Course Outline. 1. MATLAB tutorial 2. Motion of systems that can be idealized as particles
|
|
- Raymond Richards
- 5 years ago
- Views:
Transcription
1 Couse Oulne. MATLAB uoal. Moon of syses ha can be dealzed as pacles Descpon of oon, coodnae syses; Newon s laws; Calculang foces equed o nduce pescbed oon; Deng and solng equaons of oon 3. Conseaon laws fo syses of pacles Wo, powe and enegy; Lnea pulse and oenu Angula oenu 4. Vbaons Exa opcs Chaacescs of baons; baon of fee DO syses Vbaon of daped DO syses oced Vbaons 5. Moon of syses ha can be dealzed as gd bodes Descpon of oaonal oon neacs; geas, pulleys and he ollng wheel Ineal popees of gd bodes; oenu and enegy Dynacs of gd bodes
2 Pacle Dynacs concep checls Undesand he concep of an neal fae Be able o dealze an engneeng desgn as a se of pacles, and now when hs dealzaon wll ge accuae esuls Descbe he oon of a syse of pacles (eg coponens n a fxed coodnae syse; coponens n a pola coodnae syse, ec) Be able o dffeenae poson ecos (wh pope use of he chan ule!) o deene elocy and acceleaon; and be able o negae acceleaon o elocy o deene poson eco. Be able o descbe oon n noal-angenal and pola coodnaes (eg be able o we down eco coponens of elocy and acceleaon n es of speed, adus of cuaue of pah, o coodnaes n he cylndcal-pola syse). Be able o cone beween Caesan o noal-angenal o pola coodnae descpons of oon Be able o daw a coec fee body daga showng foces acng on syse dealzed as pacles Be able o we down Newon s laws of oon n ecangula, noal-angenal, and pola coodnae syses Be able o oban an addonal oen balance equaon fo a gd body ong whou oaon o oang abou a fxed axs a consan ae. Be able o use Newon s laws of oon o sole fo unnown acceleaons o foces n a syse of pacles Use Newon s laws of oon o dee dffeenal equaons goenng he oon of a syse of pacles Be able o e-we second ode dffeenal equaons as a pa of fs-ode dffeenal equaons n a fo ha MATLAB can sole
3 Ineal fae non acceleang, non oang efeence fae Pacle pon ass a soe poson n space Poson Veco Velocy Veco ( ) = x( ) + y( ) + z( ) () = () + () + () x y z d dx dy dz = ( x+ y+ z) = + + d d d d dx dy dz x() = y() = z() = d d d Decon of elocy eco s paallel o pah Magnude of elocy eco s dsance aeled / e Acceleaon Veco O () (+d) d d dy () () () () x d a = a z x + ay + az = ( x+ y+ z) = + + d d d d Also Pacle Kneacs d d () x y d () () z x y z d x d y d z a = = a = = a = = d d d d d d d dy () x d a () () z x = x ay = y az = z dx dy dz () d pah of pacle
4 Pacle Kneacs Sagh lne oon wh consan acceleaon = X + V + a = ( V + a) = a a Te/elocy/poson dependen acceleaon use calculus = X + () d = V + a() d d g() a = = f ( ) d = g() d d f () V x () dx g() = = f ( x) d = () d d f () X d = ax ( ) d d dx d = ax ( ) = ax ( ) dx d dx () x () V d = a( x) dx
5 Pacle Kneacs Ccula Moon a cons speed θ = ω s= Rθ V = ωr ( cosθ snθ ) R( sn cos ) = R + = ω θ+ θ = V V a= ω R(cosθ+ sn θ) = ω Rn= n R Geneal ccula oon ( cosθ snθ ) R( sn cos ) = R + = ω θ+ θ = V a= Rα( snθ+ cos θ) Rω (cosθ+ sn θ) dv V = αr + ω Rn= + n d R ω = dθ / d α = dω / d = d θ / d s = Rθ V = ds / d = Rω snθ cosθ R n θ=ω Rsn θ Rcosθ snθ cosθ R n θ Rsn θ Rcosθ
6 Pacle Kneacs Moon along an abay pah = V dv V a= + n d R R n s Radus of cuaue R = d x d y + ds ds = xs ( ) + y(s) Pola Coodnaes e θ e d dθ = e + e d d θ d dθ d θ d dθ a= e + + e d d d d d θ θ
7 Usng Newon s laws Calculang foces equed o cause pescbed oon Idealze syse ee body daga Kneacs (descbe oon usually goal s o fnd foula fo acceleaon) =a fo each pacle. M c = (fo seadly o non-oang gd bodes o faes only) Sole fo unnown foces o acceleaons (us le sacs)
8 Usng Newon s laws o dee equaons of oon. Idealze syse. Inoduce aables o descbe oon (ofen x,y coods, bu we wll see ohe exaples) 3. We down, dffeenae o ge a 4. Daw BD 5. = a 6. If necessay, elnae eacon foces 7. Resul wll be dffeenal equaons fo coods defned n (), e.g. d x dx + λ + x = Y snω d d 8. Idenfy nal condons, and sole ODE
9 Moon of a poecle n eahs gay X Y Z d d = + + = Vx Vy Vz = + + X V ( ) ( ) = X + Vx + Y + Vy + Z + Vz g ( V ) ( V ) ( V g) = + + a= g x y z
10 Reaangng dffeenal equaons fo MATLAB Exaple d y d dy + ζωn + ωny = d Inoduce = dy / d Then d y d = ζωn ωny Ths has fo dw d y = f(, w) w =
11 Conseaon Conseaon laws fo Laws pacles: concep Concep checls Checls Know he defnons of powe (o ae of wo) of a foce, and wo done by a foce Know he defnon of nec enegy of a pacle Undesand powe-wo-nec enegy elaons fo a pacle Be able o use wo/powe/nec enegy o sole pobles nolng pacle oon Be able o dsngush beween conseae and non-conseae foces Be able o calculae he poenal enegy of a conseae foce Be able o calculae he foce assocaed wh a poenal enegy funcon Know he wo-enegy elaon fo a syse of pacles; (enegy conseaon fo a closed syse) Use enegy conseaon o analyze oon of conseae syses of pacles Know he defnon of he lnea pulse of a foce Know he defnon of lnea oenu of a pacle Undesand he pulse-oenu (and foce-oenu) elaons fo a pacle Undesand pulse-oenu elaons fo a syse of pacles (oenu conseaon fo a closed syse) Be able o use pulse-oenu o analyze oon of pacles and syses of pacles Know he defnon of esuon coeffcen fo a collson Pedc changes n elocy of wo colldng pacles n D and 3D usng oenu and he esuon foula Know he defnon of angula pulse of a foce Know he defnon of angula oenu of a pacle Undesand he angula pulse-oenu elaon Be able o use angula oenu o sole cenal foce pobles/pac pobles
12 Wo-Enegy elaons fo a sngle pacle Rae of wo done by a foce (powe deeloped by foce) P = O P Toal wo done by a foce W d W = = d O () P Knec enegy T= = + + ( ) x y z Powe-nec enegy elaon Wo-nec enegy elaon dt P = d W = d = T T O P
13 Poenal Enegy Poenal enegy of a conseae foce (pa) U( ) = d+ consan = gad( U ) Type of foce Gay acng on a pacle nea eahs suface Gaaonal foce exeed on ass by ass M a he ogn Poenal enegy U = gy GM U = y O P oce exeed by a spng wh sffness and unseched lengh L oce acng beween wo chaged pacles U = ( L ) QQ +Q +Q U = 4πε oce exeed by one olecule of a noble gas (e.g. He, A, ec) on anohe (Lennad Jones poenal). a s he equlbu spacng beween olecules, and E s he enegy of he bond. 6 a a U = E
14 Enegy Relaon fo a Conseae Syse Inenal oces: (foces exeed by one pa of he syse on anohe) Exenal oces: (any ohe foces) R Syse s conseae f all nenal foces ae conseae foces (o consan foces) 4 R R 3 R 3 R R 3 R Enegy elaon fo a conseae syse = = Toal KE T Toal PE U Exenal Powe P () Exenal wo W P() d = Toal KE T Toal PE U ( ) W = T + U T + U Specal case zeo enal wo: + = + T U T U KE+PE = consan
15 Ipulse-Moenu fo a sngle pacle Defnons Lnea Ipulse of a foce Lnea oenu of a pacle I= () d p= O () Ipulse-Moenu elaons d = p d I= p p = p=p O () = p=p
16 Ipulse-Moenu Ipulse-oenu fo fo a syse a syse of pacles of pacles R oce exeed on pacle by pacle Exenal foce on pacle Velocy of pacle 4 R R 3 R 3 R R 3 R Toal Exenal oce Toal Exenal Ipulse 4 3 () I = () d 4 3 Ipulse-oenu fo he syse: d = p d I = p p = 3 Toal oenu p = 3 Toal oenu p Specal case zeo enal pulse: p = p (Lnea oenu conseed)
17 Collsons x A A x A A * x B x B B B Moenu Resuon foula + = + A B A B A x B x A x B x ( ) = e B A B A = ( + e) + ( ) B B A B A A = + ( + e) + B ( ) A A B B A A B A A A A B n B B B Moenu Resuon foula + = + B A B A B A B A B A B A B A ( ) ( ) ( e) ( ) = + n n + + ( ) ( ) B B A B A = + e n n B A ( ) ( ) A A B B A = + + e n n B A
18 Angula Ipulse-Moenu Equaons fo a Pacle pacle Angula Ipulse Angula Moenu Ipulse-Moenu elaons A= () () d h= p= d = h d x O y () () z A= h h Specal Case A= h = h Angula oenu conseed Useful fo cenal foce pobles (when foces on a pacle always ac hough a sngle pon, eg planeay gay)
s = rθ Chapter 10: Rotation 10.1: What is physics?
Chape : oaon Angula poson, velocy, acceleaon Consan angula acceleaon Angula and lnea quanes oaonal knec enegy oaonal nea Toque Newon s nd law o oaon Wok and oaonal knec enegy.: Wha s physcs? In pevous
More information5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )
5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma
More informationField due to a collection of N discrete point charges: r is in the direction from
Physcs 46 Fomula Shee Exam Coulomb s Law qq Felec = k ˆ (Fo example, f F s he elecc foce ha q exes on q, hen ˆ s a un veco n he decon fom q o q.) Elecc Feld elaed o he elecc foce by: Felec = qe (elecc
More informationChapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
More informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More informationHomework 8: Rigid Body Dynamics Due Friday April 21, 2017
EN40: Dynacs and Vbraons Hoework 8: gd Body Dynacs Due Frday Aprl 1, 017 School of Engneerng Brown Unversy 1. The earh s roaon rae has been esaed o decrease so as o ncrease he lengh of a day a a rae of
More informationL4:4. motion from the accelerometer. to recover the simple flutter. Later, we will work out how. readings L4:3
elave moon L4:1 To appl Newon's laws we need measuemens made fom a 'fed,' neal efeence fame (unacceleaed, non-oang) n man applcaons, measuemens ae made moe smpl fom movng efeence fames We hen need a wa
More informationMotion in Two Dimensions
Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The
More informationLecture 5. Plane Wave Reflection and Transmission
Lecue 5 Plane Wave Reflecon and Tansmsson Incden wave: 1z E ( z) xˆ E (0) e 1 H ( z) yˆ E (0) e 1 Nomal Incdence (Revew) z 1 (,, ) E H S y (,, ) 1 1 1 Refleced wave: 1z E ( z) xˆ E E (0) e S H 1 1z H (
More informationESS 265 Spring Quarter 2005 Kinetic Simulations
SS 65 Spng Quae 5 Knec Sulaon Lecue une 9 5 An aple of an lecoagnec Pacle Code A an eaple of a knec ulaon we wll ue a one denonal elecoagnec ulaon code called KMPO deeloped b Yohhau Oua and Hoh Mauoo.
More information2 shear strain / L for small angle
Sac quaons F F M al Sess omal sess foce coss-seconal aea eage Shea Sess shea sess shea foce coss-seconal aea llowable Sess Faco of Safe F. S San falue Shea San falue san change n lengh ognal lengh Hooke
More informationGo over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
More informationCourse Outline. 1. MATLAB tutorial 2. Motion of systems that can be idealized as particles
Couse Outlne. MATLAB tutoal. Moton of systems that can be dealzed as patcles Descpton of moton, coodnate systems; Newton s laws; Calculatng foces equed to nduce pescbed moton; Devng and solvng equatons
More informationResponse of MDOF systems
Response of MDOF syses Degree of freedo DOF: he nu nuber of ndependen coordnaes requred o deerne copleely he posons of all pars of a syse a any nsan of e. wo DOF syses hree DOF syses he noral ode analyss
More informationPHY121 Formula Sheet
HY Foula Sheet One Denson t t Equatons o oton l Δ t Δ d d d d a d + at t + at a + t + ½at² + a( - ) ojectle oton y cos θ sn θ gt ( cos θ) t y ( sn θ) t ½ gt y a a sn θ g sn θ g otatonal a a a + a t Ccula
More informationPhysics 1501 Lecture 19
Physcs 1501 ectue 19 Physcs 1501: ectue 19 Today s Agenda Announceents HW#7: due Oct. 1 Mdte 1: aveage 45 % Topcs otatonal Kneatcs otatonal Enegy Moents of Ineta Physcs 1501: ectue 19, Pg 1 Suay (wth copason
More informationMolecular dynamics modeling of thermal and mechanical properties
Molecula dynamcs modelng of hemal and mechancal popees Alejando Sachan School of Maeals Engneeng Pudue Unvesy sachan@pudue.edu Maeals a molecula scales Molecula maeals Ceamcs Meals Maeals popees chas Maeals
More informationChapters 2 Kinematics. Position, Distance, Displacement
Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen
More informationPhysics 201 Lecture 15
Phscs 0 Lecue 5 l Goals Lecue 5 v Elo consevaon of oenu n D & D v Inouce oenu an Iulse Coens on oenu Consevaon l oe geneal han consevaon of echancal eneg l oenu Consevaon occus n sses wh no ne eenal foces
More informationToday - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
More informationPhysics 207 Lecture 16
Physcs 07 Lectue 6 Goals: Lectue 6 Chapte Extend the patcle odel to gd-bodes Undestand the equlbu of an extended object. Analyze ollng oton Undestand otaton about a fxed axs. Eploy consevaton of angula
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More informationModern Energy Functional for Nuclei and Nuclear Matter. By: Alberto Hinojosa, Texas A&M University REU Cyclotron 2008 Mentor: Dr.
Moden Enegy Funconal fo Nucle and Nuclea Mae By: lbeo noosa Teas &M Unvesy REU Cycloon 008 Meno: D. Shalom Shlomo Oulne. Inoducon.. The many-body poblem and he aee-fock mehod. 3. Skyme neacon. 4. aee-fock
More informationCHAPTER 10: LINEAR DISCRIMINATION
HAPER : LINEAR DISRIMINAION Dscmnan-based lassfcaon 3 In classfcaon h K classes ( k ) We defned dsmnan funcon g () = K hen gven an es eample e chose (pedced) s class label as f g () as he mamum among g
More informationMass-Spring Systems Surface Reconstruction
Mass-Spng Syses Physally-Based Modelng: Mass-Spng Syses M. Ale O. Vasles Mass-Spng Syses Mass-Spng Syses Snake pleenaon: Snake pleenaon: Iage Poessng / Sae Reonson: Iage poessng/ Sae Reonson: Mass-Spng
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
More informationNanoparticles. Educts. Nucleus formation. Nucleus. Growth. Primary particle. Agglomeration Deagglomeration. Agglomerate
ucs Nucleus Nucleus omaon cal supesauaon Mng o eucs, empeaue, ec. Pmay pacle Gowh Inegaon o uson-lme pacle gowh Nanopacles Agglomeaon eagglomeaon Agglomeae Sablsaon o he nanopacles agans agglomeaon! anspo
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
More informationRotation: All around us: wheels, skaters, ballet, gymnasts, helicopter, rotors, mobile engines, CD disks, Atomic world: electrons spin, orbit.
Chape 0 Spn an bal n Ran: All aun us: wheels, skaes, balle, gynass, helcpe, s, ble engnes, CD sks, Ac wl: elecns spn, b. Unese: planes spn an bng he sun, galaxes spn, Chape 4 kneacs Chape 0 ynacs 0. Se
More informationToday s topic: IMPULSE AND MOMENTUM CONSERVATION
Today s opc: MPULSE ND MOMENTUM CONSERVTON Reew of Las Week s Lecure Elasc Poenal Energy: x: dsplaceen fro equlbru x = : equlbru poson Work-Energy Theore: W o W W W g noncons W non el W noncons K K K (
More informationOutline. GW approximation. Electrons in solids. The Green Function. Total energy---well solved Single particle excitation---under developing
Peenaon fo Theoecal Condened Mae Phyc n TU Beln Geen-Funcon and GW appoxmaon Xnzheng L Theoy Depamen FHI May.8h 2005 Elecon n old Oulne Toal enegy---well olved Sngle pacle excaon---unde developng The Geen
More informationEN40: Dynamics and Vibrations. Midterm Examination Tuesday March
EN4: Dynaics and Vibations Midte Exaination Tuesday Mach 8 16 School of Engineeing Bown Univesity NME: Geneal Instuctions No collaboation of any kind is peitted on this exaination. You ay bing double sided
More informationPrediction of modal properties of circular disc with pre-stressed fields
MAEC Web of Confeences 157 0034 018 MMS 017 hps://do.og/10.1051/aecconf/0181570034 Pedcon of odal popees of ccula dsc h pe-sessed felds Mlan Naď 1* Rasslav Ďuš 1 bo Nánás 1 1 Slovak Unvesy of echnology
More informationSharif University of Technology - CEDRA By: Professor Ali Meghdari
Shaif Univesiy of echnology - CEDRA By: Pofesso Ali Meghai Pupose: o exen he Enegy appoach in eiving euaions of oion i.e. Lagange s Meho fo Mechanical Syses. opics: Genealize Cooinaes Lagangian Euaion
More informationName of the Student:
Engneeng Mahemacs 05 SUBJEC NAME : Pobably & Random Pocess SUBJEC CODE : MA645 MAERIAL NAME : Fomula Maeal MAERIAL CODE : JM08AM007 REGULAION : R03 UPDAED ON : Febuay 05 (Scan he above QR code fo he dec
More informationN 1. Time points are determined by the
upplemena Mehods Geneaon of scan sgnals In hs secon we descbe n deal how scan sgnals fo 3D scannng wee geneaed. can geneaon was done n hee seps: Fs, he dve sgnal fo he peo-focusng elemen was geneaed o
More informationPHY2053 Summer C 2013 Exam 1 Solutions
PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The
More informationWORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
More informationRELATIVE MOTION OF SYSTEMS IN A PARAMETRIC FORMULATION OF MECHANICS UDC Đorđe Mušicki
FCT UNIVESITTIS Sees: Mechancs, uoac Conol an obocs Vol.3, N o,, pp. 39-35 ELTIVE MOTION OF SYSTEMS IN PMETIC FOMULTION OF MECHNICS UDC 53. Đođe Mušck Faculy of Physcs, Unvesy of Belgae, an Maheacal Insue
More informationDetermination of the rheological properties of thin plate under transient vibration
(3) 89 95 Deenaon of he heologcal popees of hn plae unde ansen vbaon Absac The acle deals wh syseac analyss of he ansen vbaon of ecangula vscoelasc ohoopc hn D plae. The analyss s focused on specfc defoaon
More informationRotary motion
ectue 8 RTARY TN F THE RGD BDY Notes: ectue 8 - Rgd bod Rgd bod: j const numbe of degees of feedom 6 3 tanslatonal + 3 ota motons m j m j Constants educe numbe of degees of feedom non-fee object: 6-p
More informationLecture 9: Dynamic Properties
Shor Course on Molecular Dynamcs Smulaon Lecure 9: Dynamc Properes Professor A. Marn Purdue Unversy Hgh Level Course Oulne 1. MD Bascs. Poenal Energy Funcons 3. Inegraon Algorhms 4. Temperaure Conrol 5.
More informationDynamics of Rigid Bodies
Dynamcs of Rgd Bodes A gd body s one n whch the dstances between consttuent patcles s constant thoughout the moton of the body,.e. t keeps ts shape. Thee ae two knds of gd body moton: 1. Tanslatonal Rectlnea
More information( ) ( ) ( ) ( ) ( ) ( ) j ( ) A. b) Theorem
b) Theoe The u of he eco pojecon of eco n ll uull pependcul (n he ene of he cl poduc) decon equl o he eco. ( ) n e e o The pojecon conue he eco coponen of he eco. poof. n e ( ) ( ) ( ) e e e e e e e e
More informationPHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More informationReflection and Refraction
Chape 1 Reflecon and Refacon We ae now neesed n eplong wha happens when a plane wave avelng n one medum encounes an neface (bounday) wh anohe medum. Undesandng hs phenomenon allows us o undesand hngs lke:
More informationRadial Motion of Two Mutually Attracting Particles
Radal Moon of Two Muually Aacng Pacles Cal E. Mungan, U.S. Naval Academy, Annapols, MD A pa of masses o oppose-sgn chages eleased fom es wll move decly owad each ohe unde he acon of he nvesedsance-squaed
More informationChapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
More informationb g b g b g Chapter 2 Wave Motion 2.1 One Dimensional Waves A wave : A self-sustaining disturbance of the medium Hecht;8/30/2010; 2-1
Chape Wave Moon Hech;8/30/010; -1.1 One Dmensonal Waves A wave : A self-susanng dsubance of he medum Waves n a spng A longudnal wave A ansvese wave : Medum dsplacemen // Decon of he wave : Medum dsplacemen
More informationBasic molecular dynamics
1.1, 3.1, 1.333,. Inoducon o Modelng and Smulaon Spng 11 Pa I Connuum and pacle mehods Basc molecula dynamcs Lecue Makus J. Buehle Laboaoy fo Aomsc and Molecula Mechancs Depamen of Cvl and Envonmenal Engneeng
More information2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles
/4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla
More informationChapter 13 - Universal Gravitation
Chapte 3 - Unesal Gataton In Chapte 5 we studed Newton s thee laws of moton. In addton to these laws, Newton fomulated the law of unesal gataton. Ths law states that two masses ae attacted by a foce gen
More informationRotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1
Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1 Leanng Objectes What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t What we
More informationDisplacement, Velocity, and Acceleration. (WHERE and WHEN?)
Dsplacemen, Velocy, and Acceleraon (WHERE and WHEN?) Mah resources Append A n your book! Symbols and meanng Algebra Geomery (olumes, ec.) Trgonomery Append A Logarhms Remnder You wll do well n hs class
More informationcalculating electromagnetic
Theoeal mehods fo alulang eleomagne felds fom lghnng dshage ajeev Thoapplll oyal Insue of Tehnology KTH Sweden ajeev.thoapplll@ee.kh.se Oulne Despon of he poblem Thee dffeen mehods fo feld alulaons - Dpole
More informationTRANSIENTS. Lecture 5 ELEC-E8409 High Voltage Engineering
TRANSIENTS Lece 5 ELECE8409 Hgh Volage Engneeng TRANSIENT VOLTAGES A ansen even s a sholved oscllaon (sgnfcanly fase han opeang feqency) n a sysem cased by a sdden change of volage, cen o load. Tansen
More informationChapter 8. Linear Momentum, Impulse, and Collisions
Chapte 8 Lnea oentu, Ipulse, and Collsons 8. Lnea oentu and Ipulse The lnea oentu p of a patcle of ass ovng wth velocty v s defned as: p " v ote that p s a vecto that ponts n the sae decton as the velocty
More informationMay 29, 2018, 8:45~10:15 IB011 Advanced Lecture on Semiconductor Electronics #7
May 9, 8, 8:5~:5 I Advanced Lecue on Semconduco leconcs #7 # Dae Chape 7 May 9 Chape 5.Deec and Cae Cae Scaeng Ionzed mpuy scaeng, Alloy scaeng, Neual mpuy scaeng, Ineace oughness scaeng, Auge / Scaeng
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationChapter Finite Difference Method for Ordinary Differential Equations
Chape 8.7 Fne Dffeence Mehod fo Odnay Dffeenal Eqaons Afe eadng hs chape, yo shold be able o. Undesand wha he fne dffeence mehod s and how o se o solve poblems. Wha s he fne dffeence mehod? The fne dffeence
More informationScattering at an Interface: Oblique Incidence
Course Insrucor Dr. Raymond C. Rumpf Offce: A 337 Phone: (915) 747 6958 E Mal: rcrumpf@uep.edu EE 4347 Appled Elecromagnecs Topc 3g Scaerng a an Inerface: Oblque Incdence Scaerng These Oblque noes may
More information1 Constant Real Rate C 1
Consan Real Rae. Real Rae of Inees Suppose you ae equally happy wh uns of he consumpon good oday o 5 uns of he consumpon good n peod s me. C 5 Tha means you ll be pepaed o gve up uns oday n eun fo 5 uns
More informationajanuary't I11 F or,'.
',f,". ; q - c. ^. L.+T,..LJ.\ ; - ~,.,.,.,,,E k }."...,'s Y l.+ : '. " = /.. :4.,Y., _.,,. "-.. - '// ' 7< s k," ;< - " fn 07 265.-.-,... - ma/ \/ e 3 p~~f v-acecu ean d a e.eng nee ng sn ~yoo y namcs
More informationOne-dimensional kinematics
Phscs 45 Fomula Sheet Eam 3 One-dmensonal knematcs Vectos dsplacement: Δ total dstance taveled aveage speed total tme Δ aveage veloct: vav t t Δ nstantaneous veloct: v lm Δ t v aveage acceleaton: aav t
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationExam 3: Equation Summary
MAACHUETT INTITUTE OF TECHNOLOGY Depatment of Physics Physics 8. TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t = Exam 3: Equation ummay = Impulse: I F( t ) = p Toque: τ =,P dp F P τ =,P
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More information(,,, ) (,,, ). In addition, there are three other consumers, -2, -1, and 0. Consumer -2 has the utility function
MACROECONOMIC THEORY T J KEHOE ECON 87 SPRING 5 PROBLEM SET # Conder an overlappng generaon economy le ha n queon 5 on problem e n whch conumer lve for perod The uly funcon of he conumer born n perod,
More informationQualifying Examination Electricity and Magnetism Solutions January 12, 2006
1 Qualifying Examination Electicity and Magnetism Solutions Januay 12, 2006 PROBLEM EA. a. Fist, we conside a unit length of cylinde to find the elationship between the total chage pe unit length λ and
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More information10/15/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101
10/15/01 PHY 11 C Geneal Physcs I 11 AM-1:15 PM MWF Oln 101 Plan fo Lectue 14: Chapte 1 Statc equlbu 1. Balancng foces and toques; stablty. Cente of gavty. Wll dscuss elastcty n Lectue 15 (Chapte 15) 10/14/01
More informationPhysics 207 Lecture 13
Physics 07 Lecue 3 Physics 07, Lecue 3, Oc. 8 Agenda: Chape 9, finish, Chape 0 Sa Chape 9: Moenu and Collision Ipulse Cene of ass Chape 0: oaional Kineaics oaional Enegy Moens of Ineia Paallel axis heoe
More informationPhysics 11b Lecture #2. Electric Field Electric Flux Gauss s Law
Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More information2/20/2013. EE 101 Midterm 2 Review
//3 EE Mderm eew //3 Volage-mplfer Model The npu ressance s he equalen ressance see when lookng no he npu ermnals of he amplfer. o s he oupu ressance. I causes he oupu olage o decrease as he load ressance
More informationMotion of Wavepackets in Non-Hermitian. Quantum Mechanics
Moon of Wavepaces n Non-Herman Quanum Mechancs Nmrod Moseyev Deparmen of Chemsry and Mnerva Cener for Non-lnear Physcs of Complex Sysems, Technon-Israel Insue of Technology www.echnon echnon.ac..ac.l\~nmrod
More informationRelative and Circular Motion
Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1 Mechanics Lecue 3 Slide 2 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 0 Canoncal Transformaons (Chaper 9) Wha We Dd Las Tme Hamlon s Prncple n he Hamlonan formalsm Dervaon was smple δi δ Addonal end-pon consrans pq H( q, p, ) d 0 δ q ( ) δq ( ) δ
More informationCHAPTER 13 LAGRANGIAN MECHANICS
CHAPTER 3 AGRANGIAN MECHANICS 3 Inoucon The usual way of usng newonan mechancs o solve a poblem n ynamcs s fs of all o aw a lage, clea agam of he sysem, usng a ule an a compass Then mak n he foces on he
More informationWater Hammer in Pipes
Waer Haer Hydraulcs and Hydraulc Machnes Waer Haer n Pes H Pressure wave A B If waer s flowng along a long e and s suddenly brough o res by he closng of a valve, or by any slar cause, here wll be a sudden
More informationChapter 6 Plane Motion of Rigid Bodies
Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he
More informationRotor profile design in a hypogerotor pump
Jounal of Mechancal Scence and Technology (009 459~470 Jounal of Mechancal Scence and Technology www.spngelnk.com/conen/78-494x DOI 0.007/s06-009-007-y oo pofle desgn n a hypogeoo pump Soon-Man Kwon *,
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationDynamics of Rotational Motion
Dynamics of Rotational Motion Toque: the otational analogue of foce Toque = foce x moment am τ = l moment am = pependicula distance though which the foce acts a.k.a. leve am l l l l τ = l = sin φ = tan
More informationMath 209 Assignment 9 Solutions
Math 9 Assignment 9 olutions 1. Evaluate 4y + 1 d whee is the fist octant pat of y x cut out by x + y + z 1. olution We need a paametic epesentation of the suface. (x, z). Now detemine the nomal vecto:
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More information8. HAMILTONIAN MECHANICS
8. HAMILTONIAN MECHANICS In ode o poceed fom he classcal fomulaon of Maxwell's elecodynamcs o he quanum mechancal descpon a new mahemacal language wll be needed. In he pevous secons he elecomagnec feld
More informationTime-Dependent Density Functional Theory in Condensed Matter Physics
Exenal Revew on Cene fo Compuaonal Scences Unvesy of Tsukuba 013..18-0 Tme-Dependen Densy Funconal Theoy n Condensed Mae Physcs K. YABANA Cene fo Compuaonal Scences Unvesy of Tsukuba Collaboaos: G.F. Besch
More information24-2: Electric Potential Energy. 24-1: What is physics
D. Iyad SAADEDDIN Chapte 4: Electc Potental Electc potental Enegy and Electc potental Calculatng the E-potental fom E-feld fo dffeent chage dstbutons Calculatng the E-feld fom E-potental Potental of a
More informationA VISCOPLASTIC MODEL OF ASYMMETRICAL COLD ROLLING
SISOM 4, BUCHAEST, - May A VISCOPLASTIC MODEL OF ASYMMETICAL COLD OLLING odca IOAN Spu Hae Unvesy Buchaes, odcaoan7@homal.com Absac: In hs pape s gven a soluon of asymmecal sp ollng poblem usng a Bngham
More informationChapter Fifiteen. Surfaces Revisited
Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid
More informationTHE PHYSICS BEHIND THE SODACONSTRUCTOR. by Jeckyll
THE PHYSICS BEHIND THE SODACONSTRUCTOR b Jeckll THE PHYSICS BEHIND THE SODACONSTRUCTOR - b Jeckll /3 CONTENTS. INTRODUCTION 5. UNITS OF MEASUREMENT 7 3. DETERMINATION OF THE PHYSICAL CONSTANTS ADOPTED
More informationExam 3: Equation Summary
MAACHUETT INTITUTE OF TECHNOLOGY Depatment of Physics Physics 8. TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t = Exam 3: Equation ummay = Impulse: I F( t ) = p Toque: τ =,P dp F P τ =,P
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationKEPLER S LAWS AND PLANETARY ORBITS
KEPE S AWS AND PANETAY OBITS 1. Selected popeties of pola coodinates and ellipses Pola coodinates: I take a some what extended view of pola coodinates in that I allow fo a z diection (cylindical coodinates
More informationRotations.
oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse
More informationComprehensive Integrated Simulation and Optimization of LPP for EUV Lithography Devices
Comprehense Inegraed Smulaon and Opmaon of LPP for EUV Lhograph Deces A. Hassanen V. Su V. Moroo T. Su B. Rce (Inel) Fourh Inernaonal EUVL Smposum San Dego CA Noember 7-9 2005 Argonne Naonal Laboraor Offce
More information