# 2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles

Size: px
Start display at page:

Download "2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles"

Transcription

1 /4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla to the knetc eneg. Newton s nd Law fo a Sngle Bod. The te ate of the change of the oentu of a patcle s equal to the net foce actng on the patcle. υ ( υ) p a The oentu foulaton of Newton s law s oe nclusve as t s applcable to bodes and sstes wth vaable ass. p A few pontes: The lnea oentu of an object changes (and theefoe thee s a net foce actng on t) f The veloct changes n agntude The veloct changes n decton The ass of the bod changes Eaple- a ball hts a wall Collsons p p f p υ ) υ ) υ ) p p p f p p υ snθ υ snθ υ snθ p υ cosθ + υ cosθ 0 p p f p 0 υ ) υ ) p If the ball stcks to the wall the foce s salle than f t bounces. θ I II III Befoe and afte the collson the oentu of a bod changes. Thee s a net foce actng on the bod. p The collson takes te (although qute sall). The foce vaes dung the te of the collson. The total change of the oentu of the bod dung the collson s: p p f p F net Ipulse

2 /4/04 Ipulse fo a sngle collson The pulse of a foce s a vecto. F aea unde the cuve The aea below the two cuves s the sae! sae pulse F The pont ass The pont ass s a phscal appoaton of a eal object that has densons. How good s ths ths appoaton??? Can we appl Newton s laws and all we leaned so fa to a bg, etended object, o to a sste of objects that ae not even attached to each othe? F p p f p The change of the lnea oentu s equal to the pulse of the actng foce. Sste of patcles A bod can have a coplcated shape We can epesent the bod as a su of salle pats Appl Newton s law to each pat. F a n F F a F a, F, a The Cente of ass The cente of ass () of a sste of patcles s the pont that oves as though the sste s ass s concentated n ths pont and all etenal foces ae appled thee. n Ipotant note: We can substtute the ente sste wth a sngle pont! s a geoetcal pont (t ght be outsde of the bod). We can eplace the object wth pont ass at the cente of ass! The oton of the bat s descbed b the oton of the. Eaple: asses Two patcles have asses and and postons and espectvel. Fnd the cente of ass of the sste ) + ) >> 0.5( co + )

3 /4/04 Cente of ass of a Sste Sste of patcles z z If a bod has a set and t has a unfo denst then the s on the lne of set. The cente of set concdes wth the. A few pontes. The ght be outsde the object Eaple Fnd the of a 48 unfo sheet of plwood wth the uppe a ght quadant eoved (a4ft). a a a ;(, ) (, ) a a 3a a ;(, ) (, ) 4 + ( a / ) + (3a / ) 5a 0 ft ( a / ) + ( a / 4) 5a 5 ft Newton s Second Law fo a Sste of Patcles The su of all etenal foces actng on the sste s equal to the poduct of the total ass of the sste and the acceleaton of the cente of ass a. F net a - su of foces that ae etenal to the sste (?) s the total ass It does not gve nfoaton on the acceleaton of the ndvdual objects of the sste. If no etenal foces ae pesent the cente of ass wll sta at est o ove wth constant veloct! Eaple Poble A 0 long boat stas at est n a qute lake. A tutle wth a ass, s ognall standng at the ght end of the boat. The tutle walks to the othe end of the boat. Does the boat ove? If so how fa? Soluton Yes the boat wll ove, but the cente of ass of the boat+tutle sste wll sta at est. L + L befoe afte (0.5L + ) L/ L (0.5L + ) + 0.5L + L + L + L 0 L/ L 3

4 /4/04 Eaple Poble A cannon shell s fed wth an ntal veloct of 50 /s at an angle 45 o to the hozontal. When the shell s at the hghest pont of ts tajecto, t eplodes nto two peces, and. falls staght down fo the hghest pont afte the eploson. If, whee does land elatve to the ntal fng pont? 45 o Soluton The wll follow the tajecto of the ognal cannon shell and fnal c can be found wth the ange equaton. υ0 R sn θ 55 g 0.5R + R + R R + R 3 3R R R 50 Lnea oentu of a Sste of patcles The vecto su of the lnea oentu of all patcles n the sste! P p + p + p pn P υ + υ + υ υ Can show wth soe wok P υ Total ass 3 3 veloct n n υ Newton s nd Law fo a sste of patcles The net foce (the vecto su of all etenal foces) actng on the sste of patcles s equal to the ate of change of the the total lnea oentu of the sste. P The lnea oentu of a sste eans constant f no net etenal foce s actng on the sste. Consevaton of Lnea oentu If a sste s closed and solated the oentu of the sste s constant. P constant P 0 If no net etenal foce s actng on the sste then the oentu s conseved p f + p f p nf p + p If the net foce on a closed sste s zeo n a gven decton (as) the oentu n ths decton cannot change. p n Eaple A cannon fes a shell at 60 o angle to the hozontal. The shell ntal veloct s v s 00 /s. If the ato of the asses of the cannon and the shell s 00 fnd the veloct of the cannon afte the shot was fed. P P f 0 p c + p s p c p s s υ s s υ s cosθ p c c υ c υ c s c υ s cosθ υ c cos /s p c p s Etenal foces n : F g F N oentu s conseved n θ 4

5 /4/04 oentu and Knetc Eneg consevaton Laws echancal eneg consevaton Condtons: solated sste, (no etenal foces) closed sste, (do not lose bodes) consevatve foces. (no fcton, dag ) Lnea oentu consevaton Condtons: solated sste, closed sste. Elastc Collsons Elastc collsons: no defoatons, no heatng of the bodes, no eplosons,no cashng sound. Eaples: two balls collde and sepaate afte the collson (pool gaes). Consevaton laws: lnea oentu s conseved knetc eneg s conseved. Inelastc collsons Inelastc collsons: thee s defoaton, o heatng, o eploson, o sound Eaples: a bullet hts a taget and goes though the taget; Copletel nelastc collsons: two balls collde and stck togethe; a bullet hts a taget and eans nsde; a ball s thown n a cat and stas thee Consevaton laws: Lnea oentu s conseved Knetc eneg s NOT CONSERVED v v v f befoe afte Inelastc Collsons n D What happens befoe and afte the collson? Lnea oentu of the sste s conseved Knetc eneg of the sste s not conseved p + p p f + p f υ + υ υ f + υ f We have onl equaton. We have 6 paaetes. We need to know 5 of the to fnd the 6th. If we know all ntal condtons (asses of the bodes, veloctes befoe the collson) we stll cannot fnd both veloctes afte the collson! Copletel nelastc collson D What happens befoe and afte the collson? Lnea oentu of the sste s conseved Knetc eneg of the sste s not conseved Afte the collson the two bodes ove togethe wth a coon veloct V. Eaple Poble: ballstc pendulu If ou know the heght and the asses, fnd the ntal veloct of the bullet. h p + p p f + p f υ + υ ( + )V v v Dung the collson: oentu consevaton Afte the collson: oentu consevaton V υ + υ + v f υ 0 ( + )V υ 0 + V ( + )V ( + )gh V gh V V υ 0 + gh 5

6 /4/04 Elastc Collsons n D What happens befoe and afte the collson? Lnea oentu of the sste s conseved Knetc eneg of the sste s conseved Eaple: statona taget plang pool The taget does not ove v 0 p + p p f + p f υ υ f + υ f υ + υ υ f + υ f K + K K f + K f υ + υ υ f + υ f If we know the ntal veloctes and the asses then we can fnd both fnal veloctes. v v v f v f befoe afte υ υ f + υ f υ f + υ υ f + υ v f v v f Specal cases the two asses ae the sae υ f 0 υ f υ << assve taget (lke wall) v Eaple: ovng taget Both bodes ae ovng befoe the collson. Ths s the ost geneal case and ou can deve the est of the cases fo these foulas υ f υ υ f υ >> assve pojectle (cannon ball and png-pong ball) υ f υ v v υ f + υ + + υ υ f + υ + + υ υ f υ Elastc Collsons n D p + p p f + p f v K + K K f + K f v oentu equatons (fo and ) eneg equaton. We have total of 8 paaetes. We need to know 5 of the paaetes to detene the est of the. β v f v f α 6

### 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

### 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 :

### Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum

Recall that there was ore to oton than just spee A ore coplete escrpton of oton s the concept of lnear oentu: p v (8.) Beng a prouct of a scalar () an a vector (v), oentu s a vector: p v p y v y p z v

### Fundamental principles

JU 07/HL Dnacs and contol of echancal sstes Date Da (0/08) Da (03/08) Da 3 (05/08) Da 4 (07/08) Da 5 (09/08) Da 6 (/08) Content Reve of the bascs of echancs. Kneatcs of gd bodes coodnate tansfoaton, angula

### Physics 207 Lecture 16

Physcs 07 Lectue 6 Goals: Lectue 6 Chapte Extend the patcle odel to gd-bodes Undestand the equlbu of an extended object. Analyze ollng oton Undestand otaton about a fxed axs. Eploy consevaton of angula

### Linear Momentum. Center of Mass.

Lecture 16 Chapter 9 Physcs I 11.06.2013 Lnear oentu. Center of ass. Course webste: http://faculty.ul.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.ul.edu/danylov2013/physcs1fall.htl

### 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

### 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

### gravity r2,1 r2 r1 by m 2,1

Gavtaton Many of the foundatons of classcal echancs wee fst dscoveed when phlosophes (ealy scentsts and atheatcans) ted to explan the oton of planets and stas. Newton s ost faous fo unfyng the oton of

### 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

### 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

### How does the momentum before an elastic and an inelastic collision compare to the momentum after the collision?

Experent 9 Conseraton o Lnear Moentu - Collsons In ths experent you wll be ntroduced to the denton o lnear oentu. You wll learn the derence between an elastc and an nelastc collson. You wll explore how

### PHY126 Summer Session I, 2008

PHY6 Summe Sesson I, 8 Most of nfomaton s avalable at: http://nngoup.phscs.sunsb.edu/~chak/phy6-8 ncludng the sllabus and lectue sldes. Read sllabus and watch fo mpotant announcements. Homewok assgnment

### Rigid Bodies: Equivalent Systems of Forces

Engneeng Statcs, ENGR 2301 Chapte 3 Rgd Bodes: Equvalent Sstems of oces Intoducton Teatment of a bod as a sngle patcle s not alwas possble. In geneal, the se of the bod and the specfc ponts of applcaton

### 10/15/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101

10/15/01 PHY 11 C Geneal Physcs I 11 AM-1:15 PM MWF Oln 101 Plan fo Lectue 14: Chapte 1 Statc equlbu 1. Balancng foces and toques; stablty. Cente of gavty. Wll dscuss elastcty n Lectue 15 (Chapte 15) 10/14/01

### Chapter 8. Momentum, Impulse and Collisions (continued) 10/22/2014 Physics 218

Chater 8 Moentu, Iulse and Collsons (contnued 0//04 Physcs 8 Learnng Goals The eanng of the oentu of a artcle(syste and how the ulse of the net force actng on a artcle causes the oentu to change. The condtons

### Scalars and Vectors Scalar

Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg

### Momentum and Collisions. Rosendo Physics 12-B

Moentu and Collsons Rosendo Physcs -B Conseraton o Energy Moentu Ipulse Conseraton o Moentu -D Collsons -D Collsons The Center o Mass Lnear Moentu and Collsons February 7, 08 Conseraton o Energy D E =

### 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.

### 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,

### LINEAR MOMENTUM Physical quantities that we have been using to characterize the motion of a particle

LINEAR MOMENTUM Physical quantities that we have been using to chaacteize the otion of a paticle v Mass Velocity v Kinetic enegy v F Mechanical enegy + U Linea oentu of a paticle (1) is a vecto! Siple

### Chapter 8. Momentum Impulse and Collisions. Analysis of motion: 2 key ideas. Newton s laws of motion. Conservation of Energy

Chapter 8 Moentu Ipulse and Collsons Analyss o oton: key deas Newton s laws o oton Conseraton o Energy Newton s Laws st Law: An object at rest or traelng n unor oton wll rean at rest or traelng n unor

### 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

### 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

### Lecture 09 Systems of Particles and Conservation of Linear Momentum

Lecture 09 Systes o Partcles and Conseraton o Lnear oentu 9. Lnear oentu and Its Conseraton 9. Isolated Syste lnear oentu: P F dp dt d( dt d dt a solated syste F ext 0 dp dp F, F dt dt dp dp d F F 0, 0

### Physics 1501 Lecture 19

Physcs 1501 ectue 19 Physcs 1501: ectue 19 Today s Agenda Announceents HW#7: due Oct. 1 Mdte 1: aveage 45 % Topcs otatonal Kneatcs otatonal Enegy Moents of Ineta Physcs 1501: ectue 19, Pg 1 Suay (wth copason

### Elastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.

Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday

### 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

### 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

### Physic 231 Lecture 14

Physc 3 Lecture 4 Man ponts o last lecture: Ipulses: orces that last only a short te Moentu p Ipulse-Moentu theore F t p ( ) Ipulse-Moentu theore ptot, p, p, p, p, ptot, Moentu and external orces F p ext

### Chapter Fifiteen. Surfaces Revisited

Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)

### PHYS 1443 Section 003 Lecture #21

PHYS 443 Secton 003 Lectue # Wednesday, Nov. 7, 00 D. Jaehoon Yu. Gavtatonal eld. negy n Planetay and Satellte Motons 3. scape Speed 4. lud and Pessue 5. Vaaton of Pessue and Depth 6. Absolute and Relatve

### 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

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

GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: -------------------------------------------------------------------------------------------------------------------------------------------

### Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak Lnear Momentum Lnear momentum o an object o mass m movng wth a velocty v s dened to be p mv Momentum and lnear momentum

### total If no external forces act, the total linear momentum of the system is conserved. This occurs in collisions and explosions.

Lesson 0: Collsons, Rotatonal netc Energy, Torque, Center o Graty (Sectons 7.8 Last te we used ewton s second law to deelop the pulse-oentu theore. In words, the theore states that the change n lnear oentu

### Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2

Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of

### 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

### Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

### Objectives. Chapter 6. Learning Outcome. Newton's Laws in Action. Reflection: Reflection: 6.2 Gravitational Field

Chapte 6 Gataton Objectes 6. Newton's Law o nesal Gataton 6. Gatatonal Feld 6. Gatatonal Potental 6. Satellte oton n Ccula Obts 6.5 scape Velocty Leanng Outcoe (a and use the oula / (b explan the eanng

### 10/2/2003 PHY Lecture 9 1

Announceents. Exa wll be returned at the end of class. Please rework the exa, to help soldfy your knowledge of ths ateral. (Up to 0 extra cre ponts granted for reworked exa turn n old exa, correctons on

### Engineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems

Engneeng echancs oce esultants, Toques, Scala oducts, Equvalent oce sstems Tata cgaw-hll Companes, 008 Resultant of Two oces foce: acton of one bod on anothe; chaacteed b ts pont of applcaton, magntude,

### BALANCING OF ROTATING MASSES

www.getyun.co YIS OF HIES IG OF ROTTIG SSES www.getyun.co Rotatng centelne: The otatng centelne beng defned as the axs about whch the oto would otate f not constaned by ts beangs. (lso called the Pncple

### Rectilinear motion. Lecture 2: Kinematics of Particles. External motion is known, find force. External forces are known, find motion

Lecture : Kneatcs of Partcles Rectlnear oton Straght-Lne oton [.1] Analtcal solutons for poston/veloct [.1] Solvng equatons of oton Analtcal solutons (1 D revew) [.1] Nuercal solutons [.1] Nuercal ntegraton

### CHAPTER 10 ROTATIONAL MOTION

CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The

### Lecture 23: Central Force Motion

Lectue 3: Cental Foce Motion Many of the foces we encounte in natue act between two paticles along the line connecting the Gavity, electicity, and the stong nuclea foce ae exaples These types of foces

### Chapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41.

Chapte I Matces, Vectos, & Vecto Calculus -, -9, -0, -, -7, -8, -5, -7, -36, -37, -4. . Concept of a Scala Consde the aa of patcles shown n the fgue. he mass of the patcle at (,) can be epessed as. M (,

### Physics 101 Lecture 9 Linear Momentum and Collisions

Physcs 0 Lecture 9 Lnear Momentum and Collsons Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum and Collsons q q q q q q q Conseraton o Energy Momentum Impulse Conseraton o Momentum -D Collsons

### 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

### r dt dt Momentum (specifically Linear Momentum) defined r r so r r note: momentum is a vector p x , p y = mv x = mv y , p z = mv z

Moentu, Ipulse and Collisions Moentu eeyday connotations? physical eaning the tue easue of otion (what changes in esponse to applied foces) d d ΣF ( ) dt dt Moentu (specifically Linea Moentu) defined p

### 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

### Easy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is

Chapte 8 Homewok Solutions Easy P8. Assume the velocity of the blood is constant ove the 0.60 s. Then the patient s body and pallet will have a constant velocity of 6 0 5 m 3.75 0 4 m/ s 0.60 s in the

### BALANCING OF ROTATING MASSES

VTU EUST PROGRE - 7 YIS OF HIES Subject ode - E 54 IG OF ROTTIG SSES otes opled by: VIJYVITH OGE SSOITE PROFESSOR EPRTET OF EHI EGIEERIG OEGE OF EGIEERIG HSS -57. KRTK oble:94488954 E-al:vvb@cehassan.ac.n

### Physics 201 Lecture 15

Phscs 0 Lecue 5 l Goals Lecue 5 v Elo consevaon of oenu n D & D v Inouce oenu an Iulse Coens on oenu Consevaon l oe geneal han consevaon of echancal eneg l oenu Consevaon occus n sses wh no ne eenal foces

### 30 The Electric Field Due to a Continuous Distribution of Charge on a Line

hapte 0 The Electic Field Due to a ontinuous Distibution of hage on a Line 0 The Electic Field Due to a ontinuous Distibution of hage on a Line Evey integal ust include a diffeential (such as d, dt, dq,

### VIII Dynamics of Systems of Particles

VIII Dyacs of Systes of Patcles Cete of ass: Cete of ass Lea oetu of a Syste Agula oetu of a syste Ketc & Potetal Eegy of a Syste oto of Two Iteactg Bodes: The Reduced ass Collsos: o Elastc Collsos R whee:

### 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

### Physics 202, Lecture 2. Announcements

Physcs 202, Lectue 2 Today s Topcs Announcements Electc Felds Moe on the Electc Foce (Coulomb s Law The Electc Feld Moton of Chaged Patcles n an Electc Feld Announcements Homewok Assgnment #1: WebAssgn

### 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:

### p p +... = p j + p Conservation Laws in Physics q Physical states, process, and state quantities: Physics 201, Lecture 14 Today s Topics

Physcs 0, Lecture 4 Conseraton Laws n Physcs q Physcal states, process, and state quanttes: Today s Topcs Partcle Syste n state Process Partcle Syste n state q Lnear Moentu And Collsons (Chapter 9.-9.4)

### Momentum. Momentum. Impulse. Momentum and Collisions

Momentum Momentum and Collsons From Newton s laws: orce must be present to change an object s elocty (speed and/or drecton) Wsh to consder eects o collsons and correspondng change n elocty Gol ball ntally

### Ch. 4: FOC 9, 13, 16, 18. Problems 20, 24, 38, 48, 77, 83 & 115;

WEEK-3 Recitation PHYS 3 eb 4, 09 Ch. 4: OC 9, 3,, 8. Pobles 0, 4, 38, 48, 77, 83 & 5; Ch. 4: OC Questions 9, 3,, 8. 9. (e) Newton s law of gavitation gives the answe diectl. ccoding to this law the weight

### Linear Momentum. Center of Mass.

Lecture 6 Chapter 9 Physcs I 03.3.04 Lnear omentum. Center of ass. Course webste: http://faculty.uml.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcssprng.html

### 1. Starting with the local version of the first law of thermodynamics q. derive the statement of the first law of thermodynamics for a control volume

EN10: Contnuum Mechancs Homewok 5: Alcaton of contnuum mechancs to fluds Due 1:00 noon Fda Febua 4th chool of Engneeng Bown Unvest 1. tatng wth the local veson of the fst law of themodnamcs q jdj q t and

### Integral Vector Operations and Related Theorems Applications in Mechanics and E&M

Dola Bagayoko (0) Integal Vecto Opeatons and elated Theoems Applcatons n Mechancs and E&M Ι Basc Defnton Please efe to you calculus evewed below. Ι, ΙΙ, andιιι notes and textbooks fo detals on the concepts

### 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

### FARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09

FARADAY'S LAW No. of lectues allocated Actual No. of lectues dates : 3 9/5/09-14 /5/09 31.1 Faaday's Law of Induction In the pevious chapte we leaned that electic cuent poduces agnetic field. Afte this

### VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.

Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth

### Physics 201 Lecture 4

Phscs 1 Lectue 4 ltoda: hapte 3 Lectue 4 v Intoduce scalas and vectos v Peom basc vecto aleba (addton and subtacton) v Inteconvet between atesan & Pola coodnates Stat n nteestn 1D moton poblem: ace 9.8

### ATMO 551a Fall 08. Diffusion

Diffusion Diffusion is a net tanspot of olecules o enegy o oentu o fo a egion of highe concentation to one of lowe concentation by ando olecula) otion. We will look at diffusion in gases. Mean fee path

### The Forming Theory and the NC Machining for The Rotary Burs with the Spectral Edge Distribution

oden Appled Scence The Fomn Theoy and the NC achnn fo The Rotay us wth the Spectal Ede Dstbuton Huan Lu Depatment of echancal Enneen, Zhejan Unvesty of Scence and Technoloy Hanzhou, c.y. chan, 310023,

### Review of Vector Algebra and Vector Calculus Operations

Revew of Vecto Algeba and Vecto Calculus Opeatons Tpes of vaables n Flud Mechancs Repesentaton of vectos Dffeent coodnate sstems Base vecto elatons Scala and vecto poducts Stess Newton s law of vscost

### PHYS 1443 Section 002

PHYS 443 Secton 00 Lecture #6 Wednesday, Nov. 5, 008 Dr. Jae Yu Collsons Elastc and Inelastc Collsons Two Dmensonal Collsons Center o ass Fundamentals o Rotatonal otons Wednesday, Nov. 5, 008 PHYS PHYS

### The Finite Strip Method (FSM) 1. Introduction

The Fnte Stp ethod (FS). ntoducton Ths s the ethod of se-nuecal and se-analtcal natue. t s sutale fo the analss of ectangula plates and plane-stess eleents o stuctues eng the conaton of oth. Theefoe, the

### Physics 207 Lecture 13. Lecture 13

Physcs 07 Lecture 3 Goals: Lecture 3 Chapter 0 Understand the relatonshp between moton and energy Defne Potental Energy n a Hooke s Law sprng Develop and explot conservaton of energy prncple n problem

### Momentum is conserved if no external force

Goals: Lectue 13 Chapte 9 v Employ consevation of momentum in 1 D & 2D v Examine foces ove time (aka Impulse) Chapte 10 v Undestand the elationship between motion and enegy Assignments: l HW5, due tomoow

### 1121 T Question 1

1121 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, tavelling on the sae path in the sae diection as you, at a constant speed

### Physics 105: Mechanics Lecture 13

Physcs 05: Mechancs Lecture 3 Wenda Cao NJIT Physcs Department Momentum and Momentum Conseraton Momentum Impulse Conseraton o Momentum Collsons Lnear Momentum A new undamental quantty, lke orce, energy

### 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

### 1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F)

EN40: Dynacs and Vbratons Hoework 4: Work, Energy and Lnear Moentu Due Frday March 6 th School of Engneerng Brown Unversty 1. The Rydberg potental s a sple odel of atoc nteractons. It specfes the potental

### Chapter 23: Electric Potential

Chapte 23: Electc Potental Electc Potental Enegy It tuns out (won t show ths) that the tostatc foce, qq 1 2 F ˆ = k, s consevatve. 2 Recall, fo any consevatve foce, t s always possble to wte the wok done

### Collisions! Short, Sharp Shocks

d b n, b d,, -4 Introducng Collsons Quz 9 L9 Mult-artcle Systes 6-8 Scatterng 9- Collson Colcatons L Collsons 5, Derent Reerence Fraes ranslatonal ngular Moentu Quz RE a RE b RE c EP9 RE a; HW: Pr s 3*,,

### SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9

SPH4 nit 6.3 Gavitational Potential negy Page of Notes Physics ool box he gavitational potential enegy of a syste of two (spheical) asses is diectly popotional to the poduct of thei asses, and invesely

### EMU Physics Department.

Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons

### 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

### Please initial the statement below to show that you have read it

EN40: Dynacs and Vbatons Fnal Exanaton Wednesday May 18 011 School of Engneeng own Unvesty NAME: Geneal Instuctons No collaboaton of any knd s petted on ths exanaton. You ay use double sded pages of efeence

### Page 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces

Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Non-constant forces Imulse-momentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs

### Phys101 Lectures 13, 14 Momentum and Collisions

Phs0 Lectures 3, 4 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 7-,,3,4,5,6,7,8,9,0. Page Moentu is a vector:

### r ˆr F = Section 2: Newton s Law of Gravitation m 2 m 1 Consider two masses and, separated by distance Gravitational force on due to is

Section : Newton s Law of Gavitation In 1686 Isaac Newton published his Univesal Law of Gavitation. This explained avity as a foce of attaction between all atte in the Univese, causin e.. apples to fall

### CSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4

CSJM Unvesty Class: B.Sc.-II Sub:Physcs Pape-II Ttle: Electomagnetcs Unt-: Electostatcs Lectue: to 4 Electostatcs: It deals the study of behavo of statc o statonay Chages. Electc Chage: It s popety by

### 7/1/2008. Adhi Harmoko S. a c = v 2 /r. F c = m x a c = m x v 2 /r. Ontang Anting Moment of Inertia. Energy

7//008 Adh Haoko S Ontang Antng Moent of neta Enegy Passenge undego unfo ccula oton (ccula path at constant speed) Theefoe, thee ust be a: centpetal acceleaton, a c. Theefoe thee ust be a centpetal foce,

FAADAY'S LAW 31.1 Faaday's Law of Induction In the peious chapte we leaned that electic cuent poduces agnetic field. Afte this ipotant discoey, scientists wondeed: if electic cuent poduces agnetic field,

### ( ) ( ) Review of Force. Review of Force. r = =... Example 1. What is the dot product for F r. Solution: Example 2 ( )

: PHYS 55 (Pat, Topic ) Eample Solutions p. Review of Foce Eample ( ) ( ) What is the dot poduct fo F =,,3 and G = 4,5,6? F G = F G + F G + F G = 4 +... = 3 z z Phs55 -: Foce Fields Review of Foce Eample

### CSU ATS601 Fall Other reading: Vallis 2.1, 2.2; Marshall and Plumb Ch. 6; Holton Ch. 2; Schubert Ch r or v i = v r + r (3.

3 Eath s Rotaton 3.1 Rotatng Famewok Othe eadng: Valls 2.1, 2.2; Mashall and Plumb Ch. 6; Holton Ch. 2; Schubet Ch. 3 Consde the poston vecto (the same as C n the fgue above) otatng at angula velocty.

### Chapt. 9 Systems of Particles and Conservation of Linear Momentum

Chapt. 9 Systes o Patcles ad Coseato o Lea oetu 9. Lea oetu ad Its Coseato 9. Isolated Syste lea oetu: P F dp d( d a solated syste F ext 0 dp dp F F dp dp d F F 0 0 ( P P P tot cost p p p p the law o coseato

### Remark: Positive work is done on an object when the point of application of the force moves in the direction of the force.

Unt 5 Work and Energy 5. Work and knetc energy 5. Work - energy theore 5.3 Potenta energy 5.4 Tota energy 5.5 Energy dagra o a ass-sprng syste 5.6 A genera study o the potenta energy curve 5. Work and

### Rotating Disk Electrode -a hydrodynamic method

Rotatng Dsk Electode -a hdodnamc method Fe Lu Ma 3, 0 ente fo Electochemcal Engneeng Reseach Depatment of hemcal and Bomolecula Engneeng Rotatng Dsk Electode A otatng dsk electode RDE s a hdodnamc wokng

### Electric Charge and Field

lectic Chage and ield Chapte 6 (Giancoli) All sections ecept 6.0 (Gauss s law) Compaison between the lectic and the Gavitational foces Both have long ange, The electic chage of an object plas the same