Newtonian Relativity
|
|
- Flora Hampton
- 5 years ago
- Views:
Transcription
1 Newonian Relaii A referene frame in whih Newon s laws are alid is alled an inerial frame Newonian priniple of relaii or Galilean inariane If Newon s laws are alid in one referene frame, hen he are also alid in a referene frame moing a niform eloi relaie o he firs ssem Ths his moing frame is also an inerial frame
2 Consider Newonian Relaii
3 Newonian Relaii Galilean ransformaion Noe ime is he same in boh ssems 3
4 Newonian Relaii Noe Newon s laws are alid in boh frames The fore and aeleraion are he same in boh frames There is no wa o dee whih frame is moing and whih is a res d d F ma m m ma d d d d d F ma m m m d d d F F 4
5 Loren Transformaion We immediael see he Galilean ransformaion is inonsisen wih Einsein s poslaes If he eloi of ligh in frame K, he eloi of ligh V in frame K The Loren ransformaion saisfies Einsein s poslaes and also redes o he Galilean ransformaion a low eloiies A deriaion is gien in Thornon and Re p30-3 5
6 6 Loren Transformaion / / where β
7 7 Loren Transformaion Time dilaion reisied Le Δ be he proper ime ineral measred b a lok fied a 0 in K The loks in S read a ime longer han he proper ime. The moing lok in S rns slow. V V V V Δ Δ 0 0
8 Loren Transformaion Lengh onraion reisied Consider a measring rod wih proper lengh Δ -. The ineral Δ as iewed in S ms hae he posiions measred a he same ime 0 in S. V V Δ Δ / The lengh of he moing obje as measred in S is shorer han he proper lengh V V 0 0 8
9 9 Loren Transformaion Clok snhroniaion reisied Consider wo loks snhronied in S. Clok B a and lok A a. Wha imes do he read a ime 0 in S? Agrees wih resls from he homework L V V V V V A B A B
10 Bea and Gamma β 0
11 Inarians Inarian qaniies hae he same ale in all inerial frames In he ne homework, o ll show s is he same for all inerial frames s s s s
12 Inarians Consider wo eens and We define he spaeime ineral as Δs Δ -Δ Three ases Lighlike Δs 0 The wo eens an be onneed onl b a ligh signal Spaelike Δs >0 The wo eens are no asall onneed. We an find an inerial frame where he eens or a he same ime b a differen posiions in spae Timelike Δs <0 The wo eens are asall onneed. We an find an inerial frame where he eens or a he same posiion in spae b a differen imes
13 Addiion of Veloiies Reall he Galilean ransformaion beween wo frames K and K where K moes wih eloi wih respe o K Consider an obje moing wih eloi in K and in K d d d d d d 3
14 Galilean Transformaion Noe ime is he same in boh ssems 4
15 5 Addiion of Veloiies We know he Loren ransformaion shold be sed insead so d d d d d d similarl
16 6 Loren Transformaion / / where β
17 7 Addiion of Veloiies Swapping primed and nprimed ariables and leing go o
18 8 Addiion of Veloiies Eample - le, 0, 0 Eample - le 0,, 0 0 0,, V V V V θ an 0,,
19 Addiion of Veloiies A roke blass off from he earh a 0.90 A seond roke follows in he same direion a eloi 0.98 Wha is he relaie eloi of he rokes sing a Galilean ransformaion Wha is he relaie eloi of he rokes sing a Loren ransformaion? 9
20 Loren Transformaion Las ime we arged ha and The mos general linear ransformaion for f, is α α A low eloiies, and α/ V V The inerse ransformaion is he same eep for he sign of relaie moion V 0
21 Loren Transformaion For a ligh plse in S we hae For a ligh plse in S we hae Then V V V V V V V
22 Loren Transformaion For he ransformaion V [ V V] V V
Can you guess. 1/18/2016. Classical Relativity: Reference Frames. a x = a x
/8/06 PHYS 34 Modern Phsis Speial relaii I Classial Relaii: Referene Frames Inerial Frame of Referene (IFR): In suh frame, he Newons firs and seond laws of moion appl. Eample: A rain moing a a Consan eloi.
More informationChapter 1 Relativity
Chaper Relaii - Posulaes of Speial Relaii and Loren Transformaion The s posulae: The laws of phsis ma be epressed in equaions haing he same form in all frames of referene moing a onsan eloi wih respe o
More informationThe Special Theory of Relativity
The Speial Theor of Relaii The Speial Theor of Relaii Chaper I. Conradiions in phsis?. Galilean Transformaions of lassial mehanis 3. The effe on Mawell s equaions ligh 4. Mihelson-Morle eperimen 5. insein
More informationThe Special Theory of Relativity Chapter II
The Speial Theory of Relaiiy Chaper II 1. Relaiisi Kinemais. Time dilaion and spae rael 3. Lengh onraion 4. Lorenz ransformaions 5. Paradoes? Simulaneiy/Relaiiy If one obserer sees he eens as simulaneous,
More informationLIGHT and SPECIAL RELATIVITY
VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT LIGHT and SPECIAL RELATIVITY LENGTH CONTRACTION RELATIVISTIC ADDITION OF VELOCITIES Time is a relaie quaniy: differen obserers an measuremen differen ime
More information2.3 The Lorentz Transformation Eq.
Announemen Course webage h://highenergy.hys.u.edu/~slee/4/ Tebook PHYS-4 Leure 4 HW (due 9/3 Chaer, 6, 36, 4, 45, 5, 5, 55, 58 Se. 8, 6.3 The Lorenz Transformaion q. We an use γ o wrie our ransformaions.
More informationPHYS-3301 Lecture 5. Chapter 2. Announcement. Sep. 12, Special Relativity. What about y and z coordinates? (x - direction of motion)
Announemen Course webpage hp://www.phys.u.edu/~slee/33/ Tebook PHYS-33 Leure 5 HW (due 9/4) Chaper, 6, 36, 4, 45, 5, 5, 55, 58 Sep., 7 Chaper Speial Relaiiy. Basi Ideas. Consequenes of Einsein s Posulaes
More informationThe Full Mathematics of: SPECIAL Relativity. By: PRASANNA PAKKIAM
The Fll Mahemais of: SPECIL Relaii : PRSNN PKKIM CONTENTS INTRODUCTION 3 TIME DILTION & LENGTH CONTRCTION 4 LORENZ TRNSFORMTIONS & COMPOSITION OF VELOCITIES 6 RELTIVISTIC MSS RELTIVISTIC ENERGY 3 ibliograph
More informationVelocity is a relative quantity
Veloci is a relaie quani Disenangling Coordinaes PHY2053, Fall 2013, Lecure 6 Newon s Laws 2 PHY2053, Fall 2013, Lecure 6 Newon s Laws 3 R. Field 9/6/2012 Uniersi of Florida PHY 2053 Page 8 Reference Frames
More informationGeneralized The General Relativity Using Generalized Lorentz Transformation
P P P P IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. www.ijise.om ISSN 348 7968 Generalized The General Relaiiy Using Generalized Lorenz Transformaion
More informationDerivation of longitudinal Doppler shift equation between two moving bodies in reference frame at rest
Deriaion o longiudinal Doppler shi equaion beween wo moing bodies in reerene rame a res Masanori Sao Honda Eleronis Co., d., Oyamazuka, Oiwa-ho, Toyohashi, ihi 44-393, Japan E-mail: msao@honda-el.o.jp
More information1 st axiom: PRINCIPLE OF RELATIVITY The laws of physics are the same in every inertial frame of reference.
SPECIAL ELATIVITY Alber EINSTEIN inrodued his SPECIAL THEOY OF ELATIVITY in 905. To undersand he heory, we will firs reiew he bakground, he heoreial and experimenal deelopmens sine Newon. SPECIAL means
More informationMocanu Paradox of Different Types of Lorentz Transformations
Page Moanu Parado of Differen Types of Lorenz Transformaions A R aizid and M S Alam * Deparmen of usiness Adminisraion Leading niersiy Sylhe 300 angladesh Deparmen of Physis Shahjalal niersiy of Siene
More informationThe Lorentz Transformation
The Lorenz Transformaion Relaiviy and Asrophysics Lecure 06 Terry Herer Ouline Coordinae ransformaions Lorenz Transformaion Saemen Proof Addiion of velociies Parial proof Examples of velociy addiion Proof
More informationDoppler Effect. PHYS-2402 Lecture 6. Chapter 2. Announcement. Feb. 3, Special Relativity. Quiz 1: Thursday 30 min; Chap.2
Announemen Course webpage hp://highenergy.phys.u.edu/~slee/40/ Tebook PHYS-40 Leure 6 Quiz : Thursday 30 min; Chap. Feb. 3, 05 HW (due /0) 0, 6, 36, 4, 46, 5, 55, 70, 76, 87, 9, Doppler Effe Chaper Speial
More informationA Dynamic Approach to De Broglie's Theory
Apeiron, Vol., No. 3, Jly 5 74 A Dynami Approah o De Broglie's Theory Nizar Hamdan Deparmen of Physis, Uniersiy of Aleppo P.O. Box 83, Aleppo, SYRIA e-mail:nhamdan59@homail.om Einsein's relaiiy (SRT) [],
More informationRelativity III. Review: Kinetic Energy. Example: He beam from THIA K = 300keV v =? Exact vs non-relativistic calculations Q.37-3.
Relatiity III Today: Time dilation eamples The Lorentz Transformation Four-dimensional spaetime The inariant interal Eamples Reiew: Kineti Energy General relation for total energy: Rest energy, 0: Kineti
More informationOn Einstein s Non-Simultaneity, Length-Contraction and Time-Dilation. Johan F Prins
On Einsein s Non-Simulaneiy, engh-conraion and Time-Dilaion Johan F Prins CATHODIXX, P. O. Bo 537, Cresa 8, Gaueng, Souh Afia Non-simulaneiy of wo simulaneous eens whih our a differen posiions wihin an
More informationModern Physics. Two major parts: modern relativity, first 4-6 lectures
Modern Physis Fall/Winer 900, Max Plank s paper Ueber das Gesez der Energieereilung im Normalsperum, Annalen der Physik IV, 553 (90 peak in 90s/30s Two major pars: modern relaiiy, firs 4-6 leures Quanum
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationAnnouncements. Lecture 6 Chapter. 2 Special Relativity. Relativistic Dynamics. Relativistic Kinetic Energy. Relativistic Momentum
Announemens HW: Ch.-70, 75, 76, 87, 9, 97, 99, 104, 111 HW1 due: now, HW due: /08 (by lass hour) No lab his week; New TA (Ganga) Physis Colloquium (Thursday a 3:40m) Quiz 1: Feb 8 h. (30 min) -- Cha. ***
More informationA Special Hour with Relativity
A Special Hour wih Relaiviy Kenneh Chu The Graduae Colloquium Deparmen of Mahemaics Universiy of Uah Oc 29, 2002 Absrac Wha promped Einsen: Incompaibiliies beween Newonian Mechanics and Maxwell s Elecromagneism.
More informationKinematics in two dimensions
Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5
More informationRelativistic Dynamics
Announemen Course webage h://highenergy.hys.u.edu/~slee/4/ Tebook PHYS-4 Leure Se., 5 Leure Noes, HW Assignmens, Physis Colloquium, e.. Relaiisi Dynamis Chaer Seial Relaiiy. Basi Ideas. Consequenes of
More informationNotes follow and parts taken from sources in Bibliography
PHYS 33 Noes follow and pars aken from soures in ibliograph leromoie Fore To begin suding elerodnamis, we firs look a he onneion beween fields and urrens. We an wrie Ohm s law, whih ou hae seen in inroduor
More informationChapter 12: Velocity, acceleration, and forces
To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable
More informationSpecial relativity. The Michelson-Morley experiment
Speial relaiiy Aording o he Twin Parado, a spae raeler leaing his win broher behind on Earh, migh reurn some years laer o find ha his win has aged muh more han he has, or, if he spen a lifeime in spae,
More informationThe Paradox of Twins Described in a Three-dimensional Space-time Frame
The Paradox of Twins Described in a Three-dimensional Space-ime Frame Tower Chen E_mail: chen@uguam.uog.edu Division of Mahemaical Sciences Universiy of Guam, USA Zeon Chen E_mail: zeon_chen@yahoo.com
More information1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a
Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.
More informationEquations of motion for constant acceleration
Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
More informationPhysics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)
Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.1-3.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as
More informationKinematics of Wheeled Robots
1 Kinemaics of Wheeled Robos hps://www.ouube.com/wach?=gis41ujlbu 2 Wheeled Mobile Robos robo can hae one or more wheels ha can proide seering direcional conrol power eer a force agains he ground an ideal
More informationChapter 3 Kinematics in Two Dimensions
Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo
More informationOn the Electrodynamics of Moving Bodies by A. Einstein 1905 June 30
On he lerodnamis of Moing Bodies b insein 95 June 3 I is nown ha Mawell s elerodnamis as usuall undersood a he presen ime when applied o moing bodies leads o asmmeries whih do no appear o be inheren in
More informationDeriving the Useful Expression for Time Dilation in the Presence Of the Gravitation by means of a Light Clock
IOSR Journal of Applied Physis (IOSR-JAP) e-issn: 78-486Volue 7, Issue Ver II (Mar - Apr 5), PP 7- wwwiosrjournalsorg Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans of
More informationPhysics Notes - Ch. 2 Motion in One Dimension
Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,
More informationEinstein built his theory of special relativity on two fundamental assumptions or postulates about the way nature behaves.
In he heory of speial relaiviy, an even, suh as he launhing of he spae shule in Figure 8., is a physial happening ha ours a a erain plae and ime. In his drawing wo observers are wahing he lif-off, one
More informationTwin Paradox Revisited
Twin Parado Revisied Relaiviy and Asrophysics Lecure 19 Terry Herer Ouline Simulaneiy Again Sample Problem L- Twin Parado Revisied Time dilaion viewpoin Lengh conracion viewpoin Parado & why i s no! Problem
More informationCourse II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle
Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s
More information2-d Motion: Constant Acceleration
-d Moion: Consan Acceleaion Kinemaic Equaions o Moion (eco Fom Acceleaion eco (consan eloci eco (uncion o Posiion eco (uncion o The eloci eco and posiion eco ae a uncion o he ime. eloci eco a ime. Posiion
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informations in boxe wers ans Put
Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationUnit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3
A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:
More informationThe Maxwell Equations, the Lorentz Field and the Electromagnetic Nanofield with Regard to the Question of Relativity
The Maxwell Equaions, he Lorenz Field and he Elecromagneic Nanofield wih Regard o he Quesion of Relaiviy Daniele Sasso * Absrac We discuss he Elecromagneic Theory in some main respecs and specifically
More informationChapter 2. Motion along a straight line
Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics
More informationDifferential Geometry: Revisiting Curvatures
Differenial Geomery: Reisiing Curaures Curaure and Graphs Recall: hus, up o a roaion in he x-y plane, we hae: f 1 ( x, y) x y he alues 1 and are he principal curaures a p and he corresponding direcions
More informationThis is an example to show you how SMath can calculate the movement of kinematic mechanisms.
Dec :5:6 - Kinemaics model of Simple Arm.sm This file is provided for educaional purposes as guidance for he use of he sofware ool. I is no guaraeed o be free from errors or ommissions. The mehods and
More informationOne-Dimensional Kinematics
One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
More informationMain Ideas in Class Today
Main Ideas in Class Toda Inroducion o Falling Appl Consan a Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs Refers o objecs
More informationBrock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension
Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiion-ime graphs, elociy-ime graphs, and heir
More informationx y θ = 31.8 = 48.0 N. a 3.00 m/s
4.5.IDENTIY: Vecor addiion. SET UP: Use a coordinae sse where he dog A. The forces are skeched in igure 4.5. EXECUTE: + -ais is in he direcion of, A he force applied b =+ 70 N, = 0 A B B A = cos60.0 =
More informationKinematics: Motion in One Dimension
Kinemaics: Moion in One Dimension When yo drie, yo are spposed o follow he hree-second ailgaing rle. When he car in fron of yo passes a sign a he side of he road, yor car shold be far enogh behind i ha
More informationPage 1 o 13 1. The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 ligh-years away. Express his disance in meers. ( ligh-year is he disance coered by ligh in one year. Ligh
More informationAtmospheric Dynamics 11:670:324. Class Time: Tuesdays and Fridays 9:15-10:35
Amospheric Dnamics 11:67:324 Class ime: esdas and Fridas 9:15-1:35 Insrcors: Dr. Anhon J. Broccoli (ENR 229 broccoli@ensci.rgers.ed 848-932-5749 Dr. Benjamin Linner (ENR 25 linner@ensci.rgers.ed 848-932-5731
More informationChapter 35. Special Theory of Relativity (1905)
Chapter 35 Speial Theory of Relatiity (1905) 1. Postulates of the Speial Theory of Relatiity: A. The laws of physis are the same in all oordinate systems either at rest or moing at onstant eloity with
More informationQ2.4 Average velocity equals instantaneous velocity when the speed is constant and motion is in a straight line.
CHAPTER MOTION ALONG A STRAIGHT LINE Discussion Quesions Q. The speedomeer measures he magniude of he insananeous eloci, he speed. I does no measure eloci because i does no measure direcion. Q. Graph (d).
More informationINSTANTANEOUS VELOCITY
INSTANTANEOUS VELOCITY I claim ha ha if acceleraion is consan, hen he elociy is a linear funcion of ime and he posiion a quadraic funcion of ime. We wan o inesigae hose claims, and a he same ime, work
More informationOn the invariance of the speed of light
On he inariance of he speed of ligh Shan Gao Uni for he Hisory and hilosophy of Science and Cenre for Time, Uniersiy of Sydney, NSW 006, sralia. Insie for he Hisory of Naral Sciences, Chinese cademy of
More informationIntegration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum.
Inegraion of he equaion of moion wih respec o ime raher han displacemen leads o he equaions of impulse and momenum. These equaions greal faciliae he soluion of man problems in which he applied forces ac
More informationLet us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
More informationChapter 39 Relativity
Chapter 39 Relatiity from relatie motion to relatiity 39. The Priniple of Galilean Relatiity The laws of mehanis mst be the same in all inertial frames of referene. Galilean spae-time transformation eqations
More informationAnnouncements. Today s class. The Lorentz transformation. Lorentz transformation (Relativistic version of Galileo transformation)
Announements Reading for Monda:. -.5 HW 3 is posted. Due net Wed. noon. The Frida was a TYPO! IT I DUE WEDNEDAY! Toda s lass Lorent transformation Doppler shift First Midterm is on the 6 th. Will oer relatiit
More informationThe Special Theory of Relativity
The Speial Theory of Relatiity Galilean Newtonian Relatiity Galileo Galilei Isaa Newton Definition of an inertial referene frame: One in whih Newton s first law is alid. onstant if F0 Earth is rotating
More informationHYPOTHESIS TESTING. four steps. 1. State the hypothesis and the criterion. 2. Compute the test statistic. 3. Compute the p-value. 4.
Inrodcion o Saisics in Psychology PSY Professor Greg Francis Lecre 24 Hypohesis esing for correlaions Is here a correlaion beween homework and exam grades? for seps. Sae he hypohesis and he crierion 2.
More informationWELCOME TO 1103 PERIOD 3. Homework Exercise #2 is due at the beginning of class. Please put it on the stool in the front of the classroom.
WELCOME TO 1103 PERIOD 3 Homework Exercise #2 is due a he beginning of class. Please pu i on he sool in he fron of he classroom. Ring of Truh: Change 1) Give examples of some energy ransformaions in he
More informationI. OBJECTIVE OF THE EXPERIMENT.
I. OBJECTIVE OF THE EXPERIMENT. Swissmero raels a high speeds hrough a unnel a low pressure. I will hereore undergo ricion ha can be due o: ) Viscosiy o gas (c. "Viscosiy o gas" eperimen) ) The air in
More information3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
More informationAgenda 2/12/2017. Modern Physics for Frommies V Gravitation Lecture 6. Special Relativity Einstein s Postulates. Einstein s Postulates
/1/17 Fromm Institute for Lifelong Learning Uniersit of San Franiso Modern Phsis for Frommies V Graitation Leture 6 Agenda Speial Relatiit Einstein s Postulates 15 Februar 17 Modern Phsis V Leture 6 1
More informationBe able to sketch a function defined parametrically. (by hand and by calculator)
Pre Calculus Uni : Parameric and Polar Equaions (7) Te References: Pre Calculus wih Limis; Larson, Hoseler, Edwards. B he end of he uni, ou should be able o complee he problems below. The eacher ma provide
More informationLAB # 2 - Equilibrium (static)
AB # - Equilibrium (saic) Inroducion Isaac Newon's conribuion o physics was o recognize ha despie he seeming compleiy of he Unierse, he moion of is pars is guided by surprisingly simple aws. Newon's inspiraion
More informationPhysics 20 Lesson 5 Graphical Analysis Acceleration
Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiion-ime graph is equal o he velociy of
More information4. Voltage Induction in Three-Phase Machines
4. Volage Indion in Three-Phase Mahines NIVERSITÄT 4/1 FARADAY s law of indion a b Eah hange of flx, whih is linked o ondor loop C, ases an inded volage i in ha loop; he inded volage is he negaive rae
More informationKinematics in two Dimensions
Lecure 5 Chaper 4 Phsics I Kinemaics in wo Dimensions Course websie: hp://facul.uml.edu/andri_danlo/teachin/phsicsi PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics Toda we are oin o discuss:
More informationEinstein s theory of special relativity
Einstein s theory of speial relatiity Announements: First homework assignment is online. You will need to read about time dilation (1.8) to answer problem #3 and for the definition of γ for problem #4.
More informationPhysics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension
Physics for Scieniss and Engineers Chaper Kinemaics in One Dimension Spring, 8 Ho Jung Paik Kinemaics Describes moion while ignoring he agens (forces) ha caused he moion For now, will consider moion in
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationand v y . The changes occur, respectively, because of the acceleration components a x and a y
Week 3 Reciaion: Chaper3 : Problems: 1, 16, 9, 37, 41, 71. 1. A spacecraf is raveling wih a veloci of v0 = 5480 m/s along he + direcion. Two engines are urned on for a ime of 84 s. One engine gives he
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 informationHYPOTHESIS TESTING. four steps. 1. State the hypothesis. 2. Set the criterion for rejecting. 3. Compute the test statistics. 4. Interpret the results.
Inrodcion o Saisics in Psychology PSY Professor Greg Francis Lecre 23 Hypohesis esing for correlaions Is here a correlaion beween homework and exam grades? for seps. Sae he hypohesis. 2. Se he crierion
More informationGravity and SHM Review Questions
Graviy an SHM Review Quesions 1. The mass of Plane X is one-enh ha of he Earh, an is iameer is one-half ha of he Earh. The acceleraion ue o raviy a he surface of Plane X is mos nearly m/s (B) 4m/s (C)
More informationModule 3: The Damped Oscillator-II Lecture 3: The Damped Oscillator-II
Module 3: The Damped Oscillaor-II Lecure 3: The Damped Oscillaor-II 3. Over-damped Oscillaions. This refers o he siuaion where β > ω (3.) The wo roos are and α = β + α 2 = β β 2 ω 2 = (3.2) β 2 ω 2 = 2
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationHOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.
HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =
More informationTraveling Waves. Chapter Introduction
Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from
More informationCORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams
Inrodcion o Saisics in sychology SY 1 rofessor Greg Francis Lecre 1 correlaion Did I damage my dagher s eyes? CORRELATION wo ariables may be relaed SAT scores, GA hors in herapy, self-eseem grade on homeworks,
More informationHence light World Lines of moving bodies always make an angle of less than 45 to the ct-axes.
For = second c=30 8 m and ligh ravels 30 8 m. c Hence ligh World Lines always make an angle of 45 o he c-aes. For = second c=30 8 m and for observer ravelling a v
More informationIntegration Over Manifolds with Variable Coordinate Density
Inegraion Over Manifolds wih Variable Coordinae Densiy Absrac Chrisopher A. Lafore clafore@gmail.com In his paper, he inegraion of a funcion over a curved manifold is examined in he case where he curvaure
More information3. Differential Equations
3. Differenial Equaions 3.. inear Differenial Equaions of Firs rder A firs order differenial equaion is an equaion of he form d() d ( ) = F ( (),) (3.) As noed above, here will in general be a whole la
More informationTalukder and Ahmad: Relativistic Rule of Multiplication of Velocities Consistent with Lorentz Einstein Law of Addition and Derivation (26-41)
Takder and Ahad: Reaiisi Re of Mipiaion of Veoiies Consisen wih Lorenz Einsein Law of Addiion and Deriaion (6-4) Reaiisi Re of Mipiaion of Veoiies Consisen wih Lorenz Einsein Law of Addiion and Deriaion
More informationAmit Mehra. Indian School of Business, Hyderabad, INDIA Vijay Mookerjee
RESEARCH ARTICLE HUMAN CAPITAL DEVELOPMENT FOR PROGRAMMERS USING OPEN SOURCE SOFTWARE Ami Mehra Indian Shool of Business, Hyderabad, INDIA {Ami_Mehra@isb.edu} Vijay Mookerjee Shool of Managemen, Uniersiy
More informationQ2.1 This is the x t graph of the motion of a particle. Of the four points P, Q, R, and S, the velocity v x is greatest (most positive) at
Q2.1 This is he x graph of he moion of a paricle. Of he four poins P, Q, R, and S, he velociy is greaes (mos posiive) a A. poin P. B. poin Q. C. poin R. D. poin S. E. no enough informaion in he graph o
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationCORRELATION. two variables may be related. SAT scores, GPA hours in therapy, self-esteem grade on homeworks, grade on exams
Inrodcion o Saisics in sychology SY 1 rofessor Greg Francis Lecre 1 correlaion How changes in one ariable correspond o change in anoher ariable. wo ariables may be relaed SAT scores, GA hors in herapy,
More informationAddition of velocities. Taking differentials of the Lorentz transformation, relative velocities may be calculated:
Addition of veloities Taking differentials of the Lorentz transformation, relative veloities may be allated: So that defining veloities as: x dx/dt, y dy/dt, x dx /dt, et. it is easily shown that: With
More informationFarr High School NATIONAL 5 PHYSICS. Unit 3 Dynamics and Space. Exam Questions
Farr High School NATIONAL 5 PHYSICS Uni Dynamics and Space Exam Quesions VELOCITY AND DISPLACEMENT D B D 4 E 5 B 6 E 7 E 8 C VELOCITY TIME GRAPHS (a) I is acceleraing Speeding up (NOT going down he flume
More informationExam I. Name. Answer: a. W B > W A if the volume of the ice cubes is greater than the volume of the water.
Name Exam I 1) A hole is punched in a full milk caron, 10 cm below he op. Wha is he iniial veloci of ouflow? a. 1.4 m/s b. 2.0 m/s c. 2.8 m/s d. 3.9 m/s e. 2.8 m/s Answer: a 2) In a wind unnel he pressure
More information4.5 Constant Acceleration
4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),
More informationPropagation of spherical electromagnetic waves in different inertial frames; an alternative to the Lorentz transformation
Propagaion of spherical elecromagneic waves in differen inerial frames; an alernaive o he Lorenz ransformaion Teimuraz Bregadze ebr50@yahoo.com The applicaion of he Lorenz ransformaion, which assumes planar
More information