Kepler's 1 st Law by Newton
|
|
- Myles Atkins
- 5 years ago
- Views:
Transcription
1 Astonom 10 Section 1 MWF Astonom Building This Class (Lectue 7): Gavitation Net Class: Theo of Planeta Motion HW # Due Fida! Missed nd planetaium date. (onl 5 left), including tonight Stadial Obseving epot is available Music: Eathbound Dain Dda What is F? Angula Momentum L = mv What about gavit guaanteed that dl/dt =0? Conseved!!!! Outline How things move in a gavit field. Keple's 1 st Law b Newton Newton also found moe options that satisfied his univesal law of gavit Fo an attactive invese squae law foce, can show that the obits ae conic sections with the othe bod at one focus.
2 Cicula Obit: Special Case mv c F = ma = Eample: Cicula speed at 1 AU fom Sun is m/s Keple's nd Law b Newton 1 da = ω dt v θ Keple's nd Law b Newton Do obits in Newton s fomalism sweep out equal aea in equal time? d θ = ωdt v θ Keple's nd Law b Newton 1 da = ω dt v = ω da = 1 v dt v θ
3 Keple's nd Law b Newton v θ Keple's nd Law b Newton The poduct of mass, obital velocit, and obital adius is constant while in obit. Keple's nd Law b Newton Then θ v da dt 1 L m = Constant!! Keple's 3 d Law b Newton Remembe v c = G fo a M cicula motion so GM 4 π 3 a = P
4 Keple's 3 d Law b Newton Remembe Keple's 3 d Law Newton s found a geneal vesion with his Law of Gavit P = a 3 GM 4 π k P = (P in eas, a in AUs, M in sola masses) k =1 Spaceflight Rockets opeate b Newton's 3d Law Action: Gas epelled out the end of the ocket Reaction: Rocket is pushed upwad 3 a The Powe of Newton s Laws An astonome named Edmund Halle was intigued that a comet appeaed about eve 76 eas Was it the same comet eve time? Using Newton s Laws, Halle detemined the comet s obit aound the Sun Pedicted its etun in 1758 It will be back in 061! Spaceflight Rockets opeate b Newton's 3d Law Action: Gas epelled out the end of the ocket Reaction: Rocket is pushed upwad
5 Obiting the Eath In obit, spacecaft is falling aound the Eath A spacecaft must have a velocit of 8,000 km/h (17,000 mph) to sta in obit If its velocit eceeds 11 km/sec (5,000 mph), it can escape the Eath s gavit Result Now we know that the obiting planets ae just pepetuall falling bodies. This includes the shuttle, satellites, etc. Weightlessness is just like falling. Thee is gavit on the shuttle, but as one is in feefall it is not noticeable. Keple had thought biefl about this, but he decided he needed foces along the diection of the velocit, not pependicula to it. So Newton ealized that like an apple falling fom a tee o a eall big tee, the moon must have a foce towad the Eath. Newton did not discove gavit, but he ealized that it was univesal. Geosnchonous Obit At a distance of 4,00 km fom the Eath's cente, a satellite takes 4 hous to obit the Eath Equal to the Eath's otation If a satellite is above the Eath's equato, it will appea stationa fom the gound This obit is called geosnchonous Useful fo communication satellites Receives can point at one spot in the sk Applications We now have two tools in ou bo: Newton's laws of motion: how things move with, without foces applied Newton's gavit: the net foce on sola sstem bodies Now, we need to out the two togethe: how do bodies move unde the invese squae foce of gavit.
6 Kinetic Eneg Potential Eneg of Gavit U = G Mm Potential Eneg of Gavit f U = F i d Potential Eneg of Gavit U = G Mm Negative potential eneg? What s up with that? It eall implies that the object is bound b the gavitational field. In ode to escape the pull of gavit, it has to be given that much eneg. The onl phsicall meaningful quantit is elative changes in potential eneg.
7 Total Eneg in Gavit TE = KE + PE Conseved!!!! Obits Conside a cicle with e=0 Obits Can classif obits with total eneg. Can wite a cicle o ellipse in pola coodinates as: Obits Conside a cicle with e=0 TE < 0!!
8 What? Negative total eneg? Obits Is that due to spook antimatte? No it means that ou have to suppl eneg to sstem to beak it apat. When paticles at est, fa awa, KE = PE = 0. To get to this situation, have to input eneg to an obiting sstem. Since eneg is conseved, can't spontaneousl get this eneg, so sstem is bound! Note: KE = -1/PE geneall tue fo gavitating sstems in equilibium: viial theoem" Geneal Obits ellipse: 0 < e < 1 It tuns out that TE depends onl on a, not on e Fom consevation of eneg can see: Geneal Obits ellipse: 0 < e < 1 It tuns out that TE depends onl on a, not on e Fom consevation of eneg can see: < 0!! Bound! Geneal Obits ellipse: 0 < e < 1 It tuns out that TE depends onl on a, not on e Fom consevation of eneg can see: v = GM 1 a This is called the Vis Viva equation. The most hand obital equation.
9 Geneal Obits paabola: e = 1 Can wite as: Whee p is distance at closest appoach. Just unbound sstem (can bael escape to = ) E = 0 o KE = -PE Fo Eath. V escape = 11km/s = 5000 mph. v escape = G M Geneal Obits hpebola: e > 1 Can wite as: ( θ ) = (1 1 + e e ) a cos θ Completel unbound sstem (escapes to = ) E > 0 That implies that v > 0 at =
Chapter 13: Gravitation
v m m F G Chapte 13: Gavitation The foce that makes an apple fall is the same foce that holds moon in obit. Newton s law of gavitation: Evey paticle attacts any othe paticle with a gavitation foce given
More informationRadius of the Moon is 1700 km and the mass is 7.3x 10^22 kg Stone. Moon
xample: A 1-kg stone is thown vetically up fom the suface of the Moon by Supeman. The maximum height fom the suface eached by the stone is the same as the adius of the moon. Assuming no ai esistance and
More informationGravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun
Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law
More informationF 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation
Physics 201, Lectue 22 Review Today s Topics n Univesal Gavitation (Chapte 13.1-13.3) n Newton s Law of Univesal Gavitation n Popeties of Gavitational Foce n Planet Obits; Keple s Laws by Newton s Law
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationm1 m2 M 2 = M -1 L 3 T -2
GAVITATION Newton s Univesal law of gavitation. Evey paticle of matte in this univese attacts evey othe paticle with a foce which vaies diectly as the poduct of thei masses and invesely as the squae of
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationAY 7A - Fall 2010 Section Worksheet 2 - Solutions Energy and Kepler s Law
AY 7A - Fall 00 Section Woksheet - Solutions Enegy and Keple s Law. Escape Velocity (a) A planet is obiting aound a sta. What is the total obital enegy of the planet? (i.e. Total Enegy = Potential Enegy
More informationPhysics: Work & Energy Beyond Earth Guided Inquiry
Physics: Wok & Enegy Beyond Eath Guided Inquiy Elliptical Obits Keple s Fist Law states that all planets move in an elliptical path aound the Sun. This concept can be extended to celestial bodies beyond
More informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity
More informationMechanics Physics 151
Mechanics Physics 151 Lectue 5 Cental Foce Poblem (Chapte 3) What We Did Last Time Intoduced Hamilton s Pinciple Action integal is stationay fo the actual path Deived Lagange s Equations Used calculus
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 informationKEPLER S LAWS OF PLANETARY MOTION
EPER S AWS OF PANETARY MOTION 1. Intoduction We ae now in a position to apply what we have leaned about the coss poduct and vecto valued functions to deive eple s aws of planetay motion. These laws wee
More informationMath Notes on Kepler s first law 1. r(t) kp(t)
Math 7 - Notes on Keple s fist law Planetay motion and Keple s Laws We conside the motion of a single planet about the sun; fo simplicity, we assign coodinates in R 3 so that the position of the sun is
More informationChap 5. Circular Motion: Gravitation
Chap 5. Cicula Motion: Gavitation Sec. 5.1 - Unifom Cicula Motion A body moves in unifom cicula motion, if the magnitude of the velocity vecto is constant and the diection changes at evey point and is
More informationUniform Circular Motion
Unifom Cicula Motion constant speed Pick a point in the objects motion... What diection is the velocity? HINT Think about what diection the object would tavel if the sting wee cut Unifom Cicula Motion
More informationEscape Velocity. GMm ] B
1 PHY2048 Mach 31, 2006 Escape Velocity Newton s law of gavity: F G = Gm 1m 2 2, whee G = 667 10 11 N m 2 /kg 2 2 3 10 10 N m 2 /kg 2 is Newton s Gavitational Constant Useful facts: R E = 6 10 6 m M E
More informationCentral Force Motion
Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More informationMODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLIN MODUL 5 ADVANCD MCHANICS GRAVITATIONAL FILD: MOTION OF PLANTS AND SATLLITS SATLLITS: Obital motion of object of mass m about a massive object of mass M (m
More informationCh 13 Universal Gravitation
Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)
More informationPHYSICS 220. Lecture 08. Textbook Sections Lecture 8 Purdue University, Physics 220 1
PHYSICS 0 Lectue 08 Cicula Motion Textbook Sections 5.3 5.5 Lectue 8 Pudue Univesity, Physics 0 1 Oveview Last Lectue Cicula Motion θ angula position adians ω angula velocity adians/second α angula acceleation
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Revision Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Wok... 5 Gavitational field... 5 Potential enegy... 7 Kinetic enegy... 8 Pojectile... 9
More informationHistory of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist
Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and astonomy
More informationFrom Newton to Einstein. Mid-Term Test, 12a.m. Thur. 13 th Nov Duration: 50 minutes. There are 20 marks in Section A and 30 in Section B.
Fom Newton to Einstein Mid-Tem Test, a.m. Thu. 3 th Nov. 008 Duation: 50 minutes. Thee ae 0 maks in Section A and 30 in Section B. Use g = 0 ms in numeical calculations. You ma use the following epessions
More informationExtra notes for circular motion: Circular motion : v keeps changing, maybe both speed and
Exta notes fo cicula motion: Cicula motion : v keeps changing, maybe both speed and diection ae changing. At least v diection is changing. Hence a 0. Acceleation NEEDED to stay on cicula obit: a cp v /,
More informationHW6 Physics 311 Mechanics
HW6 Physics 311 Mechanics Fall 015 Physics depatment Univesity of Wisconsin, Madison Instucto: Pofesso Stefan Westehoff By Nasse M. Abbasi June 1, 016 Contents 0.1 Poblem 1.........................................
More informationBetween any two masses, there exists a mutual attractive force.
YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce
More informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Mo3on 2. Newton s Law of Univesal Gavita3on 3. Calcula3ng satellite obital paametes (assuming cicula mo3on) Scala & Vectos Scala: a physical quan3ty
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical
More informationω = θ θ o = θ θ = s r v = rω
Unifom Cicula Motion Unifom cicula motion is the motion of an object taveling at a constant(unifom) speed in a cicula path. Fist we must define the angula displacement and angula velocity The angula displacement
More informationChapter 5: Uniform Circular Motion
Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad
More informationGravitation. AP/Honors Physics 1 Mr. Velazquez
Gavitation AP/Honos Physics 1 M. Velazquez Newton s Law of Gavitation Newton was the fist to make the connection between objects falling on Eath and the motion of the planets To illustate this connection
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 6- THE LAW OF GRAVITATION Essential Idea: The Newtonian idea of gavitational foce acting between two spheical bodies and the laws of mechanics
More informationUnderstanding the Concepts
Chistian Bache Phsics Depatment Bn Maw College Undestanding the Concepts PHYSICS 101-10 Homewok Assignment #5 - Solutions 5.7. A cclist making a tun must make use of a centipetal foce, one that is pependicula
More informationObjective Notes Summary
Objective Notes Summay An object moving in unifom cicula motion has constant speed but not constant velocity because the diection is changing. The velocity vecto in tangent to the cicle, the acceleation
More informationForce of gravity and its potential function
F. W. Phs0 E:\Ecel files\ch gavitational foce and potential.doc page of 6 0/0/005 8:9 PM Last pinted 0/0/005 8:9:00 PM Foce of gavit and its potential function (.) Let us calculate the potential function
More informationExperiment 09: Angular momentum
Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok
More informationAST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1
Please ead this fist... AST S: The oigin and evolution of the Univese Intoduction to Mathematical Handout This is an unusually long hand-out and one which uses in places mathematics that you may not be
More informationHoizontal Cicula Motion 1. A paticle of mass m is tied to a light sting and otated with a speed v along a cicula path of adius. If T is tension in the sting and mg is gavitational foce on the paticle then,
More information10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11.
NSWRS - P Physics Multiple hoice Pactice Gavitation Solution nswe 1. m mv Obital speed is found fom setting which gives v whee M is the object being obited. Notice that satellite mass does not affect obital
More informationNewton s Laws, Kepler s Laws, and Planetary Orbits
Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion
More informationCHAPTER 5: Circular Motion; Gravitation
CHAPER 5: Cicula Motion; Gavitation Solution Guide to WebAssign Pobles 5.1 [1] (a) Find the centipetal acceleation fo Eq. 5-1.. a R v ( 1.5 s) 1.10 1.4 s (b) he net hoizontal foce is causing the centipetal
More informationChapter 12. Kinetics of Particles: Newton s Second Law
Chapte 1. Kinetics of Paticles: Newton s Second Law Intoduction Newton s Second Law of Motion Linea Momentum of a Paticle Systems of Units Equations of Motion Dynamic Equilibium Angula Momentum of a Paticle
More informationAMM PBL Members: Chin Guan Wei p Huang Pengfei p Lim Wilson p Yap Jun Da p Class: ME/MS803M/AM05
AMM PBL Membes: Chin Guan Wei p3674 Huang Pengfei p36783 Lim Wilson p36808 Yap Jun Da p36697 Class: MEMS803MAM05 The common values that we use ae: G=6.674 x 0 - m 3 kg - s - Radius of Eath ()= 637km [Fom
More informationRecap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)
a = c v 2 Recap Centipetal acceleation: m/s 2 (towads cente of cuvatue) A centipetal foce F c is equied to keep a body in cicula motion: This foce poduces centipetal acceleation that continuously changes
More informationLecture 22. PE = GMm r TE = GMm 2a. T 2 = 4π 2 GM. Main points of today s lecture: Gravitational potential energy: Total energy of orbit:
Lectue Main points of today s lectue: Gavitational potential enegy: Total enegy of obit: PE = GMm TE = GMm a Keple s laws and the elation between the obital peiod and obital adius. T = 4π GM a3 Midtem
More informationPotential Energy and Conservation of Energy
Potential Enegy and Consevation of Enegy Consevative Foces Definition: Consevative Foce If the wok done by a foce in moving an object fom an initial point to a final point is independent of the path (A
More informationOrbits. Newton suggested that an object could be put into orbit if it were launched from a high hill at a high speed
Satellites & Obits Obits Newton suggested that an object could be put into obit if it wee launched fom a high hill at a high speed If the launch speed was high enough, the object would fall aound Eath
More informationPHYSICS NOTES GRAVITATION
GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely
More informationCircular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.
Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement
More informationPaths of planet Mars in sky
Section 4 Gavity and the Sola System The oldest common-sense view is that the eath is stationay (and flat?) and the stas, sun and planets evolve aound it. This GEOCENTRIC MODEL was poposed explicitly by
More informationF g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N
Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the
More informationPractice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287
Pactice Undestanding Concepts 1. Detemine the gavitational potential enegy of the Eath Moon system, given that the aveage distance between thei centes is 3.84 10 5 km, and the mass of the Moon is 0.0123
More information10. Universal Gravitation
10. Univesal Gavitation Hee it is folks, the end of the echanics section of the couse! This is an appopiate place to complete the study of mechanics, because with his Law of Univesal Gavitation, Newton
More informationCentral Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.
Cental oce Poblem ind the motion of two bodies inteacting via a cental foce. Cental oce Motion 8.01 W14D1 Examples: Gavitational foce (Keple poblem): 1 1, ( ) G mm Linea estoing foce: ( ) k 1, Two Body
More informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),
More informationChapter 4. Newton s Laws of Motion
Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto
More informationPhysics 201 Lecture 18
Phsics 0 ectue 8 ectue 8 Goals: Define and anale toque ntoduce the coss poduct Relate otational dnamics to toque Discuss wok and wok eneg theoem with espect to otational motion Specif olling motion (cente
More information- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.
- 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU
More informationQuiz 6--Work, Gravitation, Circular Motion, Torque. (60 pts available, 50 points possible)
Name: Class: Date: ID: A Quiz 6--Wok, Gavitation, Cicula Motion, Toque. (60 pts available, 50 points possible) Multiple Choice, 2 point each Identify the choice that best completes the statement o answes
More informationChap13. Universal Gravitation
Chap13. Uniesal Gaitation Leel : AP Physics Instucto : Kim 13.1 Newton s Law of Uniesal Gaitation - Fomula fo Newton s Law of Gaitation F g = G m 1m 2 2 F21 m1 F12 12 m2 - m 1, m 2 is the mass of the object,
More informationUniversal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
More information1) Consider a particle moving with constant speed that experiences no net force. What path must this particle be taking?
Chapte 5 Test Cicula Motion and Gavitation 1) Conside a paticle moving with constant speed that expeiences no net foce. What path must this paticle be taking? A) It is moving in a paabola. B) It is moving
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationF(r) = r f (r) 4.8. Central forces The most interesting problems in classical mechanics are about central forces.
4.8. Cental foces The most inteesting poblems in classical mechanics ae about cental foces. Definition of a cental foce: (i) the diection of the foce F() is paallel o antipaallel to ; in othe wods, fo
More informationPhysics 312 Introduction to Astrophysics Lecture 7
Physics 312 Intoduction to Astophysics Lectue 7 James Buckley buckley@wuphys.wustl.edu Lectue 7 Eath/Moon System Tidal Foces Tides M= mass of moon o sun F 1 = GMm 2 F 2 = GMm ( + ) 2 Diffeence in gavitational
More informationLecture 19 Angular momentum. Chapter
PHYS 172H: Moden Mechanics Fall 2010 Lectue 19 ngula momentum Chapte 11.4 11.7 The angula momentum pinciple dp = F dl =? net d ( p ) d dp = p+ = v γ mv = = 0 The angula momentum pinciple fo a point paticle
More informationLau Chi Hin The Chinese University of Hong Kong
Lau Chi Hin The Chinese Univesit of Hong Kong Can Antson each the othe end? 1cms 1 Can I each the othe end? Rubbe band 1m 1ms 1 Can Antson each the othe end? Gottfied Wilhelm Leibniz (1646-1716) Isaac
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.033 Decembe 5, 003 Poblem Set 10 Solutions Poblem 1 M s y x test paticle The figue above depicts the geomety of the poblem. The position
More informationTAMPINES JUNIOR COLLEGE 2009 JC1 H2 PHYSICS GRAVITATIONAL FIELD
TAMPINES JUNIOR COLLEGE 009 JC1 H PHYSICS GRAVITATIONAL FIELD OBJECTIVES Candidates should be able to: (a) show an undestanding of the concept of a gavitational field as an example of field of foce and
More informationPhysics 121: Electricity & Magnetism Lecture 1
Phsics 121: Electicit & Magnetism Lectue 1 Dale E. Ga Wenda Cao NJIT Phsics Depatment Intoduction to Clices 1. What ea ae ou?. Feshman. Sophomoe C. Junio D. Senio E. Othe Intoduction to Clices 2. How man
More informationMMAT5520. Lau Chi Hin The Chinese University of Hong Kong
MMAT550 Lau Chi Hin The Chinese Univesit of Hong Kong Isaac Newton (1643-177) Keple s Laws of planeta motion 1. The obit is an ellipse with the sun at one of the foci.. A line joining a planet and the
More informationGravity Notes for PHYS Joe Wolfe, UNSW
Gavity Notes fo PHYS 111-1131. Joe Wolfe, UNSW 1 Gavity: whee does it fit in? Gavity [geneal elativity] Electic foce* gavitons photons Weak nuclea foce intemediate vecto bosons Stong nuclea foce Colou
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 informationPhysics 231 Lecture 21
Physics 3 Lectue Main points o today s lectue: Angula momentum: L Newton s law o univesal gavitation: GMm F PE GMm Keple s laws and the elation between the obital peiod and obital adius. T π GM 4 3 Rolling
More informationPhysics 101 Lecture 6 Circular Motion
Physics 101 Lectue 6 Cicula Motion Assist. Pof. D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Equilibium, Example 1 q What is the smallest value of the foce F such that the.0-kg block will not slide
More informationMODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE MODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES SATELLITES: Obital motion of object of mass m about a massive object of mass M (m
More informationPhysics 207 Lecture 5. Lecture 5
Lectue 5 Goals: Addess sstems with multiple acceleations in 2- dimensions (including linea, pojectile and cicula motion) Discen diffeent efeence fames and undestand how the elate to paticle motion in stationa
More informationTutorial Exercises: Central Forces
Tutoial Execises: Cental Foces. Tuning Points fo the Keple potential (a) Wite down the two fist integals fo cental motion in the Keple potential V () = µm/ using J fo the angula momentum and E fo the total
More information= v 2. a c. = G m m 1 2. F g G = Review 5: Gravitation and Two-Dimensional Motion
Review 5: Gavitation and Two-Dimensional Motion Review 5 Gavitation and Two-Dimensional Motion 2 d = 1 2 at F = ma 1. A busy waitess slides a plate of apple pie alon a counte to a huny custome sittin nea
More informationPHYS Dynamics of Space Vehicles
PHYS 4110 - Dynamics of Space Vehicles Chapte 3: Two Body Poblem Eath, Moon, Mas, and Beyond D. Jinjun Shan, Pofesso of Space Engineeing Depatment of Eath and Space Science and Engineeing Room 55, Petie
More informationRecall from last week:
Recall fom last week: Length of a cuve '( t) dt b Ac length s( t) a a Ac length paametization ( s) with '( s) 1 '( t) Unit tangent vecto T '(s) '( t) dt Cuvatue: s ds T t t t t t 3 t ds u du '( t) dt Pincipal
More informationBasic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional
More informationPhysics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 6: motion in two and three dimensions III. Slide 6-1
Physics 1501 Fall 2008 Mechanics, Themodynamics, Waves, Fluids Lectue 6: motion in two and thee dimensions III Slide 6-1 Recap: elative motion An object moves with velocity v elative to one fame of efeence.
More informationDYNAMICS OF UNIFORM CIRCULAR MOTION
Chapte 5 Dynamics of Unifom Cicula Motion Chapte 5 DYNAMICS OF UNIFOM CICULA MOTION PEVIEW An object which is moing in a cicula path with a constant speed is said to be in unifom cicula motion. Fo an object
More informationPhysics 111. Ch 12: Gravity. Newton s Universal Gravity. R - hat. the equation. = Gm 1 m 2. F g 2 1. ˆr 2 1. Gravity G =
ics Announcements day, embe 9, 004 Ch 1: Gavity Univesal Law Potential Enegy Keple s Laws Ch 15: Fluids density hydostatic equilibium Pascal s Pinciple This week s lab will be anothe physics wokshop -
More informationr cos, and y r sin with the origin of coordinate system located at
Lectue 3-3 Kinematics of Rotation Duing ou peious lectues we hae consideed diffeent examples of motion in one and seeal dimensions. But in each case the moing object was consideed as a paticle-like object,
More informationCircular Orbits. and g =
using analyse planetay and satellite motion modelled as unifom cicula motion in a univesal gavitation field, a = v = 4π and g = T GM1 GM and F = 1M SATELLITES IN OBIT A satellite is any object that is
More informationChapter 5. Uniform Circular Motion. a c =v 2 /r
Chapte 5 Unifom Cicula Motion a c =v 2 / Unifom cicula motion: Motion in a cicula path with constant speed s v 1) Speed and peiod Peiod, T: time fo one evolution Speed is elated to peiod: Path fo one evolution:
More informationChapter 1: Mathematical Concepts and Vectors
Chapte : Mathematical Concepts and Vectos giga G 9 mega M 6 kilo k 3 centi c - milli m -3 mico μ -6 nano n -9 in =.54 cm m = cm = 3.8 t mi = 58 t = 69 m h = 36 s da = 86,4 s ea = 365.5 das You must know
More informationWhen a mass moves because of a force, we can define several types of problem.
Mechanics Lectue 4 3D Foces, gadient opeato, momentum 3D Foces When a mass moves because of a foce, we can define seveal types of poblem. ) When we know the foce F as a function of time t, F=F(t). ) When
More informationGRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1
Einstein Classes, Unit No. 0, 0, Vahman Ring Roa Plaza, Vikas Pui Extn., New Delhi -8 Ph. : 96905, 857, E-mail einsteinclasses00@gmail.com, PG GRAVITATION Einstein Classes, Unit No. 0, 0, Vahman Ring Roa
More informationFrom last times. MTE1 results. Quiz 1. GAUSS LAW for any closed surface. What is the Electric Flux? How to calculate Electric Flux?
om last times MTE1 esults Mean 75% = 90/120 Electic chages and foce Electic ield and was to calculate it Motion of chages in E-field Gauss Law Toda: Moe on Gauss law and conductos in electostatic equilibium
More informationPhysics 111 Lecture 5 Circular Motion
Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight
More informationPhysics C Rotational Motion Name: ANSWER KEY_ AP Review Packet
Linea and angula analogs Linea Rotation x position x displacement v velocity a T tangential acceleation Vectos in otational motion Use the ight hand ule to detemine diection of the vecto! Don t foget centipetal
More informationPhysics 181. Assignment 4
Physics 181 Assignment 4 Solutions 1. A sphee has within it a gavitational field given by g = g, whee g is constant and is the position vecto of the field point elative to the cente of the sphee. This
More informationb) (5) What average force magnitude was applied by the students working together?
Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults
More informationPHYS 1114, Lecture 21, March 6 Contents:
PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam
More informationAH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion
AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed
More information