Ch.4 Motion in 2D. Ch.4 Motion in 2D

Size: px
Start display at page:

Download "Ch.4 Motion in 2D. Ch.4 Motion in 2D"

Transcription

1 Moion in plne, such s in he sceen, is clled 2-dimensionl (2D) moion. 1. Posiion, displcemen nd eloci ecos If he picle s posiion is ( 1, 1 ) 1, nd ( 2, 2 ) 2, he posiions ecos e 1 = = 2 2 Aege eloci eco V g = = In he limi b -> 0, we he he insnneous eloci eco s Obecies To undesnd he eco nue of 2D moion To genelize 1D moion o 2D moion To descibe specil 2D moion: poecile moion To undesnd unifom cicul moion The displcemen eco is defined s he chnge in posiion = 2 1 = ( 2 1 ) i^ + ( 2 1 ) o = Wh if we diide b, e.g., = 3 i^ 1 (m), i would ell how fs he posiion chnges, wih sense of diecion, i.e. he eloci eco V = lim -> 0 = d d d d = V V V = d/d, V = d/d : he - nd - componens of eloci. Noe h eloci is in he diecion of, which in he limi of -> 0 is ngen o he ph 2 Speed = V + V 2 Checkpoin 1 Checkpoin 1 Checkpoin 1 A picle is moing in cicul ph s shown. In picul insn, is eloci is found o be V = 2 i^ 2 (m/s) A picle is moing in cicul ph s shown. In picul insn, is eloci is found o be V = 2 i^ 2 (m/s) A picle is moing in cicul ph s shown. In picul insn, is eloci is found o be V = 2 i^ 2 (m/s) Assume he moion is clockwise, which qudn is he picle in h insn? Dw he eloci eco on he digm. Assume he moion is clockwise, which qudn is he picle in h insn? Dw he eloci eco on he digm. Moe he eloci eco unil i is ngen o he ph, which is he 1 s qudn Assume he moion is clockwise, which qudn is he picle in h insn? Dw he eloci eco on he digm. Whee is he picle if he moion is coune clockwise? Moe he eloci eco unil i is ngen o he ph, which is he 1 s qudn In n cse, wh is he speed? 2 2 m/s 1

2 2. Acceleion eco (Ag) Acceleion should be defined s = g = = chnge in eloci ime inel The diecion of cceleion is in he sme diecion s If eloci (no speed!) chnges, in eihe mgniude o diecion, hen is no zeo, nd cceleion is no zeo. Fo emple, V 1 = 2 i^ 2 (m/s), V 2 = 2 2 (m/s) Hs mgniude chnged? Diecion? Is cceleion zeo? Insnneous cceleion Fom g = = In he limi -> 0, insnneous cceleion is gien b d = d = d d whee = d d nd = d d e he - nd -componens Since = d/d, = d/d, so = d 2 /d 2, = d 2 /d 2 Undesnding cceleion nd eloci Q: Is i possible o moe wih consn speed, nd e cceleion is no zeo? chnge in eloci Acceleion = ime inel Emple: Acceleion of c ounding cone wih consn speed cceleion is owd cene Hs eloci chnged? Mg o Di? Dw eco digm so h = Wh is he diecion of? cceleion? 3. Moion wih consn cceleion eco Since cceleion is gien b = fo i o be consn eco, boh is componens mus be consn, i.e. = consn, nd = consn Q: Think bck o Ch.2, wh equions descibe moion in 1D when is consn? = 0 + = ½ 2 Wh equions fo moion long Wh bou when is consn? -is when is consn? = 0 + = ½ 2 0, 0 = iniil -pos & -el = 0 + = ½ 2 0, 0 = iniil -pos & -el Noe: Moions long - nd - diecions eole in ime independenl! 2D moion is sme s 1D moion, onl wice. Checkpoin 2 (1) = , = (2) = , = (3) = 2 2 ^ i (4 + 3) (4) = (4 3-2) 3 ^ ^ Diecl compe wih = ½ 2 = i.e., 0 = -2 m, 0 = 4 m/s ½ = -3, = - 6 m/s 2 Posiion is in mees, nd ime in seconds. Ae he nd cceleion componens consn? Is cceleion eco consn? Fo he cses whee ou nswes e es, wh e he iniil posiion nd eloci ecos? 4. Poecile moion If we e o wie down giionl cceleion in he uni eco noion, we he = i^ g ^ 0 i.e., = 0, nd = - g, boh consn, g = 9.8 m/s 2 Moion unde gi lone is known s poecile moion. Subsiuing nd ino he genel equions of moion fo consn cceleion, = 0 + = ½ 2 = 0 + = ½ 2 we obin specific equions of moion fo poecile moion s = 0 = = 0 g = ½g 2 0, 0 = iniil - & -pos 0, 0 = iniil - & -el In ems of iniil speed 0 nd ngle θ 0, 0 = 0 cosθ 0, 0 = 0 sinθ 0 = 2

3 Undesnding poecile moion Mhemicll, equions of moion fo poecile moion e = 0 = 0 g = = ½ g 2 1. The hoizonl eloci emins consn, s hee is no ccel. As esul, posiion chnges linel in ime. 2. The eicl eloci deceses he e g, nd eicl posiion chnges qudicll in ime. 3. Moions long - nd - diecions eole in ime independenl! Poecile moion is sme s 1D moion, onl wice. Tems, discuss wh he iems men o ou, especill iem 3 bou independen moion. Gie n emple if possible. An emple Q: Two coins e ossed wo diffeen ws: One is dopped fom es, nohe is flung sidews hoizonll. Will hei eicl moion be he sme o diffeen? i.e., will he eicl moion be ffeced b he hoizonl moion o will he be independen of ech ohe? Conclusion fom demo: The -moion is he sme in boh cses, independen of -moion. Conesel, he -moion is no ffeced b he -moion, i.e., moing independenl of -moion. Leding o he fmous deecie obseion h bulle fied hoizonll coss leel field nd elling hundeds of mees will hi he gound he sme ime s book dopped he sme heigh nd elesed he sme ime. A numeicl emple A bll olling speed 3.3 m/s flls off he edge of he ble. The heigh of he ble is 1.0 m boe he floo. A wh ime does he bll hi he floo? How f hoizonll does i lnd fom he edge? Ides: Duing flling, he moion is pue poecile moion. If we cn sole fo ime, nd since = 0 is consn, he hoizonl nge cn be found b = - 0 = 0. How o find? S wih iniil condiions nd giens Iniil condiions: 0 = 3.3 m/s, 0 = 0. Since he chnge in eicl posiion is 1.0m s gien (noe he negie sign since decesed), we cn use = - 0 = 0 ½ g 2 = ½ g 2 o ge = sq( 2 /g), o = 0.45 s. = 0 = 1.5 m Is his he cul ph lengh? Undesnding poecile moion Gphicll, equions of moion fo poecile moion = 0 = 0 g = = ½ g 2 Skech he eloci nd posiion gphs slope = g Undesnding poecile moion The ph, o eco, of poecile moion in - plne pbol Wh so simil o -? Dw eloci ecos seel poins long he ph. Bek hem down o - nd - componens. A: nd linel eled Veloci ecos long he ph Compe ou gphs. Did s consn? Did decese consn e g? slope = 3

4 Rnk he ime A cem ngeine psses windows 1,2,3. Rnk he ime i spends pssing ech window, gees fis. Wh? Answe: 3 > 2 > 1 Rnk he ime Now on he downwd ph he cem ngeine psses windows 4,5,6. Agin nk he ime i spends pssing ech window, gees fis. Wh? Answe: 4 = 5 = 6 Reson: The hoizonl widh is he sme, nd he hoizonl eloci is consn. Anohe numeicl emple A sone is hown cliff of heigh h wih n iniil speed of 42 m/s dieced n iniil ngle of 60 deg. I sikes poin A 5.5 s le. Find he heigh h nd he mimum heigh H boe he gound. Ides: Gien iniil speed nd ngle, we cn find 0 = 0 sinθ 0 = 36.4 m/s. Tking he lunch poin o be oigin, iniil 0 =0, finl posiion is h. i.e., =h. Thus h = ½ g 2 = 51.8 m. How o find H, which is he op of fligh? If we knew he ime A he op, eicl eloci is zeo, = 0 g =0, o = 0 /g = 3.71 s. So plugging he ime ino H = = ½ g 2 = 67.6 m. Q: How o find he hoizonl posiion of poin A? Ides. Moe numeicl emples A plne fling 198 km/h nd heigh h=500 m eleses life es. Wh is he ngle Φ fom line of sigh in ode o hi he ge? Ides? Afe elese, i will ech he ge if in he ime i kes flling heigh h, i els hoizonl disnce of. n Φ = / h Need need Giens: 0 =0, 0 = 198 km/h = 55 m/s, =-500 m = - 0 = 0 ½ g 2, = sq (-2 /g) = 10.1 s = 0 = 55*10.1 = m Φ = n( / h) = 48 o Rnge of poecile moion Time of fligh: = - 0 = 0 ½ g 2, when i his gound, =0, 0= 0 ½ g 2, = 2 0 /g Rnge: = 0 = /g 0 = 0 cosθ 0, 0 = 0 sinθ 0 = 2 02 sinθ 0 cosθ 0 /g = 02 sin(2θ 0 )/g = R Tig ideni: 2 sinθ cosθ = sin(2θ) M nge sin(2θ 0 ) = 1, o θ 0 =45 o This is cnned fomul. Don use in quiz o es wihou poof. R 5. Unifom cicul moion A picle moes in sigh line wih consn speed. Is he eloci consn? Is he cceleion zeo? If picle moes in cicle wih consn speed, is he eloci consn? Is he cceleion zeo? No, becuse diecion chnges ll he ime. Since he eloci eco chnges, hee mus be cceleion. Now conside he elociies he op & side Dw eco digm so h = o Wh is he diecion of? cceleion? owd he cene 4

5 Flling owd he cene One w o hink bou cicul moion is h he picle flls coninuousl owd he cene fom sigh line. Cenipel cceleion The mgniude of cenipel cceleion is Is diecion is owd he cene, i.e., pependicul o he eloci. = 2 Le be dius of cicle, s be he fllen disnce owd he cene wihin smll ime. How e, s, eled? s =dius ( + s) 2 = 2 + () 2 o s + s 2 = 2 + () 2 If is smll, s 2 will be e in. Neglec s 2, we he 2 s = () 2, o s = ½ 2 2 Compe wih = ½ 2 in 1D, we idenif = = cceleion owd cene Esime he cenipel cceleion of he fis while full swinging ou m in cicles bou once pe second. Le =0.5 m, = 2π / = 2*3.14*0.5/1 = 3.14 m/s, = /0.5 = 19.7 m 2 /s 2 /m, i.e., m/s 2 I is bou 2g. 5

Physics 201, Lecture 5

Physics 201, Lecture 5 Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion

More information

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis   2/3/2007 Physics 253 Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp://www.ipcc.ch/spmfeb7.pdf /3/7 Phsics 53 hp://www.fonews.com/pojecs/pdf/spmfeb7.pdf /3/7 Phsics 53 3 Sus: Uni, Chpe 3 Vecos

More information

Motion on a Curve and Curvature

Motion on a Curve and Curvature Moion on Cue nd Cuue his uni is bsed on Secions 9. & 9.3, Chpe 9. All ssigned edings nd execises e fom he exbook Objecies: Mke cein h you cn define, nd use in conex, he ems, conceps nd fomuls lised below:

More information

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you

More information

Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force

Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force Insucos: ield/mche PHYSICS DEPARTMENT PHY 48 Em Sepeme 6, 4 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceied unuhoied id on his eminion. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP O

More information

1. Kinematics of Particles

1. Kinematics of Particles 1. Kinemics o Picles 1.1 Inoducion o Dnmics Dnmics - Kinemics: he sud o he geome o moion; ele displcemen, eloci, cceleion, nd ime, wihou eeence o he cuse o he moion. - Kineics: he sud o he elion eising

More information

LECTURE 5. is defined by the position vectors r, 1. and. The displacement vector (from P 1 to P 2 ) is defined through r and 1.

LECTURE 5. is defined by the position vectors r, 1. and. The displacement vector (from P 1 to P 2 ) is defined through r and 1. LECTURE 5 ] DESCRIPTION OF PARTICLE MOTION IN SPACE -The displcemen, veloci nd cceleion in -D moion evel hei veco nue (diecion) houh he cuion h one mus p o hei sin. Thei full veco menin ppes when he picle

More information

ME 141. Engineering Mechanics

ME 141. Engineering Mechanics ME 141 Engineeing Mechnics Lecue 13: Kinemics of igid bodies hmd Shhedi Shkil Lecue, ep. of Mechnicl Engg, UET E-mil: sshkil@me.bue.c.bd, shkil6791@gmil.com Websie: eche.bue.c.bd/sshkil Couesy: Veco Mechnics

More information

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information. Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl

More information

Physics 101 Lecture 4 Motion in 2D and 3D

Physics 101 Lecture 4 Motion in 2D and 3D Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd

More information

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1. Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)

More information

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

PHYSICS 1210 Exam 1 University of Wyoming 14 February points PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

Average & instantaneous velocity and acceleration Motion with constant acceleration Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission

More information

Physics 2A HW #3 Solutions

Physics 2A HW #3 Solutions Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen

More information

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = = Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he

More information

Motion in a Straight Line

Motion in a Straight Line Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in

More information

Phys 110. Answers to even numbered problems on Midterm Map

Phys 110. Answers to even numbered problems on Midterm Map Phys Answers o een numbered problems on Miderm Mp. REASONING The word per indices rio, so.35 mm per dy mens.35 mm/d, which is o be epressed s re in f/cenury. These unis differ from he gien unis in boh

More information

3 Motion with constant acceleration: Linear and projectile motion

3 Motion with constant acceleration: Linear and projectile motion 3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr

More information

Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration. Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl

More information

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218 Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy

More information

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse

More information

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor. In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd

More information

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo

More information

Axis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis.

Axis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis. Insucos: Fiel/che/Deweile PYSICS DEPATENT PY 48 Em ch 5, 5 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceie unuhoie i on his eminion. YOU TEST NUBE IS TE 5-DIGIT NUBE AT TE TOP OF EAC PAGE.

More information

Today - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations

Today - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy

More information

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt.

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt. 4/08/00 eview Fomul s icuis cice s BL B A B I I I I E...... s n n hging Q Q 0 e... n... Q Q n 0 e Q I I0e Dischging Q U Q A wie mde of bss nd nohe wie mde of silve hve he sme lengh, bu he dimee of he bss

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

Physics Worksheet Lesson 4: Linear Motion Section: Name: Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.

More information

WORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done

More information

Chapter 2 PROBLEM SOLUTIONS

Chapter 2 PROBLEM SOLUTIONS Chper PROBLEM SOLUTIONS. We ssume h you re pproximely m ll nd h he nere impulse rels uniform speed. The elpsed ime is hen Δ x m Δ = m s s. s.3 Disnces reled beween pirs of ciies re ( ) Δx = Δ = 8. km h.5

More information

PHY2048 Exam 1 Formula Sheet Vectors. Motion. v ave (3 dim) ( (1 dim) dt. ( (3 dim) Equations of Motion (Constant Acceleration)

PHY2048 Exam 1 Formula Sheet Vectors. Motion. v ave (3 dim) ( (1 dim) dt. ( (3 dim) Equations of Motion (Constant Acceleration) Insrucors: Field/Mche PHYSICS DEPATMENT PHY 48 Em Ferur, 5 Nme prin, ls firs: Signure: On m honor, I he neiher gien nor receied unuhoried id on his eminion. YOU TEST NUMBE IS THE 5-DIGIT NUMBE AT THE TOP

More information

Ans: In the rectangular loop with the assigned direction for i2: di L dt , (1) where (2) a) At t = 0, i1(t) = I1U(t) is applied and (1) becomes

Ans: In the rectangular loop with the assigned direction for i2: di L dt , (1) where (2) a) At t = 0, i1(t) = I1U(t) is applied and (1) becomes omewok # P7-3 ecngul loop of widh w nd heigh h is siued ne ve long wie cing cuen i s in Fig 7- ssume i o e ecngul pulse s shown in Fig 7- Find he induced cuen i in he ecngul loop whose self-inducnce is

More information

D zone schemes

D zone schemes Ch. 5. Enegy Bnds in Cysls 5.. -D zone schemes Fee elecons E k m h Fee elecons in cysl sinα P + cosα cosk α cos α cos k cos( k + π n α k + πn mv ob P 0 h cos α cos k n α k + π m h k E Enegy is peiodic

More information

Chapter Direct Method of Interpolation

Chapter Direct Method of Interpolation Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o

More information

Kinematics in two dimensions

Kinematics in two dimensions Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5

More information

Chapter 3 Kinematics in Two Dimensions

Chapter 3 Kinematics in Two Dimensions Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo

More information

Relative and Circular Motion

Relative and Circular Motion Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1 Mechanics Lecue 3 Slide 2 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you

More information

A Kalman filtering simulation

A Kalman filtering simulation A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer

More information

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under

More information

Reinforcement learning

Reinforcement learning CS 75 Mchine Lening Lecue b einfocemen lening Milos Huskech milos@cs.pi.edu 539 Senno Sque einfocemen lening We wn o len conol policy: : X A We see emples of bu oupus e no given Insed of we ge feedbck

More information

Chapter 4 Circular and Curvilinear Motions

Chapter 4 Circular and Curvilinear Motions Chp 4 Cicul n Cuilin Moions H w consi picls moing no long sigh lin h cuilin moion. W fis su h cicul moion, spcil cs of cuilin moion. Anoh mpl w h l sui li is h pojcil..1 Cicul Moion Unifom Cicul Moion

More information

2-d Motion: Constant Acceleration

2-d Motion: Constant Acceleration -d Moion: Consan Acceleaion Kinemaic Equaions o Moion (eco Fom Acceleaion eco (consan eloci eco (uncion o Posiion eco (uncion o The eloci eco and posiion eco ae a uncion o he ime. eloci eco a ime. Posiion

More information

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf Objecie F s w Tnsfome Moionl To be ble o fin nsfome. moionl nsfome n moionl. 331 1 331 Mwell s quion: ic Fiel D: Guss lw :KV : Guss lw H: Ampee s w Poin Fom Inegl Fom D D Q sufce loop H sufce H I enclose

More information

t s (half of the total time in the air) d?

t s (half of the total time in the air) d? .. In Cl or Homework Eercie. An Olmpic long jumper i cpble of jumping 8.0 m. Auming hi horizonl peed i 9.0 m/ he lee he ground, how long w he in he ir nd how high did he go? horizonl? 8.0m 9.0 m / 8.0

More information

Section 35 SHM and Circular Motion

Section 35 SHM and Circular Motion Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.

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

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

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2 Impope Inegls To his poin we hve only consideed inegls f() wih he is of inegion nd b finie nd he inegnd f() bounded (nd in fc coninuous ecep possibly fo finiely mny jump disconinuiies) An inegl hving eihe

More information

Chapter 4 Two-Dimensional Motion

Chapter 4 Two-Dimensional Motion D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Two-Dimensionl Motion D Motion Pemble In this chpte, we ll tnsplnt the conceptul

More information

Technical Vibration - text 2 - forced vibration, rotational vibration

Technical Vibration - text 2 - forced vibration, rotational vibration Technicl Viion - e - foced viion, oionl viion 4. oced viion, viion unde he consn eenl foce The viion unde he eenl foce. eenl The quesion is if he eenl foce e is consn o vying. If vying, wh is he foce funcion.

More information

1 Using Integration to Find Arc Lengths and Surface Areas

1 Using Integration to Find Arc Lengths and Surface Areas Novembe 9, 8 MAT86 Week Justin Ko Using Integtion to Find Ac Lengths nd Sufce Aes. Ac Length Fomul: If f () is continuous on [, b], then the c length of the cuve = f() on the intevl [, b] is given b s

More information

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS Physics h Ediion Cunell Johnson Young Sdler Soluions Mnul Soluions Mnul, Answer keys, Insrucor's Resource Mnul for ll chpers re included. Compleed downlod links: hps://esbnkre.com/downlod/physics-h-ediion-soluions-mnulcunell-johnson-young-sdler/

More information

PHYS PRACTICE EXAM 2

PHYS PRACTICE EXAM 2 PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,

More information

Chapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion.

Chapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion. Chpe Kinemic in One Dimenin Kinemic del wih he cncep h e needed decibe min. Dynmic del wih he effec h fce he n min. Tgehe, kinemic nd dynmic fm he bnch f phyic knwn Mechnic.. Diplcemen. Diplcemen.0 m 5.0

More information

Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468

Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468 ics Announcements dy, embe 28, 2004 Ch 6: Cicul Motion - centipetl cceletion Fiction Tension - the mssless sting Help this week: Wednesdy, 8-9 pm in NSC 128/119 Sundy, 6:30-8 pm in CCLIR 468 Announcements

More information

4.8 Improper Integrals

4.8 Improper Integrals 4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls

More information

September 20 Homework Solutions

September 20 Homework Solutions College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum

More information

Physics for Scientists and Engineers I

Physics for Scientists and Engineers I Physics for Scieniss nd Engineers I PHY 48, Secion 4 Dr. Beriz Roldán Cueny Uniersiy of Cenrl Florid, Physics Deprmen, Orlndo, FL Chper - Inroducion I. Generl II. Inernionl Sysem of Unis III. Conersion

More information

Equations from The Four Principal Kinetic States of Material Bodies. Copyright 2005 Joseph A. Rybczyk

Equations from The Four Principal Kinetic States of Material Bodies. Copyright 2005 Joseph A. Rybczyk Equions fom he Fou Pinipl Kinei Ses of Meil Bodies Copyigh 005 Joseph A. Rybzyk Following is omplee lis of ll of he equions used in o deied in he Fou Pinipl Kinei Ses of Meil Bodies. Eh equion is idenified

More information

Chapter 4 Kinematics in Two Dimensions

Chapter 4 Kinematics in Two Dimensions D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Kinemtics in Two Dimensions D Motion Pemble In this chpte, we ll tnsplnt the

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

Name: Per: L o s A l t o s H i g h S c h o o l. Physics Unit 1 Workbook. 1D Kinematics. Mr. Randall Room 705

Name: Per: L o s A l t o s H i g h S c h o o l. Physics Unit 1 Workbook. 1D Kinematics. Mr. Randall Room 705 Nme: Per: L o s A l o s H i g h S c h o o l Physics Uni 1 Workbook 1D Kinemics Mr. Rndll Room 705 Adm.Rndll@ml.ne www.laphysics.com Uni 1 - Objecies Te: Physics 6 h Ediion Cunel & Johnson The objecies

More information

v T Pressure Extra Molecular Stresses Constitutive equations for Stress v t Observation: the stress tensor is symmetric

v T Pressure Extra Molecular Stresses Constitutive equations for Stress v t Observation: the stress tensor is symmetric Momenum Blnce (coninued Momenum Blnce (coninued Now, wh o do wih Π? Pessue is p of i. bck o ou quesion, Now, wh o do wih? Π Pessue is p of i. Thee e ohe, nonisoopic sesses Pessue E Molecul Sesses definiion:

More information

Physics 1502: Lecture 2 Today s Agenda

Physics 1502: Lecture 2 Today s Agenda 1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics

More information

Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment

Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were

More information

Version 001 test-1 swinney (57010) 1. is constant at m/s.

Version 001 test-1 swinney (57010) 1. is constant at m/s. Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee

More information

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.

More information

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s

More information

Axis Thin spherical shell about any diameter

Axis Thin spherical shell about any diameter Insucos: Fiel/che/Deweile PYSICS DEPATET PY 48 Finl Em Apil 5, 5 me pin, ls fis: Signue: On m hono, I he neihe gien no eceie unuhoie i on his eminion. YOU TEST UBE IS TE 5-DIGIT UBE AT TE TOP OF EAC PAGE.

More information

This immediately suggests an inverse-square law for a "piece" of current along the line.

This immediately suggests an inverse-square law for a piece of current along the line. Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line

More information

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3 A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:

More 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

0 for t < 0 1 for t > 0

0 for t < 0 1 for t > 0 8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside

More information

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63)

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63) . The -coordine of pricle in curiliner oion i gien b where i in eer nd i in econd. The -coponen of ccelerion in eer per econd ured i gien b =. If he pricle h -coponen = nd when = find he gniude of he eloci

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

Physics 100: Lecture 1

Physics 100: Lecture 1 Physics : Lecure Agen for Toy Aice Scope of his course Mesuremen n Unis Funmenl unis Sysems of unis Conering beween sysems of unis Dimensionl Anlysis -D Kinemics (reiew) Aerge & insnneous elociy n ccelerion

More information

EECE 260 Electrical Circuits Prof. Mark Fowler

EECE 260 Electrical Circuits Prof. Mark Fowler EECE 60 Electicl Cicuits Pof. Mk Fowle Complex Numbe Review /6 Complex Numbes Complex numbes ise s oots of polynomils. Definition of imginy # nd some esulting popeties: ( ( )( ) )( ) Recll tht the solution

More information

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN

More information

Physics Mechanics. Rule #2: LABEL/LIST YOUR KNOWN VALUES AND THOSE DESIRED (Include units!!)

Physics Mechanics. Rule #2: LABEL/LIST YOUR KNOWN VALUES AND THOSE DESIRED (Include units!!) Phic Mechnic Rule #1: DRAW A PICTURE (Picoil Repeenion, Moion Dim, ee-bod Dim) Dw picue o wh he queion i decibin. Ue moion dim nd ee-bod dim o i ou in eein wh i oin on in he queion. Moion Dim: + ee-bod

More information

Main Ideas in Class Today

Main Ideas in Class Today Main Ideas in Class Toda Inroducion o Falling Appl Consan a Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs Refers o objecs

More 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

e t dt e t dt = lim e t dt T (1 e T ) = 1

e t dt e t dt = lim e t dt T (1 e T ) = 1 Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie

More information

Introduction to LoggerPro

Introduction to LoggerPro Inroducion o LoggerPro Sr/Sop collecion Define zero Se d collecion prmeers Auoscle D Browser Open file Sensor seup window To sr d collecion, click he green Collec buon on he ool br. There is dely of second

More information

Transformations. Ordered set of numbers: (1,2,3,4) Example: (x,y,z) coordinates of pt in space. Vectors

Transformations. Ordered set of numbers: (1,2,3,4) Example: (x,y,z) coordinates of pt in space. Vectors Trnformion Ordered e of number:,,,4 Emple:,,z coordine of p in pce. Vecor If, n i i, K, n, i uni ecor Vecor ddiion +w, +, +, + V+w w Sclr roduc,, Inner do roduc α w. w +,.,. The inner produc i SCLR!. w,.,

More information

r a + r b a + ( r b + r c)

r a + r b a + ( r b + r c) AP Phsics C Unit 2 2.1 Nme Vectos Vectos e used to epesent quntities tht e chcteized b mgnitude ( numeicl vlue with ppopite units) nd diection. The usul emple is the displcement vecto. A quntit with onl

More information

s in boxe wers ans Put

s in boxe wers ans Put Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs

More information

( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept.

( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept. Physics Lectue 3 (Wlke: Ch. 6.4-5) Connected Objects Cicul Motion Centipetl Acceletion Centipetl Foce Sept. 30, 009 Exmple: Connected Blocks Block of mss m slides on fictionless tbletop. It is connected

More information

Circular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.

Circular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can. 1 Cicula Moion Radians One evoluion is equivalen o 360 0 which is also equivalen o 2π adians. Theefoe we can say ha 360 = 2π adians, 180 = π adians, 90 = π 2 adians. Hence 1 adian = 360 2π Convesions Rule

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP UNIT # 09 PARABOLA, ELLIPSE & HYPERBOLA PARABOLA EXERCISE - 0 CHECK YOUR GRASP. Hin : Disnce beween direcri nd focus is 5. Given (, be one end of focl chord hen oher end be, lengh of focl chord 6. Focus

More information

FM Applications of Integration 1.Centroid of Area

FM Applications of Integration 1.Centroid of Area FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is

More information

MATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008)

MATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008) MATH 14 AND 15 FINAL EXAM REVIEW PACKET (Revised spring 8) The following quesions cn be used s review for Mh 14/ 15 These quesions re no cul smples of quesions h will pper on he finl em, bu hey will provide

More information

PARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section.

PARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section. wwwskshieducioncom PARABOLA Le S be given fixed poin (focus) nd le l be given fixed line (Direcrix) Le SP nd PM be he disnce of vrible poin P o he focus nd direcrix respecively nd P SP moves such h PM

More information

Computer Aided Geometric Design

Computer Aided Geometric Design Copue Aided Geoei Design Geshon Ele, Tehnion sed on ook Cohen, Riesenfeld, & Ele Geshon Ele, Tehnion Definiion 3. The Cile Given poin C in plne nd nue R 0, he ile ih ene C nd dius R is defined s he se

More information

CHAPTER 2: Describing Motion: Kinematics in One Dimension

CHAPTER 2: Describing Motion: Kinematics in One Dimension CHAPTER : Describing Moion: Kinemics in One Dimension Answers o Quesions A cr speeomeer mesures only spee I oes no gie ny informion bou he irecion, n so oes no mesure elociy By efiniion, if n objec hs

More information

Rotations.

Rotations. oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse

More information

Lecture 3: 1-D Kinematics. This Week s Announcements: Class Webpage: visit regularly

Lecture 3: 1-D Kinematics. This Week s Announcements: Class Webpage:   visit regularly Lecure 3: 1-D Kinemics This Week s Announcemens: Clss Webpge: hp://kesrel.nm.edu/~dmeier/phys121/phys121.hml isi regulrly Our TA is Lorrine Bowmn Week 2 Reding: Chper 2 - Gincoli Week 2 Assignmens: Due:

More information

What distance must an airliner travel down a runway before reaching

What distance must an airliner travel down a runway before reaching 2 LEARNING GALS By sudying his chper, you will lern: How o describe srigh-line moion in erms of erge elociy, insnneous elociy, erge ccelerion, nd insnneous ccelerion. How o inerpre grphs of posiion ersus

More information

MAGNETIC EFFECT OF CURRENT & MAGNETISM

MAGNETIC EFFECT OF CURRENT & MAGNETISM TODUCTO MAGETC EFFECT OF CUET & MAGETM The molecul theo of mgnetism ws given b Webe nd modified lte b Ewing. Oested, in 18 obseved tht mgnetic field is ssocited with n electic cuent. ince, cuent is due

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

Lecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation

Lecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation Lecue 8: Kineics of Phase Gowh in a Two-componen Sysem: geneal kineics analysis based on he dilue-soluion appoximaion Today s opics: In he las Lecues, we leaned hee diffeen ways o descibe he diffusion

More information