Ch9,10 - '9 11'- qum Eq- {5.12}, with mi 2 [1, His munbsr...

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Unformatted text preview: '9 11'- qum Eq- {5.12}, with mi 2 [1, His munbsr sf rsvslutiuas is pmpsrtiunal ta the square ul' the initial angular vslssitja so tripling the initial angular ‘lffliflflitf iflflrsflflfi the munbsr uf Immiutisns by El. ts ELI] rsv. 5.31: a} For a given radius anrl mass. this farce is pLflpuI‘biunsl tn the square 0E the angular vslssitr (W): = 2.2!} [nuts that stamina ts Iadfs is nut necessary far this part]. h} Far a given radius, the tangsntial speed is pmpnrtisnal tn the angular mlflflity‘ 5—”. .= 1-51 {again mmsrsiuu sf ths units sf sngiflar speed 15: 11st necessarij Is] [E493 (gin 31111") [m] = 15.75 mfa ur 15.7 mg“: ts thrss figull'aa-a1 and nsw'mjn 1 a_{15.TEm-;'J_ =mg_ g ass: gm? = ngi + Ma as a? = {Essa and am axis names nsarsst m the ssntsr sf ths sEhsrs at a distance d — {:2} v’fi) R - {fl.516}R- _T_ F! _E 111.13: fl—I—éMig—Mfi. ’ them I; i o-uu-s EBB: a] Expreeehig enguler frequencies in unite {if revulutieue per minute may he eeee- medated by changing the unite ef the dwemie quantities; specifically, 2W I we= hill-I- e1)” = 21] fee I#114111. 11} AL Lhe iifitiel speed, the 4001] J will he reeewered; if this is he he dune in 5.0!] eT the newer must he m‘l =Bflfl W. EJII e 9.11]: e.) The angular eeeeleretien will he mere when the speed is a. meidmmn, which is et the hettem ef the circle. The speed? here enerfl wueidei'etieue, is 'u — 2g 2 filgflfl — lees {3]. where :3 ie the angle frem the vertieel at I'ElEflHE. and 1 E w=fi= igH—rmfifl]: Efflfifl Iflfflfll a __ {25” m} [1 eeeflfifl II — LEE- raflfe. h} :1 will egein he [I when the meatball again peeeee threugh the IUWL peiut- e] em. is directed Tit-ward the center. end and = MER1fl1-ad = {1.25 redfeFflhD m} = 3.93 131.353. d} and — HER: {ingHl —- eeefiJH = {2511;} — enefl], independent ef R- 9.154: I=fumd+flead 3 2 .= Emflflg + EmLHE all. mw = Pwvw : FIE-PEER: ml. = [ILAL —- JdeHB fill J. - IUIII‘LJ +‘41h 1 HH 'r-I-r 10.33: h} The eccclcrntien dermal the shape is n = g einEil— i. the terque nhnut the center nf thc Shellie 1": RI: In = I% = gMflzfi—fi = gMHn, en- ]15. - fie. Schrmg fheee reletlnne fer c and f amultnumuely gnree %c = gei'n .9, cr e. = Egan 2 EH SE} Ihfefieinflfl fl” = 3 E? mfflg.‘ = gen = Ether: Rena 62 me?) _ 433 N The Tum-me] Force is. My (H.153, and since I 5 p.511, h} e. = 3.62 refs: since it flees net depend cn Lhe mm. The frietinnel fcrce, hcwe 9.65 N, since it dnee depend en the mate. The minimum value cf n5 is twice as large, dues net change. wen 3.15::- 111.29: a] T=Ia=f— ({lflflljfl kgjfifllflfl 1:111} {1200 Iflvfnfin} g; 35%) 2.5 a -= Ill-.37"? N-m. h] mmflt = = 25.!) I131: ~—' 157 rad. c] Tfifl = 59.2 J. _'_ '4': I 5 2 [[UEHLE kgflfllflfl 1111‘“: ([12:11] rewm‘m} (E MEL» =532L the 331112 33 in part {c}- 10.313: Far hath parts, L = Jam. 1115:). w = Win 543 L = IE'ulr'r'}. 3.} L = {mrgflvfr} = my? L = {5.97 3-: 1:31“ 1:ng93 2-: m" mjsnLan x m” m} = 2.6? 3: 1nd“ kgmfls h] L = {Ma 11113an L = {235M597 x HF“ kgflfiflfl x 1n“ mflflw rammu hr 3: 36m gym-)3: 2 ll]? :13“ lug-111333 1|].45: Apply camtifin uf angular momentum E, with; the at the nail. abject A be the bug; and abject 3 b3 the bar. Initiirzwlljg'1 all uhjecta are at IBEt- and L1 —- I}. J ual; alter the bug jump-1'5:r it has angular mementum in an: diresctifln nf rotation and L113 bar is EULHaLiIIg with angular wluulhy wa- ill the Uppflfiite directiflu. L3 = mAUAT -— IBMB WhEI'E 1" = LEE] m and I3 = é'rrag'r'fl L1 = L2 311% mam-r = Emnrflwfl 3m“ = {1.120 mug Wfi' = mg?" ELSE: a} Fteni geenietrie eeneieeratien, the ‘leeer arm and the nine ef the angle between ? anti T-i' are heth maximum if the atringia attanheei at the and hi the red. h] in terms ef the dietanee a where the airing in attaeheti, the magnitude ef the terque ia Few-gm: + hi. Thie Funetien attaiha its maximum at the hennelarg1 where :r = h, an the atrng ahenlri h-e attaeheri at the right end ef the red. e} As a funetien ef :r, 1' and hi the terqne has magnitude :eh eta 4:212 + at“ Thie farm ahewe that there are me aapeete te inereaaing the terqne; maximizing the lever 12F arm I and rnaarimiahig ein qt. Differentiating chmlggljpg : netting equal te aere give-a am — [I f EH1 + [2h];r $12]. This will he EEEEEEBIWEQE aeh the string unieaa Eh I? L in wififlh BEE-E: the string Ehfllfld be Dimensien: 12?5:t1Eu-4Dpi:-:els 1'» 11'“th 11:" the right: a: = i. lflfifl: [n Fig. {111.22} and Eq. {11122}, with the eugle H meeeured frem the vertical, einqi — heel? in Eq. {H12}. The turque is then T -— PRECISE. in"? e} we] FHmeHdH=FH [I h) In Eq. {6.1-4}T EH ie the heriemtel dietenee the peiut memes1 eud ee W - F d! u FR, the same e5 pert {e}. e) Hem K; — W # (MREMEIwE, u: = d} The turque, end henee the angular eeeeleretieluT ie greetEet 1Ie'heu 5‘ = Eh at which peiut e: = {eff} = EFEMR, end an the maximum tangentiel eeeuieretiuu ie EFfM, e} Using the value fer w feuurl in pelt {It}, and =m2R = 4FfM. 1|].Tl: 15.} Because there is He vertical metien, the teneiuu it just the weight ef the heep: T - My ={fl13fl kg}[9.3 kag} =1.Tfi N h} UeeT=Iettefi11d u.TheterL‘1ueiH HT,SuEr=RTfI=RTfMRE=TfMR= Hymn: m a - gla'R - {9.3 mjetjfliflflfl m] = 1:31.“: rech’e2 e]u:Ru=EI.E mIH'EI2 _ (1} T mule he unchanged heeeuee the meee M is the eeme, e: and e weulr'l he tmue es greet hefleuee I '15 new-fiMRE. .I. ...
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This note was uploaded on 02/17/2009 for the course PHY na taught by Professor Richardscalettar during the Spring '09 term at UC Davis.

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Ch9,10 - '9 11'- qum Eq- {5.12}, with mi 2 [1, His munbsr...

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