Table of Information and Equation Tables for AP Physics Exams

Size: px
Start display at page:

Download "Table of Information and Equation Tables for AP Physics Exams"

Transcription

1 le of Infomton n Equton le fo P Phy Em he ompnyng le of Infomton n Equton le wll e pove to tuent when they tke the P Phy Em. heefoe, tuent my NO ng the own ope of thee tle to the em oom, lthough they my ue them thoughout the ye n the le n oe to eome fml wth the ontent. le of Infomton o oth the Phy B n Phy C Em, the le of Infomton pnte ne the font ove of the multple-hoe eton n on the geen net pove wth the fee-epone eton. he tle e entl fo oth em eept fo one onventon note. Equton le o oth the Phy B n Phy C Em, the equton tle fo eh em e pnte only on the geen net pove wth the fee-epone eton. he equton tle my e ue y tuent when tkng the fee-epone eton of oth em ut NO when tkng the multple-hoe eton. he equton n the tle epe the eltonhp tht e enountee mot fequently n P Phy oue n em. oweve, the tle o not nlue ll equton tht mght poly e ue. o emple, they o not nlue mny equton tht n e eve y omnng othe equton n the tle. No o they nlue equton tht e mply pel e of ny tht e n the tle. Stuent e eponle fo unetnng the phyl pnple tht unele eh equton n fo knowng the onton fo whh eh equton pplle. he equton tle e goupe n eton ong to the mjo ontent tegoy n whh they ppe. Wthn eh eton, the ymol ue fo the vle n tht eton e efne. oweve, n ome e the me ymol ue to epeent ffeent quntte n ffeent tle. It houl e note tht thee no unfom onventon mong tetook fo the ymol ue n wtng equton. he equton tle follow mny ommon onventon, ut n ome e onteny w fe fo the ke of lty. Some eplnton out notton ue n the equton tle:. he ymol ue fo phyl ontnt e the me thoe n the le of Infomton n e efne n the le of Infomton the thn n the ght-hn olumn of the tle.. Symol n ol fe epeent veto quntte.. Supt on ymol n the equton e ue to epeent pel e of the vle efne n the ght-hn olumn. 4. he ymol efoe vle n n equton peflly nte hnge n the vle (.e., fnl vlue mnu ntl vlue). 5. Sevel ffeent ymol (e.g.,,,, h, ) e ue fo lne menon uh length. he ptul ymol ue n n equton one tht ommonly ue fo tht equton n tetook. 7 he College Bo. ll ght eeve. College Bo, vne Plement Pogm, P, n the on logo e egtee temk of the College Bo.

2 Poton m, Neuton m, m p m n BLE O INORMION OR 8 n 9 CONSNS ND CONERSION CORS 7.67 kg Eleton hge mgntue, 7 9 e.6 C.67 kg 9 eleton volt, e.6 J 8 Eleton m, m e 9. kg Spee of lght,. m - nvel gvttonl vogo nume, N 6. mol ontnt, 6.67 m kg nvel g ontnt, R 8. J (mol ) eleton ue to gvty t Eth ufe, g 9.8 m Boltzmnn ontnt,.8 J k B 7 unfe tom m unt, u.66 kg 9 Me Plnk ontnt, 4 5 h 6.6 J 4.4 e uum pemttvty, Coulom lw ontnt, uum pemelty, Mgnet ontnt, 5 h.99 J m.4 e nm 8.85 C Nm 9 k 4 9. Nm C 7 4 ( m) k 7 4 (m) 5 5 tmophee peue, tm. N m. P NI SYMBOLS mete, m mole, mol wtt, W f, klogm, kg hetz, z oulom, C tel, eon, newton, N volt, egee Celu, C mpee, pl, P ohm, eleton-volt, e kelvn, joule, J heny, PREIXES LES O RIONOMERIC NCIONS OR COMMON NLES to Pef Symol gg n meg M o 45 5 klo k tn 4 4 ent he followng onventon e ue n th em. mll m I. nle othewe tte, the fme of efeene of ny polem 6 mo ume to e netl. 9 II. he eton of ny elet uent the eton of flow of potve nno n hge (onventonl uent). po p III. o ny olte elet hge, the elet potentl efne zeo t n nfnte tne fom the hge. *I. o mehn n themoynm equton, W epeent the wok one on ytem. *Not on the le of Infomton fo Phy C, ne hemoynm not Phy C top. 7 he College Bo. ll ght eeve. t pentl.ollegeo.om (fo P pofeonl) n (fo tuent n pent).

3 DNCED PLCEMEN PYSICS B EQIONS OR 8 n 9 t t t net m f N n p mv J t p m g mgh NEWONIN MECNICS W o P vg W t P o k k m k p g f = eleton = foe f = fequeny h = heght J = mpule = knet enegy k = png ontnt = length m = m N = noml foe P = powe p = momentum = u o tne = peo t = tme = potentl enegy = veloty o pee W = wok one on ytem = poton = oeffent of fton = ngle = toque qq 4 E q E E vg ELECRICIY ND MNEISM qq q 4 4 Q C C q Q C I vg R Q t IR P I Cp C C C R R Rp R B qb n BI n B B I m B o m vg t B = e B = mgnet fel C = ptne = tne E = elet fel = emf = foe I = uent = length P = powe Q = hge q = pont hge R = etne = tne t = tme = potentl (toe) enegy = elet potentl o potentl ffeene = veloty o pee = etvty = ngle m = mgnet flu 7 he College Bo. ll ght eeve. t pentl.ollegeo.om (fo P pofeonl) n (fo tuent n pent).

4 DNCED PLCEMEN PYSICS B EQIONS OR 8 n 9 LID MECNICS ND ERML PYSICS P P gh uoy g P gy P k L P nr NkB W vg m kb ont. k R B M P Q W e e W Q C = e e = effeny = foe h = epth = te of het tnfe k = theml onutvty vg = vege moleul knet enegy = length L = thkne M = mol m n = nume of mole N = nume of moleule P = peue Q = het tnfee to ytem = tempetue = ntenl enegy = volume = veloty o pee m = oot-men-que veloty W = wok one on ytem y = heght = oeffent of lne epnon = m of moleule = enty OMIC ND NCLER PYSICS E hf p m hf h p E ( m ) E = enegy f = fequeny = knet enegy m = m p = momentum = wvelength = wok funton WES ND OPICS n n f n n n n n n f h M h f n R m m L m = epton f = fequeny o fol length h = heght L = tne M = mgnfton m = n ntege n = ne of efton R = u of uvtue = tne = pee = poton = wvelength = ngle EOMERY ND RIONOMERY Retngle = e h C = umfeene ngle = volume h S = ufe e = e Cle h = heght = length C w = wth Plleleppe = u w h Cylne S Sphee 4 S 4 Rght ngle n q 9 o tn 7 he College Bo. ll ght eeve. t pentl.ollegeo.om (fo P pofeonl) n (fo tuent n pent).

5 DNCED PLCEMEN PYSICS C EQIONS OR 8 n 9 t t t net m p t J t p p mv f N W P P m W t v g mgh net I I m m m m m L p I I t t t MECNICS = eleton = foe f = fequeny h = heght I = ottonl net J = mpule = knet enegy k = png ontnt = length L = ngul momentum m = m N = noml foe P = powe p = momentum = u o tne = poton veto = peo t = tme = potentl enegy = veloty o pee W = wok one on ytem = poton = oeffent of fton = ngle = toque = ngul pee = ngul eleton k k f m k p g ˆ qq 4 E q E Q E 4 E q Q C C Cp C C C I Q t ELECRICIY ND MNEISM q qq 4 Q C R E J I Ne R IR R R p R P I qv B M = e B = mgnet fel C = ptne = tne E = elet fel = emf = foe I = uent J = uent enty L = nutne = length n = nume of loop of we pe unt length N = nume of hge e pe unt volume P = powe Q = hge q = pont hge R = etne = tne t = tme = potentl o toe enegy = elet potentl = veloty o pee = etvty m = mgnet flu = elet ontnt I B B B I 4 I B ni m B t m I L t L LI 7 he College Bo. ll ght eeve. t pentl.ollegeo.om (fo P pofeonl) n (fo tuent n pent).

6 DNCED PLCEMEN PYSICS C EQIONS OR 8 n 9 EOMERY ND RIONOMERY CLCLS Retngle h ngle Cle h C Plleleppe w h Cylne S Sphee 4 S 4 Rght ngle = e C = umfeene = volume S = ufe e = e h = heght = length w = wth = u f f u u n n n e e n n o o n n n, n n e e ln o n n o n o q 9 tn 7 he College Bo. ll ght eeve. t pentl.ollegeo.om (fo P pofeonl) n (fo tuent n pent).

Table of Information and Equation Tables for AP Physics 1 and 2 Exams

Table of Information and Equation Tables for AP Physics 1 and 2 Exams Tle of Infoton nd Equton Tle fo P Py nd E Te opnyng Tle of Infoton nd equton tle wll e povded to tudent wen tey tke te P Py nd E. Teefoe, tudent y NOT ng te own ope of tee tle to te e oo, ltoug tey y ue

More information

AP Physics C: Electricity and Magnetism 2010 Free-Response Questions

AP Physics C: Electricity and Magnetism 2010 Free-Response Questions AP Phyc C: Electcty n Mgnet Fee-Repone Queton The College Bo The College Bo not-fo-poft ebehp octon whoe on to connect tuent to college ucce n oppotunty. Foune n 9, the College Bo copoe of oe thn 5,7 chool,

More information

AP Physics C: Mechanics

AP Physics C: Mechanics 08 AP Phyc C: Mechnc ee-repone Queton 08 The College Bod. College Bod, Advnced Plcement Pogm, AP, AP Centl, nd the con logo e egteed tdemk of the College Bod. Vt the College Bod on the Web: www.collegebod.og.

More information

PHYS 2421 Fields and Waves

PHYS 2421 Fields and Waves PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4

More information

Lecture 9-3/8/10-14 Spatial Description and Transformation

Lecture 9-3/8/10-14 Spatial Description and Transformation Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.

More information

Introduction to Robotics (Fag 3480)

Introduction to Robotics (Fag 3480) Intouton to Robot (Fg 8) Vå Robet Woo (Hw Engneeeng n pple Sene-B) Ole Jkob Elle PhD (Mofe fo IFI/UIO) Føtemnuen II Inttutt fo Infomtkk Unvetetet Olo Sekjonlee Teknolog Intevenjonenteet Olo Unvetetkehu

More information

8. Two Ion Interactions

8. Two Ion Interactions 8. Two on ntetons The moels of mgnet oe hve een se on mltonns of the fom on J J zw. Wht s the physl ogn of ths two on ntetons 8. Dpol nteton The ogn of lge moleul fels nnot e the wek mgnet pol nteton CD

More information

Physics 11-0-Formulas - Useful Information. h hc. Earth's mass Earth's radius. Speed of light. Moon's radius. Moon's mass.

Physics 11-0-Formulas - Useful Information. h hc. Earth's mass Earth's radius. Speed of light. Moon's radius. Moon's mass. Physis - 0-Fomulas - Useful Infomation unifie atomi mass unit u.66 x 0-7 kg 9 Me V/ Poton mass m p.67 x 0-7 kg Neuton mass m n.67 x 0-7 kg Eleton mass m e 9. x 0 - kg The hage of eleton e.6 x 0-9 C Avogao's

More information

AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism 08 AP Physcs C: Electcty n Mgnetsm Fee-Response Questons 08 The College Bo. College Bo, Avnce Plcement Pogm, AP, AP Centl, n the con logo e egstee temks of the College Bo. Vst the College Bo on the Web:

More information

Empirical equations for electrical parameters of asymmetrical coupled microstrip lines

Empirical equations for electrical parameters of asymmetrical coupled microstrip lines Epl equons fo elel petes of syel ouple osp lnes I.M. Bsee Eletons eseh Instute El-h steet, Dokk, o, Egypt Abstt: Epl equons e eve fo the self n utul nutne n ptne fo two syel ouple osp lnes. he obne ptne

More information

Rigid Body Dynamics. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018

Rigid Body Dynamics. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018 Rg Bo Dnmcs CSE169: Compute Anmton nstucto: Steve Roteneg UCSD, Wnte 2018 Coss Pouct k j Popetes of the Coss Pouct Coss Pouct c c c 0 0 0 c Coss Pouct c c c c c c 0 0 0 0 0 0 Coss Pouct 0 0 0 ˆ ˆ 0 0 0

More information

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof ME6 Dnms, Spng HW Slutn Ke - Pve, gemetll.e. usng wngs sethes n nltll.e. usng equtns n nequltes, tht V then V. Nte: qunttes n l tpee e vets n n egul tpee e sls. Slutn: Let, Then V V V We wnt t pve tht:

More information

Uniform Circular Motion

Uniform Circular Motion Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The

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

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , R Pen Towe Rod No Conttos Ae Bistupu Jmshedpu 8 Tel (67)89 www.penlsses.om IIT JEE themtis Ppe II PART III ATHEATICS SECTION I (Totl ks : ) (Single Coet Answe Type) This setion ontins 8 multiple hoie questions.

More information

U>, and is negative. Electric Potential Energy

U>, and is negative. Electric Potential Energy Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When

More information

Abhilasha Classes Class- XII Date: SOLUTION (Chap - 9,10,12) MM 50 Mob no

Abhilasha Classes Class- XII Date: SOLUTION (Chap - 9,10,12) MM 50 Mob no hlsh Clsses Clss- XII Dte: 0- - SOLUTION Chp - 9,0, MM 50 Mo no-996 If nd re poston vets of nd B respetvel, fnd the poston vet of pont C n B produed suh tht C B vet r C B = where = hs length nd dreton

More information

MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER

MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER I One M Queston Fnd the unt veto n the deton of Let ˆ ˆ 9 Let & If Ae the vetos & equl? But vetos e not equl sne the oespondng omponents e dstnt e detons

More information

PHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM

PHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM PHYS 0 Suen Nme: Suen Numbe: FAUTY OF SIENE Viul Miem EXAMINATION PHYSIS 0 Ino PHYSIS-EETROMAGNETISM Emines: D. Yoichi Miyh INSTRUTIONS: Aemp ll 4 quesions. All quesions hve equl weighs 0 poins ech. Answes

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

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

Matrix Methods in Kinematics

Matrix Methods in Kinematics Mtr Metho n Knemt Fe Mong Frme ' ' Fe n Rottng ' ' ' ' ' ' o n o n n o n o T Fe o n n o R Fe Mtr Metho n Knemt. Rotte bout Z (α o n n o o n n o Rotton mtr Comonent n the fe tem - Referene Mtr Metho n Knemt

More information

EE 410/510: Electromechanical Systems Chapter 3

EE 410/510: Electromechanical Systems Chapter 3 EE 4/5: Eleomehnl Syem hpe 3 hpe 3. Inoon o Powe Eleon Moelng n Applon of Op. Amp. Powe Amplfe Powe onvee Powe Amp n Anlog onolle Swhng onvee Boo onvee onvee Flyb n Fow onvee eonn n Swhng onvee 5// All

More information

Week 8. Topic 2 Properties of Logarithms

Week 8. Topic 2 Properties of Logarithms Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e

More information

Energy Dissipation Gravitational Potential Energy Power

Energy Dissipation Gravitational Potential Energy Power Lectue 4 Chpte 8 Physics I 0.8.03 negy Dissiption Gvittionl Potentil negy Powe Couse wesite: http://fculty.uml.edu/andiy_dnylov/teching/physicsi Lectue Cptue: http://echo360.uml.edu/dnylov03/physicsfll.html

More information

The formulae in this booklet have been arranged according to the unit in which they are first

The formulae in this booklet have been arranged according to the unit in which they are first Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule

More information

LA0011_11GB. Formulas and Units. Rotation 2 W. W = work in Ws = J = Nm. = ang. velocity in rad./sec. f = frequency in rev./sec.

LA0011_11GB. Formulas and Units. Rotation 2 W. W = work in Ws = J = Nm. = ang. velocity in rad./sec. f = frequency in rev./sec. Tnsmission technicl clcultions Min Fomuls Size designtions nd units ccoding to the SI-units Line moement: s m/s t s t m s 1 m t m/s t P F W F m N Rottion ω π f d/s ω π f m/s M F P M ω W M J ω J ω W Ws

More information

Electric Potential. and Equipotentials

Electric Potential. and Equipotentials Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil

More information

Chapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts

Chapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts Chpte 5: Cuent, esistnce nd Electomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m qe ndomizing Collisions (momentum, enegy) =>esulting Motion Avege motion = Dift elocity = v d

More information

A Study on Root Properties of Super Hyperbolic GKM algebra

A Study on Root Properties of Super Hyperbolic GKM algebra Stuy on Root Popetes o Supe Hypebol GKM lgeb G.Uth n M.Pyn Deptment o Mthemts Phypp s College Chenn Tmlnu In. bstt: In ths ppe the Supe hypebol genelze K-Mooy lgebs o nente type s ene n the mly s lso elte.

More information

Answers to test yourself questions

Answers to test yourself questions Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E

More information

NXO a Spatially High Order Finite Volume Numerical Method for Compressible Flows

NXO a Spatially High Order Finite Volume Numerical Method for Compressible Flows NXO Spty Hgh Ode Fnte Voume Nume Method fo Compebe Fow Jen-Me e Gouez One CFD Deptment Fouth HO CFD Wohop Heon June 4th B of the NXO heme Eue o Nve-Stoe fo pefet g w of tte dof pe e nd pe equton Voume

More information

Physics 604 Problem Set 1 Due Sept 16, 2010

Physics 604 Problem Set 1 Due Sept 16, 2010 Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside

More information

Chapter 25: Current, Resistance and Electromotive Force. ~10-4 m/s Typical speeds ~ 10 6 m/s

Chapter 25: Current, Resistance and Electromotive Force. ~10-4 m/s Typical speeds ~ 10 6 m/s Chpte 5: Cuent, esistnce nd lectomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m q ndomizing Collisions (momentum, enegy) >esulting Motion http://phys3p.sl.psu.edu/phys_nim/m/ndom_wlk.vi

More information

E-Companion: Mathematical Proofs

E-Companion: Mathematical Proofs E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth

More information

Lecture 7 Circuits Ch. 27

Lecture 7 Circuits Ch. 27 Leture 7 Cruts Ch. 7 Crtoon -Krhhoff's Lws Tops Dret Current Cruts Krhhoff's Two ules Anlyss of Cruts Exmples Ammeter nd voltmeter C ruts Demos Three uls n rut Power loss n trnsmsson lnes esstvty of penl

More information

Equations from the Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk

Equations from the Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk Equtions fo the illenniu heoy of Ineti nd vity Copyight 004 Joseph A. Rybzyk ollowing is oplete list of ll of the equtions used o deived in the illenniu heoy of Ineti nd vity. o ese of efeene the equtions

More information

ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.

ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS. GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: -------------------------------------------------------------------------------------------------------------------------------------------

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

VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors

VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors 1. Defnton A vetor s n entt tht m represent phsl quntt tht hs mgntude nd dreton s opposed to slr tht ls dreton.. Vetor Representton A vetor n e represented grphll n rrow. The length of the rrow s the mgntude

More information

Lecture 5 Single factor design and analysis

Lecture 5 Single factor design and analysis Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke

More information

π,π is the angle FROM a! TO b

π,π is the angle FROM a! TO b Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two

More information

10 Statistical Distributions Solutions

10 Statistical Distributions Solutions Communictions Engineeing MSc - Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques

More information

Physics 11b Lecture #11

Physics 11b Lecture #11 Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations Dynm o Lnke Herrhe Contrne ynm The Fethertone equton Contrne ynm pply ore to one omponent, other omponent repotone, rom ner to r, to ty tne ontrnt F Contrne Boy Dynm Chpter 4 n: Mrth mpule-be Dynm Smulton

More information

CHAPTER 25 ELECTRIC POTENTIAL

CHAPTER 25 ELECTRIC POTENTIAL CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When

More information

AP Physics Electric Potential Energy

AP Physics Electric Potential Energy AP Physics lectic Potential negy Review of some vital peviously coveed mateial. The impotance of the ealie concepts will be made clea as we poceed. Wok takes place when a foce acts ove a distance. W F

More information

" = #N d$ B. Electromagnetic Induction. v ) $ d v % l. Electromagnetic Induction and Faraday s Law. Faraday s Law of Induction

 = #N d$ B. Electromagnetic Induction. v ) $ d v % l. Electromagnetic Induction and Faraday s Law. Faraday s Law of Induction Eletromgnet Induton nd Frdy s w Eletromgnet Induton Mhel Frdy (1791-1867) dsoered tht hngng mgnet feld ould produe n eletr urrent n ondutor pled n the mgnet feld. uh urrent s lled n ndued urrent. The phenomenon

More information

Field due to a collection of N discrete point charges: r is in the direction from

Field due to a collection of N discrete point charges: r is in the direction from Physcs 46 Fomula Shee Exam Coulomb s Law qq Felec = k ˆ (Fo example, f F s he elecc foce ha q exes on q, hen ˆ s a un veco n he decon fom q o q.) Elecc Feld elaed o he elecc foce by: Felec = qe (elecc

More information

COMP 465: Data Mining More on PageRank

COMP 465: Data Mining More on PageRank COMP 465: Dt Mnng Moe on PgeRnk Sldes Adpted Fo: www.ds.og (Mnng Mssve Dtsets) Powe Iteton: Set = 1/ 1: = 2: = Goto 1 Exple: d 1/3 1/3 5/12 9/24 6/15 = 1/3 3/6 1/3 11/24 6/15 1/3 1/6 3/12 1/6 3/15 Iteton

More information

Trigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245.

Trigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245. Trgonometry Trgonometry Solutons Currulum Redy CMMG:, 4, 4 www.mthlets.om Trgonometry Solutons Bss Pge questons. Identfy f the followng trngles re rght ngled or not. Trngles,, d, e re rght ngled ndted

More information

ˆ 2. Chapter 4 The structure of diatomic molecules. 1 Treatment of variation method for the H 2+ ion 1. Shroedinger equation of H 2. e - r b.

ˆ 2. Chapter 4 The structure of diatomic molecules. 1 Treatment of variation method for the H 2+ ion 1. Shroedinger equation of H 2. e - r b. Chpte 4 The stutue of tom moleules Tetment of vton metho fo the on. hoenge equton of Bon-Oppenheme Appoxmton The eletons e muh lghte thn the nule. Nule moton s slow eltve to the eleton moton. A θ e - R

More information

CHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES

CHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES HPTER ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy So,. foce between chges 4 So, foce between chges.6 weight of

More information

Lectures # He-like systems. October 31 November 4,6

Lectures # He-like systems. October 31 November 4,6 Lectue #5-7 7 Octoe 3 oveme 4,6 Self-conitent field Htee-Foc eqution: He-lie ytem Htee-Foc eqution: cloed-hell hell ytem Chpte 3, pge 6-77, Lectue on Atomic Phyic He-lie ytem H (, h ( + h ( + h ( Z Z:

More information

PHYSICS 212 MIDTERM II 19 February 2003

PHYSICS 212 MIDTERM II 19 February 2003 PHYSICS 1 MIDERM II 19 Feruary 003 Exam s losed ook, losed notes. Use only your formula sheet. Wrte all work and answers n exam ooklets. he aks of pages wll not e graded unless you so request on the front

More information

8. INVERSE Z-TRANSFORM

8. INVERSE Z-TRANSFORM 8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere

More information

Electrons Acceleration in Active Medium

Electrons Acceleration in Active Medium Eleton Aeleaton n Atve Meum Lev Säte Tenon - Iael Inttute of Tenology Depatment of Eletal Engneeng Outlne Ovevew & Motvaton PASE: Patle Aeleaton by Stmulate Emon of aaton Wake Amplfaton Aeleaton n a gowng

More information

CHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton

CHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton Downloe fo HPTER? ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy.5 So, foce between chges 4 So, foce between chges

More information

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:

More information

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3 DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl

More information

On Fractional Operational Calculus pertaining to the product of H- functions

On Fractional Operational Calculus pertaining to the product of H- functions nenonl eh ounl of Enneen n ehnolo RE e-ssn: 2395-56 Volume: 2 ue: 3 une-25 wwwene -SSN: 2395-72 On Fonl Oeonl Clulu enn o he ou of - funon D VBL Chu, C A 2 Demen of hem, Unve of Rhn, u-3255, n E-ml : vl@hooom

More information

Physics Courseware Modern Physics

Physics Courseware Modern Physics Physis Cousewae oden Physis Enegy and oentu Relatiisti oentu: p γ Kineti enegy: K. E. ( γ ) Auxiliay equation: E + 4 p whee is the est ass and E is total enegy. Poble.- What has oe ass at est: i) A sodiu

More information

ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:

ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy: LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6

More information

Ch. 3: Forward and Inverse Kinematics

Ch. 3: Forward and Inverse Kinematics Ch. : Fowa an Invee Knemat Reap: The Denavt-Hatenbeg (DH) Conventon Repeentng eah nvual homogeneou tanfomaton a the pout of fou ba tanfomaton: pout of fou ba tanfomaton: x a x z z a a a Rot Tan Tan Rot

More information

PHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite

PHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite PHYS 015 -- Week 5 Readng Jounals today fom tables WebAssgn due Wed nte Fo exclusve use n PHYS 015. Not fo e-dstbuton. Some mateals Copyght Unvesty of Coloado, Cengage,, Peason J. Maps. Fundamental Tools

More information

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = = Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon

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

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES ELECTROMAGNETIC THEORY SOLUTIONS GATE- Q. An insulating sphee of adius a aies a hage density a os ; a. The leading ode tem fo the eleti field at a distane d, fa away fom the hage distibution, is popotional

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

VISUAL PHYSICS ONLINE EQUATION MINDMAPS

VISUAL PHYSICS ONLINE EQUATION MINDMAPS VISUAL PHYSICS ONLIN QUATION MINDMAPS quation ae eential pat of phyi, without them, we an t tat to explain ou phyial wold and make pedition. An equation tell a toy a olletion of a few ymbol ontain a wealth

More information

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97 Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10

More information

CHAPTER 7 Applications of Integration

CHAPTER 7 Applications of Integration CHAPTER 7 Applitions of Integtion Setion 7. Ae of Region Between Two Cuves.......... Setion 7. Volume: The Disk Method................. Setion 7. Volume: The Shell Method................ Setion 7. A Length

More information

8.022 (E&M) Lecture 13. What we learned about magnetism so far

8.022 (E&M) Lecture 13. What we learned about magnetism so far 8.0 (E&M) Letue 13 Topis: B s ole in Mawell s equations Veto potential Biot-Savat law and its appliations What we leaned about magnetism so fa Magneti Field B Epeiments: uents in s geneate foes on hages

More information

Topics for Review for Final Exam in Calculus 16A

Topics for Review for Final Exam in Calculus 16A Topics fo Review fo Finl Em in Clculus 16A Instucto: Zvezdelin Stnkov Contents 1. Definitions 1. Theoems nd Poblem Solving Techniques 1 3. Eecises to Review 5 4. Chet Sheet 5 1. Definitions Undestnd the

More information

Invert and multiply. Fractions express a ratio of two quantities. For example, the fraction

Invert and multiply. Fractions express a ratio of two quantities. For example, the fraction Appendi E: Mnipuling Fions Te ules fo mnipuling fions involve lgei epessions e el e sme s e ules fo mnipuling fions involve numes Te fundmenl ules fo omining nd mnipuling fions e lised elow Te uses of

More information

THIS PAGE DECLASSIFIED IAW EO 12958

THIS PAGE DECLASSIFIED IAW EO 12958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f

More information

5 - Determinants. r r. r r. r r. r s r = + det det det

5 - Determinants. r r. r r. r r. r s r = + det det det 5 - Detemts Assote wth y sque mtx A thee s ume lle the etemt of A eote A o et A. Oe wy to efe the etemt, ths futo fom the set of ll mtes to the set of el umes, s y the followg thee popetes. All mtes elow

More information

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms CS 542 Avn Dt Stutu n Alotm Exm 2 Soluton Jontn Tun 4/2/202. (5 ont) Con n oton on t tton t tutu n w t n t 2 no. Wt t mllt num o no tt t tton t tutu oul ontn. Exln you nw. Sn n mut n you o u t n t, t n

More information

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings. T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson

More information

Physics 120. Exam #1. April 15, 2011

Physics 120. Exam #1. April 15, 2011 Phyc 120 Exam #1 Aprl 15, 2011 Name Multple Choce /16 Problem #1 /28 Problem #2 /28 Problem #3 /28 Total /100 PartI:Multple Choce:Crclethebetanwertoeachqueton.Anyothermark wllnotbegvencredt.eachmultple

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Absolutely no collaboration allowed in any form

Absolutely no collaboration allowed in any form Toy Fnl Exm poste toy, ue n one week Tke home, open notes exm Absolutely no collboton llowe n ny fom Instuctos wll not nswe ny uestons elte to exm solutons o soluton ppoches Questons fo clfcton shoul be

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

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

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

( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x

( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.

More information

Advanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet

Advanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet Advanced Subsidiay GCE (H57) Advanced GCE (H557) Physics B (Advancing Physics) Data, Fomulae and Relationships Booklet The infomation in this booklet is fo the use of candidates following the Advanced

More information

Chapter I Vector Analysis

Chapter I Vector Analysis . Chpte I Vecto nlss . Vecto lgeb j It s well-nown tht n vecto cn be wtten s Vectos obe the followng lgebc ules: scl s ) ( j v v cos ) ( e Commuttv ) ( ssoctve C C ) ( ) ( v j ) ( ) ( ) ( ) ( (v) he lw

More information

Potential Energy. The change U in the potential energy. is defined to equal to the negative of the work. done by a conservative force

Potential Energy. The change U in the potential energy. is defined to equal to the negative of the work. done by a conservative force Potential negy The change U in the potential enegy is defined to equal to the negative of the wok done by a consevative foce duing the shift fom an initial to a final state. U = U U = W F c = F c d Potential

More information

ELECTRO - MAGNETIC INDUCTION

ELECTRO - MAGNETIC INDUCTION NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s

More information

K = 100 J. [kg (m/s) ] K = mv = (0.15)(36.5) !!! Lethal energies. m [kg ] J s (Joule) Kinetic Energy (energy of motion) E or KE.

K = 100 J. [kg (m/s) ] K = mv = (0.15)(36.5) !!! Lethal energies. m [kg ] J s (Joule) Kinetic Energy (energy of motion) E or KE. Knetc Energy (energy of moton) E or KE K = m v = m(v + v y + v z ) eample baseball m=0.5 kg ptche at v = 69 mph = 36.5 m/s K = mv = (0.5)(36.5) [kg (m/s) ] Unts m [kg ] J s (Joule) v = 69 mph K = 00 J

More information

Chapter 3 Vector Integral Calculus

Chapter 3 Vector Integral Calculus hapte Vecto Integal alculus I. Lne ntegals. Defnton A lne ntegal of a vecto functon F ove a cuve s F In tems of components F F F F If,, an ae functon of t, we have F F F F t t t t E.. Fn the value of the

More information

Convolutional Data Transmission System Using Real-Valued Self-Orthogonal Finite-Length Sequences

Convolutional Data Transmission System Using Real-Valued Self-Orthogonal Finite-Length Sequences Poeengs of the 5th WSEAS Intentonl Confeene on Sgnl Poessng Istnbul Tukey y 7-9 6 (pp73-78 Convolutonl Dt Tnssson Syste Usng Rel-Vlue Self-Othogonl Fnte-Length Sequenes Jong LE n Yoshho TANADA Gute Shool

More information

The Area of a Triangle

The Area of a Triangle The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest

More information

F = net force on the system (newton) F,F and F. = different forces working. E = Electric field strength (volt / meter)

F = net force on the system (newton) F,F and F. = different forces working. E = Electric field strength (volt / meter) All the Impotant Fomulae that a student should know fom. XII Physics Unit : CHAPTER - ELECTRIC CHARGES AND FIELD CHAPTER ELECTROSTATIC POTENTIAL AND CAPACITANCE S. Fomula No.. Quantization of chage Q =

More information

Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law

Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same

More information

PHYS 1114, Lecture 21, March 6 Contents:

PHYS 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 information

Physics 231 Lecture 21

Physics 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 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