Study Guide For Exam Two


 Thomasina Fitzgerald
 4 years ago
 Views:
Transcription
1 Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force F over dstance ds : SI Unts are Joules [J] = [N m] Hook's Law for Sprngs Example of a varyng force. Ideal case (frctonless and massless sprng) s a conservatve force. x = Dsplacement from sprng equlbrum. k = Sprng constant. Negatve = Restorng Force. Work done by sprng for arbtrary dsplacement: Knetc Energy W = F s = Fs cos W = F d s F sprng = kx W sprng = 1 2 k x k x 2 f Energy assocated wth a movng object. SI Unts: Joules [J] K = 1 2 m v2 WorkEnergy Theorem: Vald for both varyng and nonvaryng forces. W = Δ K = K f K Power K f K = 1 2 m v 2 f 1 2 m v 2 The rate at whch work s done or the tme rate of energy transfer. Average Power: P= Δ W Δ t
2 Instantaneous Power: P= F v SI Unts: Watts [W] = [J/ s] = [ kg m 2 / s 3 ] Potental Energy Module 08 Descrbes energy due to object's poston n space. Where potental energy s equal to zero s completely arbtrary What matters s the dfference. Examples: Gravtatonal Potental Energy Energy stored n the gravtatonal feld defned as: U gravty mgy Dfference n gravtatonal potental energy when an object changes heght: Δ U =U f U = mgy f mgy Work done by the gravtatonal force on a fallng object: W gravty = mgy mgy f = Δ U gravty Vald as long as y << Earth's radus (can assume g s constant). Sprng Elastc Potental Energy Energy stored n an deal sprng an arbtrary dstance x from equlbrum: U sprng 1 2 k x2 Dfference n sprng elastc potental energy between two ponts: Δ U =U f U = 1 2 k x 2 f 1 2 k x 2 Work done by the sprng force between two ponts: W sprng = 1 2 k x k x 2 f = Δ U sprng Conservatve Forces Occurs when: Work done on a partcle between two ponts s ndependent of path. Work done movng through a closed path s zero. Examples: Gravty Ideal Sprng
3 NonConservatve Forces Causes a change (reducton) n the total mechancal energy. Examples: Frcton Ar Resstance Conservaton of Mechancal Energy Knetc energy and potental energy are types of mechancal energy. The total mechancal energy of an solated system remans constant. If objects n that system nteract only through conservatve forces: Can also rewrte as: E = E f K +U = K f +U f Δ K +Δ U = 0 If there are nonconservatve forces such as frcton nvolved, can express the loss n mechancal energy as Knetc Frcton (ΔK NC ): Knetc Frcton K +U + Δ K NC = K f +U f Δ K +Δ U =Δ K f Δ K NC = f k s Knetc energy lost by constant frcton force f k actng n the opposte drecton of dsplacement s. Lnear Momentum Module 09 Component equatons: p= m v p x =m v x p y = m v y p z = m v z Relaton to Newton's Second Law: F x = dp x SI Unts: [ kg m / s] F= d p F y = dp y F z = dp z
4 Conservaton of Lnear Momentum Assume the system solated from outsde forces. Each mass contrbutes to the total momentum. If the tme dervatve of the total momentum s zero, the momentum must be constant. For example, for a twopartcle system where masses DO NOT stck: p total = p 1 p 2 = constant p = p f p 1 p 2 = p 1f p 2f x components: y components: z components: p 1 x + p 2 x = p 1 fx + p 2 fx m 1 v 1 x v 2 x = m 1 v 1 fx v 2 fx p 1 y + p 2 y = p 1 fy + p 2 fy m 1 v 1 y v 2 y = m 1 v 1 fy v 2 fy p 1 z + p 2 z = p 1 fz + p 2 fz m 1 v 1 z + m 2 v 2 z =m 1 v 1 fz v 2 fz Impulse In collsons, we can use the mpulse approxmaton : Can treat the tmeaveraged force as constant Assume the appled force exerted acts for a short perod of tme. Appled force s much larger than any other forces present. I = Δ p = F Δ t Types of Collsons Perfectly Inelastc Collsons Total lnear momentum s conserved. Total knetc energy s NOT conserved. Masses stck together after collson treat as one mass after collson. Inelastc Collsons Total lnear momentum s conserved. Total knetc energy s NOT conserved. Masses DO NOT stck together after collson. Elastc / Perfectly Elastc Total lnear momentum s conserved. Total knetc energy s conserved. Masses DO NOT stck together after collson.
5 Module 10 Rotatonal Moton Quanttes Arc Length Angular Dsplacement Average Angular Velocty Instantaneous Angular Velocty Average Angular Acceleraton Instantaneous Angular Acceleraton Defntons s = r θ Δ θ θ f θ ω Δ θ Δ t = θ f θ t f t ω lm Δ θ Δ t 0 Δ t = d θ ᾱ Δ ω Δ t = ω f ω t f t α lm Δ ω Δ t 0 Δ t = d ω = d2 θ 2 Angle s measured n radans: Rotatng counter clockwse s postve. Rotatng clockwse s negatve. 2 π radans = 360 degrees =1 revoluton Rotatonal Moton θ= θ o + ω o t α t 2 θ= θ o (ω o + ω) t ω = ω o + α t ω 2 = ω o α (θ θ o ) Lnear Moton x = x o + v o t a t 2 x = x o (v o + v) t v = v o + at v 2 = v o a (x x o ) Relatonshp between angular and lnear quanttes of a partcle n unform crcular moton: v t = r ω a t =r α Rotatonal Knetc Energy Moment of Inerta (I) of rgd object made of n partcles: n I = m r 2 Rotatonal knetc energy of a rotatng rgd object: K R = 1 2 I ω2
6 Module 11 Torque Force F exerted on an object about an axs at a dstance r tends to rotate the object. SI Unts: Newton meter: [N m] (Not joules) Sum each torque that contrbutes to the rotaton and a rgd object to fnd the net torque: τ= I α Instantaneous Power of a rotatng rgd object: WorkEnergy Theorem for a rotatng rgd object: Rollng Moton τ = r F τ= r F sn (θ) P= τ ω W = τ θ=δ K Δ K = 1 2 I ω 2 f 1 2 I ω 2 Must account for both rotatonal moton AND translatonal moton. Translatonal moton: v cm = R ω a cm = R α Total knetc energy: K = 1 2 I ω m v 2 cm Angular Momentum A partcle of mass m and velocty v about an axs at a dstance r has angular momentum about the axs: L= r p= r m v L= mvr sn (ϕ) The torque actng on a partcle s the tme rate of change of the angular momentum: τ = d L Angular momentum of a rgd object rotatng about an axs: L= I ω
7 Conservaton of Angular Momentum If the external net torque actng on a system s zero, then the total angular momentum s constant: Therefore: τ ext = d L = 0 L = constant L = L f I ω = I f ω f Please send comments or correctons to
Chapter 11 Angular Momentum
Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle
More informationPHYSICS 231 Review problems for midterm 2
PHYSICS 31 Revew problems for mdterm Topc 5: Energy and Work and Power Topc 6: Momentum and Collsons Topc 7: Oscllatons (sprng and pendulum) Topc 8: Rotatonal Moton The nd exam wll be Wednesday October
More informationWeek 9 Chapter 10 Section 15
Week 9 Chapter 10 Secton 15 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More information10/23/2003 PHY Lecture 14R 1
Announcements. Remember  Tuesday, Oct. 8 th, 9:30 AM Second exam (coverng Chapters 94 of HRW) Brng the followng: a) equaton sheet b) Calculator c) Pencl d) Clear head e) Note: If you have kept up wth
More informationAngular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004
Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a
More informationPeriod & Frequency. Work and Energy. Methods of Energy Transfer: Energy. WorkKE Theorem 3/4/16. Ranking: Which has the greatest kinetic energy?
Perod & Frequency Perod (T): Tme to complete one ull rotaton Frequency (): Number o rotatons completed per second. = 1/T, T = 1/ v = πr/t Work and Energy Work: W = F!d (pcks out parallel components) F
More informationPart C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis
Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta
More informationPhysics 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
More informationChapter 3 and Chapter 4
Chapter 3 and Chapter 4 Chapter 3 Energy 3. Introducton:Work Work W s energy transerred to or rom an object by means o a orce actng on the object. Energy transerred to the object s postve work, and energy
More informationA Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph
A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular
More informationPhysics 111: Mechanics Lecture 11
Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 RgdBody Rotaton
More informationSpring 2002 Lecture #13
4450 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallelas Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the mdterm
More informationSUMMARY Phys 2113 (General Physics I) Compiled by Prof. Erickson. v = r t. v = lim t 0. p = mv. a = v. a = lim
SUMMARY Phys 2113 (General Physcs I) Compled by Prof. Erckson Poston Vector (m): r = xˆx + yŷ + zẑ Average Velocty (m/s): v = r Instantaneous Velocty (m/s): v = lm 0 r = ṙ Lnear Momentum (kg m/s): p =
More informationChapter 11: Angular Momentum
Chapter 11: ngular Momentum Statc Equlbrum In Chap. 4 we studed the equlbrum of pontobjects (mass m) wth the applcaton of Newton s aws F 0 F x y, 0 Therefore, no lnear (translatonal) acceleraton, a0 For
More informationEnergy and Energy Transfer
Energy and Energy Transer Chapter 7 Scalar Product (Dot) Work Done by a Constant Force F s constant over the dsplacement r 1 Denton o the scalar (dot) product o vectors Scalar product o unt vectors = 1
More informationPhysics 181. Particle Systems
Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationChapter 11 Torque and Angular Momentum
Chapter Torque and Angular Momentum I. Torque II. Angular momentum  Defnton III. Newton s second law n angular form IV. Angular momentum  System of partcles  Rgd body  Conservaton I. Torque  Vector
More informationPhysics 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
More informationSo far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationWeek 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product
The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the
More informationPHYS 705: Classical Mechanics. Newtonian Mechanics
1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]
More informationPhysics 106 Lecture 6 Conservation of Angular Momentum SJ 7 th Ed.: Chap 11.4
Physcs 6 ecture 6 Conservaton o Angular Momentum SJ 7 th Ed.: Chap.4 Comparson: dentons o sngle partcle torque and angular momentum Angular momentum o a system o partcles o a rgd body rotatng about a xed
More informationConservation of Energy
Lecture 3 Chapter 8 Physcs I 0.3.03 Conservaton o Energy Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcsall.html 95.4, Fall 03,
More information10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 913, 1516
0/4/03 PHY 3 C General Physcs I AM :5 PM T Oln 0 Plan or Lecture 7: evew o Chapters 93, 56. Comment on exam and advce or preparaton. evew 3. Example problems 0/4/03 PHY 3 C Fall 03  Lecture 7 0/4/03
More information10/9/2003 PHY Lecture 11 1
Announcements 1. Physc Colloquum today The Physcs and Analyss of Nonnvasve Optcal Imagng. Today s lecture Bref revew of momentum & collsons Example HW problems Introducton to rotatons Defnton of angular
More informationRotational and Translational Comparison. Conservation of Angular Momentum. Angular Momentum for a System of Particles
Conservaton o Angular Momentum 8.0 WD Rotatonal and Translatonal Comparson Quantty Momentum Ang Momentum Force Torque Knetc Energy Work Power Rotaton L cm = I cm ω = dl / cm cm K = (/ ) rot P rot θ W =
More informationLinear 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
More informationModeling of Dynamic Systems
Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how
More informationK = 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 informationChapter 07: Kinetic Energy and Work
Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy.
More informationPhysics 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
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n xy plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationChapter 7. Potential Energy and Conservation of Energy
Chapter 7 Potental Energy and Conservaton o Energy 1 Forms o Energy There are many orms o energy, but they can all be put nto two categores Knetc Knetc energy s energy o moton Potental Potental energy
More informationLecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics
Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn
More informationSpring Force and Power
Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems
More informationWeek 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
More informationPHYSICS 231 Lecture 18: equilibrium & revision
PHYSICS 231 Lecture 18: equlbrum & revson Remco Zegers Walkn hour: Thursday 11:3013:30 am Helproom 1 gravtaton Only f an object s near the surface of earth one can use: F gravty =mg wth g=9.81 m/s 2
More informationPHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014
PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 WorkKnetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o
More informationRotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa
Rotatonal Dynamcs Physcs 1425 Lecture 19 Mchael Fowler, UVa Rotatonal Dynamcs Newton s Frst Law: a rotatng body wll contnue to rotate at constant angular velocty as long as there s no torque actng on t.
More informationPHYS 1441 Section 002 Lecture #16
PHYS 1441 Secton 00 Lecture #16 Monday, Mar. 4, 008 Potental Energy Conservatve and Nonconservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!
More informationChapter 8: Potential Energy and The Conservation of Total Energy
Chapter 8: Potental Energy and The Conservaton o Total Energy Work and knetc energy are energes o moton. K K K mv r v v F dr Potental energy s an energy that depends on locaton. Dmenson F x d U( x) dx
More informationImportant Dates: Post Test: Dec during recitations. If you have taken the post test, don t come to recitation!
Important Dates: Post Test: Dec. 8 0 durng rectatons. If you have taken the post test, don t come to rectaton! Post Test MakeUp Sessons n ARC 03: Sat Dec. 6, 0 AM noon, and Sun Dec. 7, 8 PM 0 PM. Post
More informationEMU Physics Department
Physcs 0 Lecture 8 Potental Energy and Conservaton Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aovgun.com Denton o Work W q The work, W, done by a constant orce on an object s dened as the product
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationPHYS 1443 Section 003 Lecture #17
PHYS 144 Secton 00 ecture #17 Wednesda, Oct. 9, 00 1. Rollng oton of a Rgd od. Torque. oment of Inerta 4. Rotatonal Knetc Energ 5. Torque and Vector Products Remember the nd term eam (ch 6 11), onda, Nov.!
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationWeek 6, Chapter 7 Sect 15
Week 6, Chapter 7 Sect 15 Work and Knetc Energy Lecture Quz The frctonal force of the floor on a large sutcase s least when the sutcase s A.pushed by a force parallel to the floor. B.dragged by a force
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1s tme nterval. The velocty of the partcle
More informationChapter Seven  Potential Energy and Conservation of Energy
Chapter Seven  Potental Energy and Conservaton o Energy 7 1 Potental Energy Potental energy. e wll nd that the potental energy o a system can only be assocated wth specc types o orces actng between members
More informationτ rf = Iα I point = mr 2 L35 F 11/14/14 a*er lecture 1
A mass s attached to a long, massless rod. The mass s close to one end of the rod. Is t easer to balance the rod on end wth the mass near the top or near the bottom? Hnt: Small α means sluggsh behavor
More information11. Dynamics in Rotating Frames of Reference
Unversty of Rhode Island DgtalCommons@URI Classcal Dynamcs Physcs Course Materals 2015 11. Dynamcs n Rotatng Frames of Reference Gerhard Müller Unversty of Rhode Island, gmuller@ur.edu Creatve Commons
More informationSCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 2 EXAMINATIONS 2011/2012 DYNAMICS ME247 DR. N.D.D. MICHÉ
s SCHOOL OF COMPUTING, ENGINEERING ND MTHEMTICS SEMESTER EXMINTIONS 011/01 DYNMICS ME47 DR. N.D.D. MICHÉ Tme allowed: THREE hours nswer: ny FOUR from SIX questons Each queston carres 5 marks Ths s a CLOSEDBOOK
More informationConservation of Angular Momentum = "Spin"
Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts
More informationDynamics of Rotational Motion
Dynamcs of Rotatonal Moton Torque: the rotatonal analogue of force Torque = force x moment arm = Fl moment arm = perpendcular dstance through whch the force acts a.k.a. leer arm l F l F l F l F = Fl =
More informationPhysics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1
Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. MultPartcle
More informationPhysics 111 Final Exam, Fall 2013, Version A
Physcs 111 Fnal Exam, Fall 013, Verson A Name (Prnt): 4 Dgt ID: Secton: Honors Code Pledge: For ethcal and farness reasons all students are pledged to comply wth the provsons of the NJIT Academc Honor
More informationPhysics 207: Lecture 27. Announcements
Physcs 07: ecture 7 Announcements akeup labs are ths week Fnal hwk assgned ths week, fnal quz next week Revew sesson on Thursday ay 9, :30 4:00pm, Here Today s Agenda Statcs recap Beam & Strngs» What
More informationChapter 9. The Dot Product (Scalar Product) The Dot Product use (Scalar Product) The Dot Product (Scalar Product) The Cross Product.
The Dot Product (Scalar Product) Chapter 9 Statcs and Torque The dot product of two vectors can be constructed by takng the component of one vector n the drecton of the other and multplyng t tmes the magntude
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationRigid body simulation
Rgd bod smulaton Rgd bod smulaton Once we consder an object wth spacal etent, partcle sstem smulaton s no longer suffcent Problems Problems Unconstraned sstem rotatonal moton torques and angular momentum
More informationPlease initial the statement below to show that you have read it
EN40: Dynamcs and Vbratons Mdterm Examnaton Thursday March 5 009 Dvson of Engneerng rown Unversty NME: Isaac Newton General Instructons No collaboraton of any knd s permtted on ths examnaton. You may brng
More informationA particle in a state of uniform motion remain in that state of motion unless acted upon by external force.
The fundamental prncples of classcal mechancs were lad down by Galleo and Newton n the 16th and 17th centures. In 1686, Newton wrote the Prncpa where he gave us three laws of moton, one law of gravty,
More informationPhysics 207 Lecture 6
Physcs 207 Lecture 6 Agenda: Physcs 207, Lecture 6, Sept. 25 Chapter 4 Frames of reference Chapter 5 ewton s Law Mass Inerta s (contact and noncontact) Frcton (a external force that opposes moton) Free
More informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and nonconservatve forces Mechancal Energy Conservaton of Mechancal
More informationPhysics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall
Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 2126 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons
More informationChapter 12 Equilibrium & Elasticity
Chapter 12 Equlbrum & Elastcty If there s a net force, an object wll experence a lnear acceleraton. (perod, end of story!) If there s a net torque, an object wll experence an angular acceleraton. (perod,
More informationPhysics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall
Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 2126 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons
More informationSpinrotation coupling of the angularly accelerated rigid body
Spnrotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 Emal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s
More informationPhysics 207, Lecture 13, Oct. 15. Energy
Physcs 07 Lecture 3 Physcs 07, Lecture 3, Oct. 5 Goals: Chapter 0 Understand the relatonshp between moton and energy Dene Potental Energy n a Hooke s Law sprng Deelop and explot conseraton o energy prncple
More informationChapter 7: Conservation of Energy
Lecture 7: Conservaton o nergy Chapter 7: Conservaton o nergy Introucton I the quantty o a subject oes not change wth tme, t means that the quantty s conserve. The quantty o that subject remans constant
More informationMechanics Cycle 3 Chapter 9++ Chapter 9++
Chapter 9++ More on Knetc Energy and Potental Energy BACK TO THE FUTURE I++ More Predctons wth Energy Conservaton Revst: Knetc energy for rotaton Potental energy M total g y CM for a body n constant gravty
More informationPY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg
PY2101 Classcal Mechancs Dr. Síle Nc Chormac, Room 215 D Kane Bldg s.ncchormac@ucc.e Lectures stll some ssues to resolve. Slots shared between PY2101 and PY2104. Hope to have t fnalsed by tomorrow. Mondays
More informationPHYS 1441 Section 002 Lecture #15
PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton Announcements Mdterm comprehensve exam
More informationLAGRANGIAN MECHANICS
LAGRANGIAN MECHANICS Generalzed Coordnates State of system of N partcles (Newtonan vew): PE, KE, Momentum, L calculated from m, r, ṙ Subscrpt covers: 1) partcles N 2) dmensons 2, 3, etc. PE U r = U x 1,
More informationPHYS 1441 Section 001 Lecture #15 Wednesday, July 8, 2015
PHYS 1441 Secton 001 Lecture #15 Wednesday, July 8, 2015 Concept of the Center of Mass Center of Mass & Center of Gravty Fundamentals of the Rotatonal Moton Rotatonal Knematcs Equatons of Rotatonal Knematcs
More informationChapter 20 Rigid Body: Translation and Rotational Motion Kinematics for Fixed Axis Rotation
Chapter 20 Rgd Body: Translaton and Rotatonal Moton Knematcs for Fxed Axs Rotaton 20.1 Introducton... 1 20.2 Constraned Moton: Translaton and Rotaton... 1 20.2.1 Rollng wthout slppng... 5 Example 20.1
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
More information2D Motion of Rigid Bodies: Falling Stick Example, WorkEnergy Principle
Example: Fallng Stck 1.003J/1.053J Dynamcs and Control I, Sprng 007 Professor Thomas Peacock 3/1/007 ecture 10 D Moton of Rgd Bodes: Fallng Stck Example, WorkEnergy Prncple Example: Fallng Stck Fgure
More informationThe classical spinrotation coupling
LOUAI H. ELZEIN 2018 All Rghts Reserved The classcal spnrotaton couplng Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 louaelzen@gmal.com Abstract Ths paper s prepared to show that a rgd
More informationLecture 20: Noether s Theorem
Lecture 20: Noether s Theorem In our revew of Newtonan Mechancs, we were remnded that some quanttes (energy, lnear momentum, and angular momentum) are conserved That s, they are constant f no external
More informationPHYS 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
More informationPhysics 2113 Lecture 14: WED 18 FEB
Physcs 2113 Jonathan Dowlng Physcs 2113 Lecture 14: WED 18 FEB Electrc Potental II Danger! Electrc Potental Energy, Unts : Electrc Potental Potental Energy = U = [J] = Joules Electrc Potental = V = U/q
More informationin state i at t i, Initial State E = E i
Physcs 01, Lecture 1 Today s Topcs n More Energy and Work (chapters 7 & 8) n Conservatve Work and Potental Energy n Sprng Force and Sprng (Elastc) Potental Energy n Conservaton of Mechanc Energy n Exercse
More informationClassical Mechanics Virtual Work & d Alembert s Principle
Classcal Mechancs Vrtual Work & d Alembert s Prncple Dpan Kumar Ghosh UMDAE Centre for Excellence n Basc Scences Kalna, Mumba 400098 August 15, 2016 1 Constrants Moton of a system of partcles s often
More informationGround Rules. PC1221 Fundamentals of Physics I. Linear Momentum, cont. Linear Momentum. Lectures 17 and 18. Linear Momentum and Collisions
PC Fundamentals of Physcs I Lectures 7 and 8 Lnear omentum and Collsons Dr Tay Seng Chuan Ground Rules Swtch off your handphone and pager Swtch off your laptop computer and keep t No talkng whle lecture
More informationMEASUREMENT OF MOMENT OF INERTIA
1. measurement MESUREMENT OF MOMENT OF INERTI The am of ths measurement s to determne the moment of nerta of the rotor of an electrc motor. 1. General relatons Rotatng moton and moment of nerta Let us
More informationChapter 10 Rotational motion
Prof. Dr. I. Nasser Chapter0_I November 6, 07 Important Terms Chapter 0 Rotatonal moton Angular Dsplacement s, r n radans where s s the length of arc and r s the radus. Angular Velocty The rate at whch
More informationEN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st
EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to
More informationClassical Mechanics ( Particles and Biparticles )
Classcal Mechancs ( Partcles and Bpartcles ) Alejandro A. Torassa Creatve Commons Attrbuton 3.0 Lcense (0) Buenos Ares, Argentna atorassa@gmal.com Abstract Ths paper consders the exstence of bpartcles
More informationˆ (0.10 m) E ( N m /C ) 36 ˆj ( j C m)
7.. = = 3 = 4 = 5. The electrc feld s constant everywhere between the plates. Ths s ndcated by the electrc feld vectors, whch are all the same length and n the same drecton. 7.5. Model: The dstances to
More informationMechanics Physics 151
Mechancs Physcs 151 Lecture 3 Lagrange s Equatons (Goldsten Chapter 1) Hamlton s Prncple (Chapter 2) What We Dd Last Tme! Dscussed multpartcle systems! Internal and external forces! Laws of acton and
More informationRecitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk.
Rectaton: Energy, Phys 207. Energy. Energes. An acorn fallng from an oak tree onto the sdewalk. The acorn ntal has gravtatonal potental energy. As t falls, t converts ths energy to knetc. When t hts the
More informationCelestial Mechanics. Basic Orbits. Why circles? Tycho Brahe. PHY celestialmechanics  J. Hedberg
PHY 454  celestalmechancs  J. Hedberg  207 Celestal Mechancs. Basc Orbts. Why crcles? 2. Tycho Brahe 3. Kepler 4. 3 laws of orbtng bodes 2. Newtonan Mechancs 3. Newton's Laws. Law of Gravtaton 2. The
More informationLinear 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
More informationPhysics 106a, Caltech 11 October, Lecture 4: Constraints, Virtual Work, etc. Constraints
Physcs 106a, Caltech 11 October, 2018 Lecture 4: Constrants, Vrtual Work, etc. Many, f not all, dynamcal problems we want to solve are constraned: not all of the possble 3 coordnates for M partcles (or
More informationTIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points
TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS, Exam Secton Verson October 8, 03 Total Weght: 00 ponts. Check your examnaton or completeness pror to startng. There are a total o nne
More informationPhysics 114 Exam 2 Spring Name:
Physcs 114 Exam Sprng 013 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red wth the amount beng
More informationPhysics 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
More information