Z—qst \S. i i i i I o «Aid com‘govxevd‘ 053 UM' (ma. momf ' %’C0W\Y)O_V\ev{t De QhTJIflM. -2:*cow\f)ovvw& 09 'qmta‘w‘qv momwfuwx influences Jtexe 3' ad‘cAWOMJ mosh'on 0% We o‘ng‘cc} cJooo+ (3cer 11(3- -g——covn(.>omev{* is associca‘u-l \oi+R kwpes +€d +3? cuis t1€T¥$ on *Q9 suflaovi‘ Leavings. ‘ FOY Ck $ mme+rCC vi (4 (ad Kt matte} comment (80$ TYA‘Q \YCOMSQxe3. %“ComPovxev\7(‘S (14:1 ° Fovce$ on Lurcin VavflSQ‘. A rigid body rotating about its axis of symmetry. 24-4- elm- ass elemevfly Fox! \m 5‘ elm 49%: gm qv 1 mg m Yd Li’ Giraud L} H mm I i a “2‘3. ¥~C0vn€ O‘Necf s eleme Te‘qeiifim o?» +Q\:M +9 mqss jimam ‘“ (Nev im‘kym“ 8 SALE: Log glclm \1 = L=I%LQ 1' - Lit ov m—(E;\ l “l 'Towaoe clue 4o Gm“)? 'Boéx 05: mass M rovixm qu A . ',COV\b‘\t\ti‘(‘ ‘MaSS r‘kic‘? .. WV 001“: us‘rkou Ucd‘ox' 12. \3 :3) A, a o. = TLX mg 3 at Q .j, 7‘ .__2, A? :Z : n. - .0 2’8 2 354mk 11%}? A (“0 W8 {5ch ME; = M? 5R1“? A f0'\+\OV\ Uec¥of 0? CM 1? = MEX—i? “3 —>; 5&3? (balm? can O‘o‘ed‘ (44.350) +G£ Puojf‘ m03+ (>9 a CM. égExchPE: Ro+ajtm§ R03 “43 UMQQVVW 1‘04 o-C pewfa L, w } +0 mass m {3 Ewe giveknLe g\o0& Pwfi d @434 ‘ 1'fimes a} HR Pivo+ cavx Produce vw ‘Hvzues Q‘oou‘i‘ +RQ Tan/0+- I: 1 ML)” {M‘bgf ($00" tfli ogvoil ‘5 Iok: M _L_ '3 a o( = my {L133 3%. J. ml." a L4 :VT‘RQ lihtawr QCCJEWJE'DM {36¢ PO‘IW‘S (HA 1& NJ ‘K dmLa/Ne \r 9mm 1% Pix/0* is azvdv‘ 3 Y‘ 3% [y’Fo‘c \*>%\q ma Row: M ok>fif EE Xmmg‘Q Two loav‘lt'des 0‘3 +2\€ enés 0? OK r04. iRot Mites cm mile 9 “MR Fez—cons (mus oi? Yotcattoln}. l "l l! R: Ysin G «r: ooR= to‘CS'mQ ,l A“ . mumfiom 90¢ gage Parka)“ Qqs chXAL'kul-P. St 1‘ ‘mY’U‘ 7- mm‘f sing :Ith‘viéuJ L's ar£ in same ééireC/‘k‘mh. To‘iwt mag. momeW‘Um = l 13mg i? ,r L: i;me Two particles of mass m at the ends of a rod that makes an angle 6 with the axis of rotation. At the instant shown here the angular momentum vectors L1 and L2 of the two particles are both in the y-z plane. makes 4‘“ Omak (6163—6) oo‘r‘t é—afxig qnql frecesscs alooo‘\‘ cUXCS QS VaY‘YCC‘eS MOVQ- L} = Loos (700-93: amw‘f Li. 1 L}.: 1w 1 SW39 —-> L213 5144:? ‘AMXAAQV mom-NORM «m‘m‘e3 1n oneox’k’ion 4‘s .6— ;; VOFeYJV 0Q +Q\e Ocl Cub) meqsoveb +Rt resi$+a~3€ .o-P +e\€ 50% ‘ln cQamacs in 1J6 may/lav memmkum. i f ~e GM cu velOci‘hk L0. 1'15 mm amend fiw: VA? ' ' Momevdmvw vcum‘es ivx (are od‘icn +0 ‘Me VAOC'llr T2“ WMSS m measuva I +£€ “Sham/we 0‘9 an B041 40 m CQ e in HS Ve‘oci‘ht. «M3 1 K 1 [j K: 429: II 90m fixagové 1—,} 2 C0Vx$\’am7\’ I; $~\3‘\t\m tohkrac’rs omA 1 Jecreasesl'KE fimufi \vxweosse. Rw figs +9, L4 Passage, +29“ \oe 0k souvce 09 {NA-erckkk. Li £2 ' ng Coucffllwx Jude) ' 0V SAMYSI SOUTCf’ is HAWK. Gaavx'ZfAA-KOWJ PE is he JCW (1M4 Become's move “Qan‘ivf q<_. edf' «what/(S. .3‘3MMN“ \MMQYQWK Off {Cc-SM-QY Q1093 HOOVE— <1$ oomrvs 0mg 193% core ‘ZDUHQJ ‘H’WOQYJ. ConSm/afiow Ce AW%SQ|CUF Momevd‘um 15-10 .7: --‘-7 &L 'c —_ dJc - . R046 0% CQQM‘IC 0% cm . mom- a 3 1 To‘RJ To vice E: Cons¥mfl* lg :0 1-:- O. ‘3’ 0 fi \ Jm‘d w OEINHMQA A” texhvnax I LMwauf 6.341 of) JR) ¥£YO (EXV*>EVi£WL€) 7er vax (or mamm/‘Yom c2 .23 on in re; BVDQ ‘§‘0 a“ {VOLU‘WJ +Qf uffmgo QmOun/é‘ 0‘9 . 7 \Nltu‘nquuk (grottocaé Eféues C‘exqm?‘{ +Qe memm W‘\ . “ Tag ‘\~o‘¥d WW6? meme/«740m 0% 0U“ im‘CJ‘ei H SUVACW“ \$ conSflfUQA ‘FOV Q ‘NCXQL Y‘Olfai’ilfi «LOQ£ q ‘Cixeé CL‘JU‘S {0.3,}-wis) ®1Q ?’%‘—0/ @4 (engevv 'cm (3‘? Qwawhv wowvn‘fum \mees +0 (—43%: z 0 1:5 3,4720 L% 3 Cmn34mvx'k :7 L; 3 Im = Cfin3W. 11w; 2 1.0% ...
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This note was uploaded on 01/31/2011 for the course PHYSICS 8.01L taught by Professor Schechter during the Fall '08 term at MIT.

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l23 - mimics 6 Ri{A Mi 2411‘ ‘l[a 0‘ cu...

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