Caltech California Institute of Technology

Caltech Division of Physics, Mathematics and Astronomy

Physics 106a - Topics in Classical Physics, Sep-Dec 2018.

Physics 106a is a 10-week intermediate course in the application of basic principles of classical physics to a wide variety of subjects.
The first half of Ph106b will continue with classical physics and special relativity. The second half, continuing through Ph106c, will cover topics in Electromagnetism.

This website is: (pdf)


Please watch this space for announcements regarding Ph 106a; things like rescheduling of lectures, typos in assignments, etc. It is your responsibility to keep up to date with the course information.

  • 12/19/18 - PLEASE fill out the TQFR! Many thanks!
  • 12/19/18 - Whew! Congratulations on a successful term! I am quite sure that we all learned a lot! Grade distributions are here.
    From the distributions: everyone worked hard on the assignments and many had near-perfect grades. But timed exams are a different story, and there was a much broader distribution. Based on assignments, many of you may be disappointed with your exam grades and final grades; I’m sorry, but I think that’s the nature of coursework.
    The total score is 50% A1-A7 (each counted equally), 15% midterm, 35% final exam.
    The note we put in your grade report are: A1,A2,A3,Mid,A4,A5,A6,A7,(A1-A7)%,TotalScore%.
    I hope everyone has a fun, relaxing and safe winter break. Then, on to Ph 106b !
    Best regards, Alan Weinstein, Feng Bi, Yongliang Zhang, Xiuqi Ma.
  • 12/10/18 - PLEASE fill out the TQFR! Many thanks!
  • 12/6/18 - Review sessions for the final exam: Sunday 12/9, 7pm, Downs 107; and Monday 12/10, 7pm, Downs 107.
  • 12/7/18 - Final exam is posted.
  • 10/26/18 - Midterm posted. Four hour limit. Due date: Friday 7pm, November 2, 2018, in the Ph 106a IN box in East Bridge. However, we're still going over it to look for typos, questions that are ambiguous or impossible to answer, etc. So you are advised to only download it when you are ready to work on it.
  • The TAs will hold midterm review sessions on Monday and Tuesday, both at 7pm in B157 West Bridge. This is *instead* of the office hours normally held on Wednesday, Thursday and Friday.
  • 11/12/18 - The midterms have been graded and returned to the "Ph 106 OUT box" in East Bridge. If you have questions about how your paper was graded, contact the TAs (not the prof).
  • 11/12/18 - I have posted the grades to REGIS. A summary is here. Remember: this is just the midterm grade; it doesn't go in your record! It is only a weak indicator of how you're doing so far, and gives no indication of what your final grade might be. As usual, the midterm can be a rude shock to many, since many of you are accustomed to working on problem sets until they're perfect; that's not really possible for the midterm. Anyway, the midterm grades were computed by counting each of the three problem sets (with equal weight) at 70% and the midterm at 30% of the total score. A total score above 85% is an A; above 70% is a B, and above 60% is a C. This is NOT necessarily how it will go for the final score and grade! Let me know if you have any questions or concerns.
    Ph 2 ab or Ph 12 abc, Ma 2.

    Tuesdays and Thursdays, 10:30-11:55, 103 Downs.
    Any changes will be announced well in advance. Please arrive on time!

    Instructor: Prof. Alan J. Weinstein
    Office: 354A West Bridge; Mail Code: 100-36; Phone: x2166; E-mail: ajw AT

    Teaching assistants:

    Textbook for Phys 106a:
    Analytical Mechanics by L.N. Hand and J.D. Finch, Cambridge University Press (1998) (on amazon).

    Much of the structure, pacing, notation, etc. is taken from this text. It is far from perfect: it doesn't have a review of elementary Newtonian mechanics; it has typos; many people think the explanations are often unclear. Looking at other texts can always help.

    Recommended texts: On reserve at Fairchild Library. Use these texts for alternate explanations or for additional problems or examples.
    • Classical Mechanics by Goldstein, Poole, and Safko (3rd edition): This is a classic textbook (I was taught the subject using an earlier edition, back in the 70s).
    • Classical Mechanics by John Taylor: a nice book, with more review of the basics than Hand and Finch, but slightly less advanced than the level of the class; it will need supplementing with other reading in a few places.
    • Mechanics by Landau and Lifshitz: classic but terse.
    • Classical Dynamics of Particles and Systems by Thornton and Marion: not as advanced as class text, and does not cover all the material, but good supplement if you find the jump from earlier classes to Ph106 too large.

    Approximately 50% problem sets, 15% midterm, 35% final exam.

    Problem Sets:
    • Problem sets and exams will be posted below on Friday of each week, due on the following Friday at 7pm in the Physics 106 IN box by the East Bridge mailboxes, and returned to the Physics 106 OUT box by the East Bridge mailboxes.
    • To satisfy Caltech privacy rules, please choose a 6 or 7 digit code and email this to me and the TAs before the first assignment is due. You will use this, and not your name, to label the assignments you hand in.
    • If your name, and not just your numerical code, appears on the assignment, you will have to pick it up directly from me.
    • Solution sets will be posted on the web.
    • You are strongly encouraged to check your work when it is returned to you.
    • Corrections to problems may be posted in the Announcements section above. If you are having trouble with a problem, be sure to check this page to see if a correction has been posted, and feel free to contact me if you think a problem has errors in it or seems overly difficult.
    • Problem sets are essential for mastering the material in this class!

    Midterm and final exams during appropriate weeks of the term (5th and 10th). Both will be take-home and "limited" open-book (only the text and class notes allowed); see Honor Code section below. The final exam will be comprehensive.

    • OFFICIAL policy: Work (the entire problem set) will be accepted up to one week late at 1/2 credit, no credit thereafter. Please put a note at the top of your problem set if it is late. You do not need to contact me or the TAs to turn in a problem set late for 1/2 credit. You must hand in the assignment in one piece (i.e.\ not a fraction on time for full credit, and the rest late for partial credit).
    • Students may request extensions from the corresponding grader (see emails above) a day or more in advance. Extension requests are governed by the honor system.
    • One extension (for up to one week) is allowed without question (your silver bullet). Please put a note at the top of your problem set that you are using your silver bullet.
    • Extension requests should be accompanied by a good excuse (eg, physical or mental illness), and should be accompanied by a letter from a doctor or the dean.
    • You must request the extension (by email to me and the TAs) before the problem set is due. (This is not necessary for your silver bullet).
    • Please put late or extension problem sets in the corresponding grader's mail box, and email them.
    • Late papers make far more work for the graders, who have their own set of pressures and deadlines as graduate students. There is no entitlement to extensions, so please do not be demanding.

    Honor Code and Collaboration policy:
    • Work is governed by the honor system.
    • You may not use sources that contain the answer to a problem or to a very similar problem. If you have come across such material in the past, so much the better; but you shouldn't go back and reference that material when working on the problem set.
    • In particular, do not use solution sets from previous years, or problem/solution books, at any time. Exams and their solutions from past years are not to be used in any fashion.
    • Collaboration is permitted on problem sets, but then you should go off alone and write it up; the work you hand in must be your own, and honestly reflect your own understanding of the material.
    • The midterm and final are not collaborative. For these you may consult your own notes (both in-class and any additional notes you take), the text by Hand and Finch, and handouts and solution sets on this website. You may not use other textbooks, the web (except for the current Ph106 website), or any other resources.
    • Mathematica or similar software may be used in problem sets for getting past some mathematical chore (if it's to the point of obscuring the physics for you). However, it is usually much better to master the mathematical analysis yourself without help from such software. If you chose to use it anyway, make sure you simplify the result as much as possible, so that it is easy to see what the math is telling you.
    • Mathematica or similar software may not be used in exams, unless explicit stated on the exam.
    • Please attend class, and section meetings!
    • Please ask questions of the TA's and the prof.
    • Please clearly write your ID number (NOT your name), date, assignment number on all of your assignments and exams. Clearly mark the problem numbers and answers.
    • Please write as neatly as possible. A human being is trying to read your work well enough to give credit!

    I greatly appreciate student feedback; feedback prior to the end-of-term TQFR evaluations lets me modify the class to fit your needs. If you want to send an anonymous comment about the course to me, click here.
    I also welcome any comments in person, by email to ajw AT, by campus mail, whatever you like.

    Lecture schedule and reading, fall term:

    Week (Tuesday) Tuesday Lecture Thursday Lecture Assignment
    (by Friday PM)
    October 2
    1. Review of Newtonian Mechanics
    Reading: Notes; HF §1.1; T Chs. 1,3,4; GPS §1.1-2
    Your favorite elementary mechanics text
    2. Variational Approach
    Reading: Notes; HF §2.1-5; T Ch6, §7.1-2
    Assignment 1,
    due next Friday.
    (TA: TBD)
    October 9
    3. The Lagrangian
    Reading: Notes
    4. Constraints, Virtual Work...
    Reading: Notes; HF §2.6-9; T §7.3-9
    Assignment 2
    (TA: TBD)
    A1 Solutions
    October 16
    5. Variational Approach with Constraints
    Reading: Notes; HF §2.6-9; T §7.3-10
    6. Equilibria and Oscillations
    Reading: Notes; HF Ch 3; T Ch 7
    Assignment 3
    (TA: TBD)
    A2 Solutions
    October 23
    7. Driven, Damped Oscillations
    Reading: Notes; HF §4.1-6; T §8.1-6
    8. Central Forces: Bound States
    Reading: Notes; HF §4.7; T §8.7, Ch 14
    Midterm Exam
    (TA: TBD)
    A3 Solutions
    October 30
    9. Central Forces: Scattering States
    Reading: Notes; HF §5.1-5; T §13.1-6
    10. Hamiltonian Dynamics I
    Reading: Notes; HF §5.6-8, Appendices; T §13.7
    Assignment 4
    (TA: TBD)
    Midterm Solutions
    November 6
    11. Hamiltonian Dynamics II
    Reading: Notes; HF Ch 6 §1-3,5, Appendix
    12: Canonical Transformations
    Reading: Notes; HF Ch 6 §4,5
    Assignment 5
    (TA: TBD)
    A4 Solutions
    November 13
    13. Hamiltonian-Jacobi Theory
    Reading: Notes; HF §7.1-4
    14. Rotations
    Reading: Notes; HF §7.7-10; T Ch 9
    Assignment 6
    (TA: TBD)
    A5 Solutions
    November 20
    15. Rotating Frames
    Reading: Notes; HF §8.1-4,12, App A,B; T §10.1-8
    No class: Thanksgiving
    No Assignment
    November 27
    16. Dynamics of Rigid Bodies I
    Reading: Notes; HF §8.6-8,10-11, App C; T §10.9-10
    17. Dynamics of Rigid Bodies II
    Reading: Notes; Euler Disk movie, paper
    Assignment 7
    (TA: TBD)
    A6 Solutions
    December 4
    18. Dynamics of Rigid Bodies: Examples
    Reading: Notes; HF Ch 9; T Ch 11.
    19. Normal Modes
    Reading: Notes; Notebook; HF §9.7; T §16.1-11
    Final exam
    (TA: TBD)
    A7 Solutions
    December 11
    No class. Optional reading:
    20. Normal Modes, continuum limit
    Reading: Notes; HF Ch 9; T Ch 11.
    Chladni plate movies: square, Violin
    No class
    Final Exam Solutions

    Acknowledgements: Most of the lecture notes and problem sets / solutions for this class were developed by Prof. Michael Cross. Many thanks to him!

    Last Updated: Dec 1, 2018
    Alan Weinstein/ajw AT