III. Electromechanical Energy Conversion

Size: px
Start display at page:

Download "III. Electromechanical Energy Conversion"

Transcription

1 . Electoancal Enegy Coneson Schematc epesentaton o an toancal enegy coneson ece coppe losses coe losses (el losses) ancal losses Deental enegy nput om tcal souce: W V t Rt e t t W net ancal enegy output Deental enegy balance eqn.: W W W el losses Fo a lossless magnetc enegy stoage system: W W W ancal losses

2 . Enegy n Magnetc Fel W W e t N t t W N W F W W F F F Coenegy wth = an F = F W F W W F

3 Fo a lnea magnetc ccut: W W F R F whee R an ae the eluctance an pemeance o the magnetc ccut espectely. Enegy & Foce n Sngly-Excte E.M.C ece Electoancal elay Assume moble amatue s ntally at open poston When the col s excte by (t), (t) s pouce n M.C. an an tomagnetc oce s exete on moble amatue tenng to algn t wth the ensest pat o M.F. When the amatue moes 3

4 Amatue Moement Slow moton case Fast moton case ( s gaually ncease ung moton) ( s constant ung moton) Nomal moton case () Slow moton W W W W W F A A 3 A A A F F A 4 F s constant ung moton W W W A 3 A 4 Shae aea ges W 4

5 () Fast moton s constant ung moton W W W W W W F A W F W F A A A A A A 3 A Shae aea ges W () Nomal moton W W W Shae aea ges W 5

6 W x W > then tcal system oes wok on the amatue W then ancal system oes wok on the amatue (a) Mechancal oce n ast moton W W W F W x W F x Note that W, x W, x W, x x x So W, x F s nepenent o x an W, x x 6

7 (a) Mechancal oce n slow moton W W W F, x F W x F, F, x F W x F, W F, x F F F x F, x F x Note that So W W F, x F W F F, x F, x W F, x x F x F s nepenent o x an W x F, x Fo a lnea magnetc ccut. When s constant ung moton W W F R F whee R an ae the eluctance an pemeance o the magnetc ccut espectely R x. When F s constant ung moton F x x 7

8 Ex-: Dee an expesson o the tomagnetc oce pouce by the E.M.D. shown n the gue an then plot aganst x. Note: ntal gap length s c an s constant ung moton Ex-: Fo the tomagnet shown below: (a) Fo V = Vc, etemne the enegy stoe n magnetc el an the ltng oce pouce (b) Fo V = Vac at 6 Hz, etemne the aeage ltng oce pouce Note: ntal gap length s 5 mm, ntenal esstance o the wnng = 6, N = 3, A c = A g = 6 x 6 = 36 cm. 8

9 3. Rotatng Machnes nea Moton nea Dsplacement x, m nea Spee, m/s Mass m, kg Foce, N Rotatonal Moton Angula Dsplacement, a Angula Spee, a/s neta J, kg m Toque T e, Nm ast moton slow moton W, x x W x F, x Fo lux nepenent o ung moton: W, Te Fo mm nepenent o ung moton: W Te F, (a) Sngly-excte ece t Fo a lnea M.C. T e T e t t 9

10 Ex: The sel nuctance n the gue as a uncton o oto poston s gen by = + cos( ) whee the stato cuent s (t) = m sn(t) () Obtan an expesson o tomagnetc toque pouce (nstantaneous toque) () et = t +, n necessay conton o non-zeo aeage toque (b) Doubly-excte ece M M t t t t M M t e t e M e M t t t t M e M e t t t t Temnal oltage equaton (n matx om): e t M M t M M ω

11 Total powe T T T T t R V cu M t M t t M t Total tcal powe nput: Coppe loss Rate o ncease n stoe enegy n MF + Elect.powe conete to. en. (n matx om) ω M M t M M Magnetc stoe enegy W M M t M t t M t t W cu M M t M t t M t T e M T e T T e n matx om:

12 Ex: T e? Ex: T e?

Chapter 13 - Universal Gravitation

Chapter 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 information

Dynamics of Rigid Bodies

Dynamics 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

Lesson 8: Work, Energy, Power (Sections ) Chapter 6 Conservation of Energy

Lesson 8: Work, Energy, Power (Sections ) Chapter 6 Conservation of Energy Lesson 8: Wok, negy, Powe (Sectons 6.-6.8) Chapte 6 Conseaton o negy Today we begn wth a ey useul concept negy. We wll encounte many amla tems that now hae ey specc dentons n physcs. Conseaton o enegy

More information

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1

Rotational 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 information

Physics 111 Lecture 11

Physics 111 Lecture 11 Physcs 111 ectue 11 Angula Momentum SJ 8th Ed.: Chap 11.1 11.4 Recap and Ovevew Coss Poduct Revsted Toque Revsted Angula Momentum Angula Fom o Newton s Second aw Angula Momentum o a System o Patcles Angula

More information

Phys 1215, First Test. September 20, minutes Name:

Phys 1215, First Test. September 20, minutes Name: Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo

More information

Physics 1: Mechanics

Physics 1: Mechanics Physcs : Mechancs Đào Ngọc Hạnh Tâm Offce: A.503, Emal: dnhtam@hcmu.edu.vn HCMIU, Vetnam Natonal Unvesty Acknowledgment: Sldes ae suppoted by Pof. Phan Bao Ngoc Contents of Physcs Pat A: Dynamcs of Mass

More information

Review. Physics 231 fall 2007

Review. Physics 231 fall 2007 Reew Physcs 3 all 7 Man ssues Knematcs - moton wth constant acceleaton D moton, D pojectle moton, otatonal moton Dynamcs (oces) Enegy (knetc and potental) (tanslatonal o otatonal moton when detals ae not

More information

Dynamics of Rotational Motion

Dynamics 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 information

One-dimensional kinematics

One-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 information

General Theory of Electric Machines 2017 Shiraz University of Technology Dr. A. Rahideh

General Theory of Electric Machines 2017 Shiraz University of Technology Dr. A. Rahideh In The ame o Go The Mot Compaonate, The Mot Mecul Geneal Theoy o Electc Machne 7 Shaz Unety o Technoloy D. A. Raheh Tale o Content. Intoucton. Tanome. Reeence Fame Theoy 4. Inucton Machne 5. Synchonou

More information

AP Physics C: Electricity and Magnetism 2013 Free-Response Questions

AP Physics C: Electricity and Magnetism 2013 Free-Response Questions AP Physcs C: Electcty an Magnetsm 3 Fee-Response Questons About the College Boa The College Boa s a msson-ven not-fo-poft oganzaton that connects stuents to college success an oppotunty. Foune n 9, the

More information

Celso José Faria de Araújo, M.Sc.

Celso José Faria de Araújo, M.Sc. Celso José Faa de Aaújo, M.c. he deal dode: (a) dode ccut symbol; (b) - chaactestc; (c) equalent ccut n the eese decton; (d) equalent ccut n the fowad decton. odes (a) Rectfe ccut. (b) nput waefom. (c)

More information

Spiral Magnetic Gradient Motor Using Axial Magnets

Spiral Magnetic Gradient Motor Using Axial Magnets Spial Magnetic Gadient Moto Using Axial Magnets Cedit: Tom Schum fo spial stato constuction Thomas Valone, PhD, PE Integity Reseach Institute Pape on Science Diect, Physics Gadients Ae Used fo All Powe

More information

Description Linear Angular position x displacement x rate of change of position v x x v average rate of change of position

Description Linear Angular position x displacement x rate of change of position v x x v average rate of change of position Chapte 5 Ccula Moton The language used to descbe otatonal moton s ey smla to the language used to descbe lnea moton. The symbols ae deent. Descpton Lnea Angula poston dsplacement ate o change o poston

More information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

PHY121 Formula Sheet

PHY121 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 information

Chapter 8. Linear Momentum, Impulse, and Collisions

Chapter 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 information

Physics Exam II Chapters 25-29

Physics Exam II Chapters 25-29 Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do

More information

(8) Gain Stage and Simple Output Stage

(8) Gain Stage and Simple Output Stage EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton

More information

Rotary motion

Rotary 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 information

Clutches and Brakes Des Mach Elem Mech. Eng. Department Chulalongkorn University

Clutches and Brakes Des Mach Elem Mech. Eng. Department Chulalongkorn University Clutches and Bakes 0330 Des Mach Elem Mech. Eng. Depatment Chulalongkon Univesity ntoduction ( Clutch and bake ae the machine elements used in tansmission and otation contol. Hee only clutch and bake using

More information

2 dependence in the electrostatic force means that it is also

2 dependence in the electrostatic force means that it is also lectc Potental negy an lectc Potental A scala el, nvolvng magntues only, s oten ease to wo wth when compae to a vecto el. Fo electc els not havng to begn wth vecto ssues woul be nce. To aange ths a scala

More information

LINEAR MOMENTUM. product of the mass m and the velocity v r of an object r r

LINEAR MOMENTUM. product of the mass m and the velocity v r of an object r r LINEAR MOMENTUM Imagne beng on a skateboad, at est that can move wthout cton on a smooth suace You catch a heavy, slow-movng ball that has been thown to you you begn to move Altenatvely you catch a lght,

More information

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER Edton CAPTER 8 VECTOR MECANCS FOR ENGNEERS: DYNAMCS Fednand P. Bee E. Russell Johnston, J. Lectue Notes: J. Walt Ole Teas Tech Unvest Knematcs of Rgd Bodes n Thee Dmensons 003 The McGaw-ll Companes, nc.

More information

Representation of Saturation in Stability Studies

Representation of Saturation in Stability Studies Inteestng summay: https://www.nap.eu/ea/8477/chapte/3 Repesentaton of atuaton n tabty tues Kunu wtes (pg ) that A goous teatment of synchonous machne pefomance ncung satuaton effects s a fute execse. Any

More information

Part V: Velocity and Acceleration Analysis of Mechanisms

Part V: Velocity and Acceleration Analysis of Mechanisms Pat V: Velocty an Acceleaton Analyss of Mechansms Ths secton wll evew the most common an cuently pactce methos fo completng the knematcs analyss of mechansms; escbng moton though velocty an acceleaton.

More information

Sensors and Actuators Introduction to sensors

Sensors and Actuators Introduction to sensors Sensos an ctuatos Intouction to sensos Sane Stuijk (s.stuijk@tue.nl) Depatment of Electical Engineeing Electonic Systems PITIE SENSORS (hapte 3., 7., 9.,.6, 3., 3.) 3 Senso classification type / quantity

More information

4. Compare the electric force holding the electron in orbit ( r = 0.53

4. Compare the electric force holding the electron in orbit ( r = 0.53 Electostatics WS Electic Foce an Fiel. Calculate the magnitue of the foce between two 3.60-µ C point chages 9.3 cm apat.. How many electons make up a chage of 30.0 µ C? 3. Two chage ust paticles exet a

More information

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D. ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic

More information

HW 7 Help. 60 s t. (4.0 rev/s)(1 min) 240 rev 1 min Solving for the distance traveled, we ll need to convert to radians:

HW 7 Help. 60 s t. (4.0 rev/s)(1 min) 240 rev 1 min Solving for the distance traveled, we ll need to convert to radians: HW 7 Help 30. ORGANIZE AND PLAN We ae given the angula velocity and the time, and we ae asked to ind the distance that is coveed. We can ist solve o the angula displacement using Equation 8.3: t. The distance

More information

Construction Figure 10.1: Jaw clutches

Construction Figure 10.1: Jaw clutches CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged. Clutches ae of thee

More information

Physics Spring 2012 Announcements: Mar 07, 2012

Physics Spring 2012 Announcements: Mar 07, 2012 Physics 00 - Sping 01 Announcements: Ma 07, 01 HW#6 due date has been extended to the moning of Wed. Ma 1. Test # (i. Ma ) will cove only chaptes 0 and 1 All of chapte will be coveed in Test #4!!! Test

More information

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to

More information

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3

More information

6. Introduction to Transistor Amplifiers: Concepts and Small-Signal Model

6. Introduction to Transistor Amplifiers: Concepts and Small-Signal Model 6. ntoucton to anssto mples: oncepts an Small-Sgnal Moel Lectue notes: Sec. 5 Sea & Smth 6 th E: Sec. 5.4, 5.6 & 6.3-6.4 Sea & Smth 5 th E: Sec. 4.4, 4.6 & 5.3-5.4 EE 65, Wnte203, F. Najmaba Founaton o

More information

Chapter 31 Faraday s Law

Chapter 31 Faraday s Law Chapte 31 Faaday s Law Change oving --> cuent --> agnetic field (static cuent --> static agnetic field) The souce of agnetic fields is cuent. The souce of electic fields is chage (electic onopole). Altenating

More information

1. A body will remain in a state of rest, or of uniform motion in a straight line unless it

1. A body will remain in a state of rest, or of uniform motion in a straight line unless it Pncples of Dnamcs: Newton's Laws of moton. : Foce Analss 1. A bod wll eman n a state of est, o of unfom moton n a staght lne unless t s acted b etenal foces to change ts state.. The ate of change of momentum

More information

EELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr.

EELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr. EELE 3331 Electomagnetic I Chapte 4 Electostatic fields Islamic Univesity of Gaza Electical Engineeing Depatment D. Talal Skaik 212 1 Electic Potential The Gavitational Analogy Moving an object upwad against

More information

Capítulo. Three Dimensions

Capítulo. Three Dimensions Capítulo Knematcs of Rgd Bodes n Thee Dmensons Mecánca Contents ntoducton Rgd Bod Angula Momentum n Thee Dmensons Pncple of mpulse and Momentum Knetc Eneg Sample Poblem 8. Sample Poblem 8. Moton of a Rgd

More information

EE 5337 Computational Electromagnetics (CEM)

EE 5337 Computational Electromagnetics (CEM) 7//28 Instucto D. Raymond Rumpf (95) 747 6958 cumpf@utep.edu EE 5337 Computatonal Electomagnetcs (CEM) Lectue #6 TMM Extas Lectue 6These notes may contan copyghted mateal obtaned unde fa use ules. Dstbuton

More information

Overview Electrical Machines and Drives

Overview Electrical Machines and Drives Overvew Electrcal achnes an Drves 7-9 1: Introucton, axwell s equatons, magnetc crcuts 11-9 1.2-3: agnetc crcuts, Prncples 14-9 3-4.2: Prncples, DC machnes 18-9 4.3-4.7: DC machnes an rves 21-9 5.2-5.6:

More information

Central Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.

Central 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 information

MAGNETIC FIELD INTRODUCTION

MAGNETIC 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 information

Chap13. Universal Gravitation

Chap13. 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 information

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig.

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig. TEST-03 TPC: MAGNETSM AND MAGNETC EFFECT F CURRENT Q. Fnd the magnetc feld ntensty due to a thn we cayng cuent n the Fg. - R 0 ( + tan) R () 0 ( ) R 0 ( + ) R 0 ( + tan ) R Q. Electons emtted wth neglgble

More information

Chapter 7-8 Rotational Motion

Chapter 7-8 Rotational Motion Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,

More information

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law Faaday s Law Faaday s Epeiments Chapte 3 Law of nduction (emf( emf) Faaday s Law Magnetic Flu Lenz s Law Geneatos nduced Electic fields Michael Faaday discoeed induction in 83 Moing the magnet induces

More information

Quiz 6--Work, Gravitation, Circular Motion, Torque. (60 pts available, 50 points possible)

Quiz 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 information

Energy in Closed Systems

Energy in Closed Systems Enegy n Closed Systems Anamta Palt palt.anamta@gmal.com Abstact The wtng ndcates a beakdown of the classcal laws. We consde consevaton of enegy wth a many body system n elaton to the nvese squae law and

More information

Chapter 4. Newton s Laws of Motion

Chapter 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 information

Physics 107 HOMEWORK ASSIGNMENT #15

Physics 107 HOMEWORK ASSIGNMENT #15 Physics 7 HOMEWORK SSIGNMENT #5 Cutnell & Johnson, 7 th eition Chapte 8: Poblem 4 Chapte 9: Poblems,, 5, 54 **4 small plastic with a mass of 6.5 x - kg an with a chage of.5 µc is suspene fom an insulating

More information

Section 26 The Laws of Rotational Motion

Section 26 The Laws of Rotational Motion Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to

More information

Boise State University Department of Electrical and Computer Engineering ECE470 Electric Machines

Boise State University Department of Electrical and Computer Engineering ECE470 Electric Machines Boie State Univeity Depatment of Electical and Compute Engineeing ECE470 Electic Machine Deivation of the Pe-Phae Steady-State Equivalent Cicuit of a hee-phae Induction Machine Nomenclatue θ: oto haft

More information

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13

More information

Chapter 10 and elements of 11, 12 Rotation of Rigid Bodies

Chapter 10 and elements of 11, 12 Rotation of Rigid Bodies Chapte 10 and elements of 11, 1 Rotaton of Rgd Bodes What s a Rgd Body? Rotatonal Knematcs Angula Velocty ω and Acceleaton α Rotaton wth Constant Acceleaton Angula vs. Lnea Knematcs Enegy n Rotatonal Moton:

More information

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1 PROBLEM SET #3A AST242 Figue 1. Two concentic co-axial cylindes each otating at a diffeent angula otation ate. A viscous fluid lies between the two cylindes. 1. Couette Flow A viscous fluid lies in the

More information

Chapter 5 Circular Motion

Chapter 5 Circular Motion Chapte 5 Ccula Moton In a gd body, the dstances between the pats o the body eman constant. We begn nestgatng the otaton o a gd body. We conclude ou nestgaton n Chapte 8. The language used to descbe otatonal

More information

a v2 r a' (4v) 2 16 v2 mg mg (2.4kg)(9.8m / s 2 ) 23.52N 23.52N N

a v2 r a' (4v) 2 16 v2 mg mg (2.4kg)(9.8m / s 2 ) 23.52N 23.52N N Conceptual ewton s Law Applcaton Test Revew 1. What s the decton o centpetal acceleaton? see unom ccula moton notes 2. What aects the magntude o a ctonal oce? see cton notes 3. What s the deence between

More information

Physics 1114: Unit 5 Hand-out Homework (Answers)

Physics 1114: Unit 5 Hand-out Homework (Answers) Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),

More information

Lab #0. Tutorial Exercises on Work and Fields

Lab #0. Tutorial Exercises on Work and Fields Lab #0 Tutoial Execises on Wok and Fields This is not a typical lab, and no pe-lab o lab epot is equied. The following execises will emind you about the concept of wok (fom 1130 o anothe intoductoy mechanics

More information

COLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER /2017

COLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER /2017 COLLEGE OF FOUNDATION AND GENERAL STUDIES PUTRAJAYA CAMPUS FINAL EXAMINATION TRIMESTER 1 016/017 PROGRAMME SUBJECT CODE : Foundaton n Engneeng : PHYF115 SUBJECT : Phscs 1 DATE : Septembe 016 DURATION :

More information

19 The Born-Oppenheimer Approximation

19 The Born-Oppenheimer Approximation 9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A

More information

General Railgun Function

General Railgun Function Geneal ailgun Function An electomagnetic ail gun uses a lage Loentz foce to fie a pojectile. The classic configuation uses two conducting ails with amatue that fits between and closes the cicuit between

More information

Physics C: Electricity and Magnetism

Physics C: Electricity and Magnetism Physics C: Electicity an Magnetism TABLE OF INFORMATION FOR CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u =. 66 7 kg = 93 MeV/ c Poton mass, m p = 67. 7 kg Neuton mass, m n = 67. 7 kg Electon

More information

A moving charged particle creates a magnetic field vector at every point in space except at its position.

A moving charged particle creates a magnetic field vector at every point in space except at its position. 1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units

More information

24-2: Electric Potential Energy. 24-1: What is physics

24-2: 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 information

Lecture 7: Angular Momentum, Hydrogen Atom

Lecture 7: Angular Momentum, Hydrogen Atom Lectue 7: Angula Momentum, Hydogen Atom Vecto Quantization of Angula Momentum and Nomalization of 3D Rigid Roto wavefunctions Conside l, so L 2 2 2. Thus, we have L 2. Thee ae thee possibilities fo L z

More information

Exam 3: Equation Summary

Exam 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 information

PHY 213. General Physics II Test 2.

PHY 213. General Physics II Test 2. Univesity of Kentucky Depatment of Physics an Astonomy PHY 3. Geneal Physics Test. Date: July, 6 Time: 9:-: Answe all questions. Name: Signatue: Section: Do not flip this page until you ae tol to o so.

More information

Answers to test yourself questions

Answers to test yourself questions Answes to test youself questions opic. Cicula motion π π a he angula speed is just ω 5. 7 ad s. he linea speed is ω 5. 7 3. 5 7. 7 m s.. 4 b he fequency is f. 8 s.. 4 3 a f. 45 ( 3. 5). m s. 3 a he aeage

More information

Basic 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 information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity

More information

Electric Field, Potential Energy, & Voltage

Electric Field, Potential Energy, & Voltage Slide 1 / 66 lectic Field, Potential negy, & oltage Wok Slide 2 / 66 Q+ Q+ The foce changes as chages move towads each othe since the foce depends on the distance between the chages. s these two chages

More information

Chapter 13 Gravitation

Chapter 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 information

Tutorial 5 Drive dynamics & control

Tutorial 5 Drive dynamics & control UNIVERSITY OF NEW SOUTH WALES Electic Dive Sytem School o Electical Engineeing & Telecommunication ELEC463 Electic Dive Sytem Tutoial 5 Dive dynamic & contol. The ollowing paamete ae known o two high peomance

More information

Moment. F r F r d. Magnitude of moment depends on magnitude of F and the length d

Moment. F r F r d. Magnitude of moment depends on magnitude of F and the length d Moment Tanslation Tanslation + Rotation This otation tenency is known as moment M of foce (toque) xis of otation may be any line which neithe intesects no paallel to the line of action of foce Magnitue

More information

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor Mcoelectoncs Ccut Analyss and Desgn Donald A. Neamen Chapte 5 The pola Juncton Tanssto In ths chapte, we wll: Dscuss the physcal stuctue and opeaton of the bpola juncton tanssto. Undestand the dc analyss

More information

Hoizontal 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 information

PHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle

PHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle 1 PHYS 705: Classcal Mechancs Devaton of Lagange Equatons fom D Alembet s Pncple 2 D Alembet s Pncple Followng a smla agument fo the vtual dsplacement to be consstent wth constants,.e, (no vtual wok fo

More information

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed?

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed? Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 10, 2012 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with

More information

Chapter 29 Magnetic Fields

Chapter 29 Magnetic Fields Chapte 9 Magnetic Fiels electic ipole +e agnetic ipole -e can t fin onopole --> cuent oel Magnetic poles always occu in pais. Thus fa, thee is no conclusie eience that an isolate agnetic onopole eists.

More information

Experiment 09: Angular momentum

Experiment 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 information

17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other

17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system

More information

Density Functional Theory I

Density Functional Theory I Densty Functonal Theoy I cholas M. Hason Depatment of Chemsty Impeal College Lonon & Computatonal Mateals Scence Daesbuy Laboatoy ncholas.hason@c.ac.uk Densty Functonal Theoy I The Many Electon Schönge

More information

PHYS 1444 Section 501 Lecture #7

PHYS 1444 Section 501 Lecture #7 PHYS 1444 Section 51 Lectue #7 Wednesday, Feb. 8, 26 Equi-potential Lines and Sufaces Electic Potential Due to Electic Dipole E detemined fom V Electostatic Potential Enegy of a System of Chages Capacitos

More information

to point uphill and to be equal to its maximum value, in which case f s, max = μsfn

to point uphill and to be equal to its maximum value, in which case f s, max = μsfn Chapte 6 16. (a) In this situation, we take f s to point uphill and to be equal to its maximum value, in which case f s, max = μsf applies, whee μ s = 0.5. pplying ewton s second law to the block of mass

More information

1.050 Engineering Mechanics I. Summary of variables/concepts. Lecture 27-37

1.050 Engineering Mechanics I. Summary of variables/concepts. Lecture 27-37 .5 Engneeng Mechancs I Summa of vaabes/concepts Lectue 7-37 Vaabe Defnton Notes & ments f secant f tangent f a b a f b f a Convet of a functon a b W v W F v R Etena wok N N δ δ N Fee eneg an pementa fee

More information

Effects of Rotor Air-gap Eccentricity on the Power Factor of Squirrel Cage Induction Machines

Effects of Rotor Air-gap Eccentricity on the Power Factor of Squirrel Cage Induction Machines Effect of Roto A-gap Eccentcty on the Powe Facto of Squel Cage Inducton Machne H. Mehgn-Kelk, J. Mlmonfaed Electc Machne and Dve Laboatoy Depament of Electcal Engneeng Amkab Unvety of echnology ehan 594,

More information

Physics 2A Chapter 11 - Universal Gravitation Fall 2017

Physics 2A Chapter 11 - Universal Gravitation Fall 2017 Physcs A Chapte - Unvesal Gavtaton Fall 07 hese notes ae ve pages. A quck summay: he text boxes n the notes contan the esults that wll compse the toolbox o Chapte. hee ae thee sectons: the law o gavtaton,

More information

Chapter 12 Equilibrium and Elasticity

Chapter 12 Equilibrium and Elasticity Chapte 12 Equlbum and Elastcty In ths chapte we wll defne equlbum and fnd the condtons needed so that an object s at equlbum. We wll then apply these condtons to a vaety of pactcal engneeng poblems of

More information

The Law of Biot-Savart & RHR P θ

The Law of Biot-Savart & RHR P θ The Law of iot-savat & RHR P R dx x Jean-aptiste iot élix Savat Phys 122 Lectue 19 G. Rybka Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy

More information

PHYS 1444 Lecture #5

PHYS 1444 Lecture #5 Shot eview Chapte 24 PHYS 1444 Lectue #5 Tuesday June 19, 212 D. Andew Bandt Capacitos and Capacitance 1 Coulom s Law The Fomula QQ Q Q F 1 2 1 2 Fomula 2 2 F k A vecto quantity. Newtons Diection of electic

More information

Phys 222 Sp 2009 Exam 1, Wed 18 Feb, 8-9:30pm Closed Book, Calculators allowed Each question is worth one point, answer all questions

Phys 222 Sp 2009 Exam 1, Wed 18 Feb, 8-9:30pm Closed Book, Calculators allowed Each question is worth one point, answer all questions Phys Sp 9 Exam, Wed 8 Feb, 8-9:3pm Closed Book, Calculatos allowed Each question is woth one point, answe all questions Fill in you Last Name, Middle initial, Fist Name You ID is the middle 9 digits on

More information

J. Electrical Systems 1-3 (2005): Regular paper

J. Electrical Systems 1-3 (2005): Regular paper K. Saii D. Rahem S. Saii A Miaoui Regula pape Coupled Analytical-Finite Element Methods fo Linea Electomagnetic Actuato Analysis JES Jounal of Electical Systems In this pape, a linea electomagnetic actuato

More information

PHYSICS NOTES GRAVITATION

PHYSICS 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 information

Synopsis : 8. ELECTROMAGNETISM

Synopsis : 8. ELECTROMAGNETISM Synopss : 8. ELECTROMAGNETISM MAGNETIC EFFECTS OF CURRENT: 1. Electomagnetsm s the banch of physcs whch deals wth elaton between electcty and magnetsm.. A statc chage poduces only electc feld but movng

More information

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N

F 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 information

Electromagnetic Forces in a Permanent Magnet Synchronous Machine with an Eccentric Rotor

Electromagnetic Forces in a Permanent Magnet Synchronous Machine with an Eccentric Rotor 568 Electomagnetc Foces n a Pemanent Magnet Synchonous Machne wth an Eccentc Roto Mcea Dan IUDEN *),**) *) Techncal Unvesty of Cluj-Napoca St. C. Dacovcu n.5, 4 Cluj-Napoca - Romana Tel: 4 64 595699, Fax:

More information

Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)

Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2) TELE4353 Moble a atellte Commucato ystems Tutoal 1 (week 3-4 4 Questo 1 ove that fo a hexagoal geomety, the co-chael euse ato s gve by: Q (3 N Whee N + j + j 1/ 1 Typcal Cellula ystem j cells up cells

More information