Mechanics I (Rutgers Physics 381) Guide for Fall 2018

About the Course and the Instructors

Professor Yuri Gershtein will be in charge of the class, to be held during the Tue Fri 4 (Busch) period (1:40pm - 3:00pm) in SEC Room 208 on Tuesday and ARC 107 on Friday. (yes, it is confusing)
Contact information for me:
  • Office: Serin W316 on Busch,
  • Phone: (848) 445-8963,
  • Fax: (732)445-4343,
  • E-mail: gershtein AT

    I follow open door policy so you do not have to make an appointment to see me. Feel free to walk in my office or call or email etc if you need help. You can also make an appointment if you prefer. There will be no office hour given the open door policy, but let me know if you want one.

    Your homeworks are graded by Jinjing Yi, jy572 AT


    Our textbook will be Classical Mechanics, 5th Ed., by David John R. Taylor (University Science Books) ISBN 9781891389221.

    Know What You Are Signing Up For

    The course will challenge you! It uses advanced math unapologetically, and the pace quickens as we get futher into the course. The second course in the sequence (382) is even more challanging. If you do not have to take this course for your degree (i.e. you are not a professional option physics major) PLEASE consider taking another course or at least talk to the undergraduate director Prof. Keeton.

    Course Philosophy and Feedback

    Hearing from you on a continual basis is extremely important. Your feedback (positive and negative) will allow us to tune the course better. Talk to me before/after class, in our offices, etc etc. You can also talk to our undergraduate director who can transmit your feedback to me anonymously if you so wish.

    Homework, Exams and Grades etc

    Homework assignments will be worth 30%, class exam 30% and the final 40%. Solutions to homework assignments and exams will be posted on the web. Since I will make every effort to post the solutions immediately, please make sure that you are not late in submitting the assignments. I plan to drop one (the worst) homework grade at the end. Subjective factors such as your effort, attendance, participation during discussions, and improvement during the term will also matter for your final grade. The exam schedule is:
    Class Exam (aka midterm):      October 12, during regular class period.
    Final Exam (CUMULATIVE!):      December 17, PH-111, noon to 3pm

    World Wide Web

    The URL for our home page is
    Any important updates, weekly links to homeworks, exams and solutions, as well as your scores and grades will appear at this website.

    Administrative Assistance

    Professor Keeton (Office: Serin W305, Phone: 848-445-8876, e-mail: keeton AT is the physics undergraduate director.

    Ms. Katherine Lam (Serin W201, (848) 445-8763, klam AT is the physics undergraduate program administrator. Please see her if you need administrative help (special permissions, etc).

    Students with Disabilities

    If you have a disability, you are urged to speak to me EARLY IN THE SEMESTER to make the necessary arrangements to support a successful learning experience. For further information, click here.


    Chapter titles, section numbers and page numbers refer to the textbook "Classical Mechanics" by John R. Taylor, Copyright 2005 by University Science Books.
    CHAPTER 1 Newton's Laws of Motion 3
    1.1 Classical Mechanics 3
    1.2 Space and Time 4
    1.3 Mass and Force 9
    1.4 Newton's First and Second Laws; Inertial Frames 13
    1.5 The Third Law and Conservation of Momentum 17
    1.6 Newton's Second Law in Cartesian Coordinates 23
    1.7 Two-Dimensional Polar Coordinates 26
    Principal Definitions and Equations of Chapter 1 33
    Problems for Chapter 1 34
    CHAPTER 2 Projectiles and Charged Particles 43
    2.1 Air Resistance 43
    2.2 Linear Air Resistance 46
    2.3 Trajectory and Range in a Linear Medium 54
    not covered 2.4 Quadratic Air Resistance 57
    2.5 Motion of a Charge in a Uniform Magnetic Field 65
    2.6 Complex Exponentials 68
    2.7 Solution for the Charge in a B Field 70
    Principal Definitions and Equations of Chapter 2 71
    Problems for Chapter 2 72
    CHAPTER 3 Momentum and Angular Momentum 83
    3.1 Conservation of Momentum 83
    3.2 Rockets 85
    3.3 The Center of Mass 87
    3.4 Angular Momentum for a Single Particle 90
    3.5 Angular Momentum for Several Particles 93
    Principal Definitions and Equations of Chapter 3 98
    Problems for Chapter 3 99
    CHAPTER 4 Energy 105
    4.1 Kinetic Energy and Work 105
    4.2 Potential Energy and Conservative Forces 109
    4.3 Force as the Gradient of Potential Energy 116
    4.4 The Second Condition that F be Conservative 118
    4.5 Time-Dependent Potential Energy 121
    4.6 Energy for Linear One-Dimensional Systems 123
    4.7 Curvilinear One-Dimensional Systems 129
    4.8 Central Forces 133
    4.9 Energy of Interaction of Two Particles 138
    4.10 The Energy of a Multiparticle System 144
    Principal Definitions and Equations of Chapter 4 148
    Problems for Chapter 4 150
    CHAPTER 5 Oscillations 161
    5.1 Hooke's Law 161
    5.2 Simple Harmonic Motion 163
    5.3 Two-Dimensional Oscillators 170
    5.4 Damped Oscillations 173
    5.5 Driven Damped Oscillations 179
    5.6 Resonance 187
    5.7 Fourier Series* 192
    5.8 Fourier Series Solution for the Driven Oscillator* 197
    5.9 The RMS Displacement; Parseval's Theorem' 203
    Principal Definitions and Equations of Chapter 5 205
    Problems for Chapter 5 207
    CHAPTER 6 Calculus of Variations 215
    6.1 Two Examples 216
    6.2 The Euler-Lagrange Equation 218
    6.3 Applications of the Euler-Lagrange Equation 221
    6.4 More than Two Variables 226
    Principal Definitions and Equations of Chapter 6 230
    Problems for Chapter 6 230
    CHAPTER 7 Lagrange's Equations 237
    7.1 Lagrange's Equations for Unconstrained Motion 238
    7.2 Constrained Systems; an Example 245
    7.3 Constrained Systems in General 247
    7.4 Proof of Lagrange's Equations with Constraints 250
    7.5 Examples of Lagrange's Equations 254
    7.6 Generalized Momenta and Ignorable Coordinates 266
    7.7 Conclusion 267
    7.8 More about Conservation Laws * 268
    not covered 7.9 Lagrange's Equations for Magnetic Forces * 272
    7.10 Lagrange Multipliers and Constraint Forces * 275
    Principal Definitions and Equations of Chapter 7 280
    Problems for Chapter 7 281
    CHAPTER 8 Two-Body Central-Force Problems 293
    8.1 The Problem 293
    8.2 CM and Relative Coordinates; Reduced Mass 295
    8.3 The Equations of Motion 297
    8.4 The Equivalent One-Dimensional Problem 300
    8.5 The Equation of the Orbit 305
    8.6 The Kepler Orbits 308
    8.7 The Unbounded Kepler Orbits 313
    8.8 Changes of Orbit 315
    Principal Definitions and Equations of Chapter 8 319
    Problems for Chapter 8 320
    CHAPTER 9 Mechanics in Noninertial Frames 327
    9.1 Acceleration without Rotation 327
    9.2 The Tides 330
    9.3 The Angular Velocity Vector 336
    9.4 Time Derivatives in a Rotating Frame 339
    9.5 Newton's Second Law in a Rotating Frame 342
    9.6 The Centrifugal Force 344
    9.7 The Coriolis Force 348
    9.8 Free Fall and the Coriolis Force 351
    9.9 The Foucault Pendulum 354
    9.10 Coriolis Force and Coriolis Acceleration 358
    Principal Definitions and Equations of Chapter 9 359
    Problems for Chapter 9 360

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    This page is maintained by Yuri Gershtein.