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UCSC - INTRO 6 - Class Notes - Week 5

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SHYHY CASINOM w wwmurowSWAAwEWINLW PRUV42WHAdhik Uniform Circular Motion - constant specd in a circle 10 = 48 40 : rotation angle As : arc length, distance traveled along circular path rradius of curvature of circular path one revolution: AsWe also discuss several other topics like mbbb trading

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= r 40 = 7(21) = 2017 (circumference of circle) Slee 21r radians 360° I radions = 1800 if speed is constant l'uniform') X = Xodo of Vot + 4 grot 2 YUY MLmhVTT TIME تدين - - de et . linear velocity of objects @ V d A's 2017 - one revolution A period. (11me for 1 revolution) Frequency F = Frev/SEC €9. speed of earth @ equator TE 1 day r = 6,400 kin 2 TTT 21 (6,400 KM). 1000 m 1 1 14 24 h 60 min." 606 V = 4 50 ils .(* 1000 mph) T ypyYYYYYYYYYYYYYHKintottunk h ere was Want something that doesn't depend on where you are (what radius) w = 40 - angle angular velocity or rate of change of angle, time how far - rotates - AS AB rote @ which particle move.s . At around circle'. STOP 10/24/16 ve Wr relationship btwn linear and angular velocity START 10/26/16 units = rad /s -- linear velocity is tangent to circle, changes direction direction of w: CW or CCW mass is @ constant speed but direction changing - AW DukunywayT UPLYVwhen யாயாயாயாயாயபுடய Luz Quick Check 4,12 QuickCheck 4.13 dana HIV JIVATPHhMhren Marine ! Vil = 1 Vpi magnitude is some, direction is different (speed is constant) AŤ - VF - V (can change in dic.or mag.) ā= Arrat I - VF - TYRAUTMOSTS ints toward center à points toward center --> "centripeta!" an Vaz (ur) ? () acceleration of uniforin circular motion y magnitude of centripetal accele N VATTINTSESTRUtzionato CTPED PUSS How ITETSSTORISTAXASS Quick Check 4.14 199990XFFFF D LLLLLLLLL OTUTKOVENTRXXXXX------- Hyrwyn MOLLYVHharts RRY PR PRES S UPOSTOPE DOSTATOSPAWNAWES Yraw MLLLLL himairamu O MODOC PUL Chapter 8 Dynamics 1 : Motion in a Planc uniform circular motion circular motion Wl constant speed centripetal forces any force causing uniform circular motion For mara m 2 ) direction is toward center of curvature, sq me direction as accelera!/01) ( ma) ac = vz/r THHYHT LELLTIVATVECOWAWCOPAS * This is not a new kind of force, Instead, it is one of our familiars forces acting in role of a force that causes a circular motion HYMYWWhem ex: motion of moon around earth - centripetal force is gravity rock whirled on end of string - centripetal force is tension ice skater making circles on rink - cent. force is friction CE DONNE SITUS AS RLPLANU EN M Ex? What coeff, of friction do car fires need on a flat curve ? The net force must point toward center of circle and only friction force is available to provide it For macam ( ) = Fisi 4 MSN = As (mg) We use is and not Fx because wheel is rolling, not shipping using in the Ms av 2 If Fs = 0 [car on icy rood) cor would continue in straight line and slide off road UVARTV VOLU IR டயயயபபா ITTER TAXI-.XX wwwxAR70WS - WWW 9 WALALLILL A PROXWW. F481 O SWw w .todoc.DOAB extechWww WWWT ME NODOLSLLLLLL CBOOT .WIN www. Ex: cor on banked curve -> no mood for friction Find o Don't tilt coord, system. Tilted axes are for Nsing :: linegi motion on incline. Need horizontal axis because au points horizontally in to center of circle There is a net cxt force toward center : Ngino Study Soup www 0 N lo Neoso _RAWIDERITKIEW --- --- - -. -... ing .. X-component of normal force is contripetal force INLARIVADOSPOTAWA. WWW ad small Om shallow bank large 8 - steep bank Fnet mä vi Neos 0 - mq = 0 -- N= malcos * : Nsino = mac - my2lr. |_pag sin nye \ cosa y tan 0 - - ovary 0= tani DOOSER 2. E Quick Check Quick Check 8.9 8.10 ra Ex: STOP 10/26/16 X HIW W W W WWWWWW Am yhm .SIV A TA Fnet z mä yi N-mg = -moc = - m (v2/n) (N-mg) is centripetal force ! N O (N=0 ---> not pushing on ground liftoff) N = mg - my2 = m(9 -12) 30 q-v2/rso GGS 170 ✓ 220g or else girborne ! www.cowWwwWw wWw Herren ECTODOS LLLL ou exwwww...WHAT THAT OCCEMYCOCOCHODOCOMO LO wwww A DITIONALITY Ex: cor on banked curve wris no need for friction I Find o Don't filt coord, system. Tilted axes are for Nsin : linead motion on incline, Need horizontal axis because au points horizontally in to center of circle There is a net txt force howard center : Nsino SECREEWTOCOCO099 Å Ncosa xt Hero Rabaldvi X-component of normal force is centrinetto! force -CUTE9ooooCDWP 992 ROPSPRETESS small Om shallow bank large 0 - steep bank AUANL WodoodoodDG A Fnet = ma y: Neos 0 - 18 q = 0 -- N=mq Icos y X : Nsino = mąco my? (29) sino - Mv. ICOSO STOP 10/26/16 tan 0 - ---- tan" START 10/28/16 LLLLLLLLLLLLAMTITO SPOREDIO ANASAYFWhere Quick Check 8,9 , tan rg Ex: Find v. Assumer is given. ERESTING FIRSX9WACHWA * X LLER rima XHAJAWALIOUS SEGNALANMASISHLAVN sou Pnet - m vi N-mq = --m0c = --- m (v2/r) (N-mg) is. centripetal force I N O (N=0 not pushing on ground oliftoff) : N = mg - imu? = m ( 9 - 12 ) 30 9-12/>0 . SSSSSSSSSSSSC ñ 2 289 or else airborne ! and L QuickCheck 8.10 xovevo SESVESLAAVALLOOOO O CO LLYTTIVITEV WWSBRIEL P Mundo HUMAN WP NUCIS Nonan for What it w Recall : W Circular Motion - circalor motion w/o changing speed consiany? (bicycle wheel slows down, CD speeds up) 10 change of angle 1.1. A change in tine SESSANSSEXUELSCREODATE DE . PREST WHAVN COEXEXTIELDOCOC OA TAARIFA artister th onqy or accelerolion ; AW - change in angular velocity rate of change of) . a. At change in time anqulor velocity unis: (rad /s) /s rad/92 a = 4 w increases Speeds up - w decreases slows down linear acceleration - fanden circle @ pot of interest I called fangensio! oceleration - QUÀVAL centripeta acceleration --- points toward center of circle nos causes circular 107/on. mac = 12/ Tvill vil AV : Vf - Vi a = A 141 AV does not point toward conter . - ä does not point toward center So net ä can be resolved into 2 comp. - at SSETTIMATE W i E STO ToConnor W WAMPON S -~ас ECUTIVENESS OLETNEMUTATUM How is 0.4. 1cated to ? : . DE lauro like yown DSBORRATHOIX - linear and angular acceleration are directly proportiono! FOTO - the greater of the car's wire's, the greater the acceleration of the car o We have defined 3 rotational quantity as - angin o velociyy V linear velocity o angular acceleration rna a linear arcileroy on LLYTAL SEDEELTEMAL OSSOWSOUH c uX TROIDOCOLAW99V995 MTU Wwwwwww ir... APSOE .DO PREPUSTNOSPIELPROSPEVKA |_Lincor volocity V: AX AT -- rate of change in position : - how fast an object moves 1 -- Unis one is Ex! A frain raveis 1.5 km in 5 minute V = 4x 1,5 km y 60 MIN = 18 km 1. A* * 5 Ihr COSTROVESE | Angular relocity -- rate of change in angle -- 1 2 1 1 2 3 4 : : 115i 4 - units are degrees is, revolution's per min, radians per second Ex: Ceiling for rotates 30 times per mute 40 30x 21 ud i 180cm *_50_min= 648,000 per hour * A-L 1 " rad * 1h Ex: Earth rotates on its axis every 24 houds ...49 271 Cody TDD-ro 100 LAT on my Lincur acceleration a = AX - rate at which velocity phanges -- hout fast an object speeds up or slows down - units are m/s EX! A herse accelerate from rost to a velocity of 15.0 m/s in 1.8is s AV VE- Vi 15,0 m/s - 0 8,33 nis 2 1.805 The horse increases its velocity by 8.33 mis ach second Angular Acceleration as 4w - rate at which angular velocity changes - how fast a rotating object speeds up or slows dow? -units are degrees / s2 revi's, rad is? Ex: A bowling balí takes 1,25 ta alla in, en aigula velocity of revis - AW: bf -- srevls - 35 revis? Wait 441. the bowling ba?' increase $ is angalar velocity by rail's fooh.. WAMWh MABLA un URGDOLLAR RIVODESSE SCARGARLY DOGODODERATED STE GANGSPOWOWOWA R EOX www. WIECTE ALAWI MALUMNI ROUILALTLAR T Nonuniform. Circular Motion - circular motion w/ a changing speed object has 90 (same od uniform circular motion) • points toward center of circle causes circular motion 00 y 2/ · Newton's 2nd. Lan wwwwwwwwww UTTGART COBORCONDUCTEDOPOWASSEROW object has 0+ (different from uniforin circular motion) 'tungent to circle @pt of interest 03 AV/At. E VOTION . SESSIPETARSE Newton's 2nd Low . (Fnet) t = 2F+=ma (constrained to be zero for uniform circular motion) equations of constant acceleration hold i 0: What are those A: Kinematics o rototiono) 6+190 © rolote W, 6, † recall ve Vot at T WWW. OS= Ar R UYWOOVUTOWOT COWOROW. verw WE yua Cel.) Yoof Vot at recall X Y *5=r voru TRAVAUTUVAUS the 15 R44 . O/04 (Wo) otom)42 03 04 Wot of t? X Xo ý test v vo + V TTTT WALLPALLU H 1 rvarar WCY Doop DE v2 - v, 2 + 2a8 XXXUL 6 * W * X a: 0p Cow)? = (0)2 + 21) (da) - w2. Wo24 2a G WORXAYWW. NATOR HANK thum 500GOK . STOP 10126116 ... .. ... . .... ... ... TILLIJW I LT I ALW www Pahine -30 Ex: Two bodies 3 Find Ti, T2, T3 ROLINS E CA Knot SLUULUH APAJAK DOO W =125 N Sa 12AWAFFALOUDSWEEVELESSOIRES S FBD. Fnet a mä Şx: 030 ly: T3 - W = 0 -> T3 :: W, = 125 N oool STON 10/21/16 START 10/24/16 RETORN PRESS # Z T2A E V&---- Tritannien Fac1 = m à xi Tzx - Tix = 0 Tz cos 53° - Ticos 379 :0 y y + Tay - 1 3 = 0 Ti sin 37° + Tas in 530 - Tz 0 (2 cos 53° -1100837" =0 (Tusin 37° * (Tasin 53° - T3 = 0 2 eqns, 2 unknowns + Tzx T2h (2 RUNGSORGERSONERY25.ARRARA MA c thart Solve o for T2 and substitute into 2) Tz = 71 ( 605 30) = 133T, Il cos 53"} Ti sin 370 + (1.33 71 )s in 530 - 125 N =0 Ti (sin 37° + 1,33 6 in 530) = 125 N L - 125 * ✓ 75. 1 N sin 37°+ 1,33 sin 5.3" T2 = 1,33 T1 = 1,33 ( 75,1N): 99:9 N. UuELLA APAPROPIONATO NOTTI Quick Check 6.3 ...? HW #4: 6.3, 6,21,6,38, 6.34, 6,41, 8.4, 8, 6, 8, 8, 8, 14, 8.16 you will learn this week Www TEBEESEMELORODITI mwema Devine mm EX ADRIAALALA VAM ----VISA M = 10 kg, m2 = 30 kg, 0 = 30 mass less rope, friction less pulley ignore UK: (for now) a) What is a of masses ? b) repeat if uk - 0.15 0 mer +VwrowTATORSHEDDUCTO 1946 WWW a) Don't know direction of a ! Assu me mu falls - 2 masses apply Fama to both SEEREMOTO -68bc99am VATRULLA sx: 0=0 ly: mig - Tamia > O -71 (I like a to be oper R ESOLM902 I mig h - NA . may T-WX = 120 T - Wsin @ smaa T-(Mzg )sino & M 2 a ViN - Wy zo N - Wcos 0 0 N - (mzq)cos 0 : 0 N= mzq cos o (choose coorde system such that x-axis is ll to surface ) PIRKS V To mag kwa K irrma OST. cos 0 = Wy/W sina - WarW -Wy = Wcos 0 Wx=Wsino 0+ 0 90 180 Oto + 90 = 180 q= 90 - 0 a = 906 190 - 0) o SARRESTR E PO C O mig-Dam, @) ☺ - M2g sino : m2a) ins. 2 unknown HESTER ARMSTRONO99WWW. 12) T = ma fm 295 in 9 Temala 495ino) substitute into o 1 miq - mala tasing ) = m, a mig - m 2 q sino = mi a + Mza a = mig - mag sino - 9 cm, - m2 sino) mit m2 mit me a = -1,22 m/s2 a opposite to our as STRONACHOA K NDIRMY .COM ARMY URUGUAY CNC V ARAM Şxi 0:0 ly: 1- m, q = 0, 0, 0) Judy Soup -->X 9 MONCLURAMBLA ALPHYL4 ' T T fx xi mzqsino - T-fkmza y: N - 1112 960s 0 - 0 fk = UK N a z gcoso m29 Oom.gama 2) (N) - 2 9 Cos 0 maqsin 0 - - u* (N) = ma a . 3 eqns, 3 unknowns N o megsin ACH 0 Tamia ym, a cinto 3) i N = n2gcos e Cinto ) m29 sine (mig + mi@)-UK (Mzg00s9) 2m2@ a: 9 (Mz sinom , -uk Mz cos 0 0. 2 7 mlsz m, f m 2 Huwa ERRESERVARVETYSK PEREMESHIRONTERAKCESOU LLLLLLLAAHhmmmh WWWWWWW U HAA WWW! RNM vain SAARI Ride AS Uniforme Circular Motion - constant speed in a circle I ho = AS 40: rotation angle As larc length, distance traveled along circular path ri radius of curvature of circular path 40145 LINA QUIVALILLA awwwwwwwSIC WATTSTEXTREVA WANAWWWWWYWRITA SEISOO TEODOSPFW1Wan one revolution : As Er40 1(211) = 27 (circumference of circle) 21 radia 15 - 360° ȚI radions = 180° if speed is constant l'uniform) X = Xa! Vott Żut 2 x = Vot da vt linear velocity of objects @ - As.. 2ur c... one revolution Ź 17 period (time for 1 revolution) a wWTAN www KUAL frequency T ORU. # 1 #rev/sec 9 speed of earth @, equator r = 6,400 km 27'r 21 (6.400 km), 1 000 1 . 1 t V = 450 m/s. (* 1000 mph) FOR T UVO LALU 1 . 24 h : 1b 60 min 60 G LLLLLAMAShTETTAVA RDGE ... w WOMENS- Want something that doesn't depend on where you are what radius) it - time 10 = angle angular velocity or rate of change of angle, how fast object rotates V = 45. = 140. r (46) = rw rate rate @ which particle in overs At A4 around circle', STOP 10/24/16 v = wr relationship DYWA linear and angular enery btwn linear and angular velocity START 10/26/16 units rad/s linear relocity 16 tangent to circle, changes direction WAH R OTTONL WWW S direction of w: CW or CCW vetur mass is @ constant speed but direction changing --> : V ETO AMA Quick Check 4,12 QuickCheck 4,13 G ODTAwwwww/STOWAWCA YA RULADA Nuwe S SO