John Taylor Classical Mechanics Homework Solutions

[ Announcements ] [ Course Info ] [ Schedule and Slides ]


  • [March 16] Regarding the material for the Final: you do not have to study the 'starred' sections as we did not cover those in class.
  • [March 16] Solutions to Homework 7 posted.
  • [March 15] Slides of Thursday Week 10 posted.
  • [March 13] Slides of Tuesday Week 10 posted.
  • [March 13] Solutions to Homework 6 posted.
  • [March 12] There will be no Homework 8. To get some practice in Lagrange's Equations, try solving Problem 7.30, which we will discuss in class this Tuesday.
  • [March 12] Slides of Week 9 posted.
  • [March 9] Note that there is no Question 4b in Homework 7.
  • [March 6] Slides of Tuesday, Week 9 posted.
  • [March 6] Date of final examination corrected to Wednesday, March 21, 8-11 am.
  • [March 5] Reduced version of Homework 7 posted.
  • [March 4] Homework 7 posted, which is due Monday, March 12, 11:30 am.
  • [March 4] Slides of Week 8 posted.
  • [Feb 25] Homework 6 posted, which is due Monday, March 5, 11:30 am.
  • [Feb 25] Slides of Week 7 posted.
  • [Feb 25] Solutions to Midterm/Homework 5 posted.
  • [Feb 16] Homework 5 posted. It should look familiar and is due earlier than normal. You have to hand in your answers before Friday February 23, 11:30 am. That way, the TA can return the Midterms at the Discussion session later that day.
  • [Feb 15] Midterm posted.
  • [Feb 13] Homework Solutions 4 posted.
  • [Feb 13] Slides of Tuesday, Week 6 (Midterm overview) posted.
  • [Feb 11] Solutions to Homework 3 have been posted.
  • [Feb 10] There will be no homework this week. Instead you should prepare for the Midterm of Thursday, February 15. The material of the Midterm consists of all of Weeks 1-5: Taylor's "Newton's Laws of Motion", "Projectiles and Charged Particles", "Momentum and Angular Momentum", and "Energy". No electronics will be allowed during the Midterm and it is closed book. You are allowed to use one letter-sized, double sided cheat sheet.
  • [Feb 10] Slides of Week 5 have been posted.
  • [Feb 4] Homework 4 is posted, which is due Monday February 12, 11:30 am. Do not hesitate to keep your answers short and to the point.
  • [Feb 4] Solutions of Homework 2 have been posted.
  • [Feb 4] Slides of Thursday Week 4 posted.
  • [Jan 30] Slides of Tuesday Week 4 posted.
  • [Jan 29] An 'improved' version of Homework 3 is posted; this time Question 1 is actually one that you have not solved before.
  • [Jan 28] Homework 3 is posted, which is due Monday February 5, 11:30 am.
  • [Jan 27] The Midterm is scheduled for Thursday, February 15; the material is all of Chapters 1, 2, 3 and 4.
  • [Jan 27] To help out a disabled student who is attending the course I am looking for a note taker for both the lectures and the discussion sessions. Please consider doing this; it pays $75. You can apply at the disabled students office at 1201 SAASB.
  • [Jan 27] Regarding Question 3b of Homework 2: you are only supposed to solve the two cases of horizontal motion and vertical motion with quadratic drag; you do not need to consider the general case.
  • [Jan 27] Slides of Week 3 have been posted.
  • [Jan 27] Homework Solutions of Week 1 have been posted.
  • [Jan 26] SH's office hours for Week 4 have changed, they are: Thursday 12:00-13:30.
  • [Jan 21] Homework 2 is posted; it is due Monday January 29, 11:30 am.
  • [Jan 18] Regarding Question 2 on the homework of Week 1: the independence of basis refers to the fact that the vector product of two vectors will always give the same vector, no matter the orthogonal 3 dimensional basis that you use to express and calculate the vectors; it does not refer to working in polar (time dependent) coordinates as we did on Tuesday, Week 2.
  • [Jan 18] Slides of Thursday, Week 2 posted.
  • [Jan 16] Slides of Tuesday, Week 2 posted.
  • [Jan 15] Homework 1 is posted; it is due Monday January 22, 11:30 am.
  • [Jan 15] Homework will be posted later today during this extended weekend.
  • [Jan 13] Office hours TAs added.
  • [Jan 11] Added slides of Thursday, Week 1.
  • [Jan 10] Added slides of Tuesday, Week 1. Homework will be added during the coming weekend.
  • [Dec 1] Added description of required textbook.
  • [August 10, 2006] Installment of the Phys 105A web site of Winter 2007.

Course Info


  • Wim van Dam
    Harold Frank Hall, Room 5109

Teaching Assistant:

  • Sungwoo Hong

Teaching Assistant:

  • Maria D'Alfonso

Description of Physics 105A-B:

  • Dynamics of a particle and systems of particles. Harmonic oscillator. Curvilinear coordinates. Central force motion. Scattering. Elementary rigid body motion. Moving coordinate systems. Lagrange's equations and generalized coordinates. Forces of constraint. Rigid body rotation. Small vibrations and normal modes. Hamilton's equations. Special relativity.

Required Textbook:

  • Classical Mechanics by John R. Taylor, University Science Books (2005)


  • Prerequisites: Physics 2 or 22 with a minimum grade of C-; Mathematics 5B (may be taken concurrently).


  • final score = 40% homework + 20% midterm + 40% final

Weekly Schedule:

  • Monday 11:30am: Homework due
  • Tuesday 9:30-10:45: Class in Broida 1640
  • Tuesday 12:30-2:30: MDA's office hours
  • Tuesday 1:30-2:30: WvD's office hours
  • Wednesday 12:30-14:00: SH's office hours
  • Wednesday 13:00-14:00: MDA's office hours
  • Thursday 9:30-10:45: Class in Broida 1640
  • Thursday 14:00-15:30: SH's office hours
  • Friday 13:00-13:50: Discussion in HSSB 1173
  • Weekend: Announcement of homework


  • I prefer that you use my office hours for your questions, rather than doing a lengthy Q&A exchange via email. When emailing me: indicate clearly that it is about Phys105A, sign off with your name, and use proper email etiquette. Thanks.

Schedule and Slides

  • Week 1 [January 8 - January 14]
    Tuesday Jan 9: class starts; formalities and overview, linear algebra and differential calculus (slides)
    Thursday Jan 11: Chapter 1: Newton's Three Laws of Motion (slides)
    Friday Jan 12: No Discussion Session today
    Homework 1, due Monday January 22, 11:30 am
    Homework Solutions 1

  • Week 2 [January 15 - January 21]
    Tuesday Jan 16: Newton's laws in polar coordinates, linear drag (slides)
    Thursday Jan 18: linear and quadratic drag (slides)
    Homework 2, due Monday January 29, 11:30 am
    Homework Solutions 2

  • Week 3 [January 22 - January 28]
    Tuesday Jan 23: motion of a charged particle in a magnetic field, conservation of linear momentum, center of mass, angular momentum of a single particle (slides)
    Thursday Jan 25: torque, angular momentum for several particles, conservation of angular momentum, central forces, moment of inertia, center of mass versus angular momentum (slides)
    Homework 3, due Monday February 5, 11:30 am
    Homework Solutions 3

  • Week 4 [January 29 - February 4]
    Tuesday Jan 30: kinetic energy, work, potential energy, conservative forces, total mechanic energy, force as the gradient of potential energy (slides)
    Thursday Feb 1: conditions on conservative forces, time dependent potentials (slides)
    Homework 4, due Monday February 12, 11:30 am
    Homework Solutions 4

  • Week 5 [February 5 - February 11]
    Tuesday Feb 6: one dimensional forces, central forces, spherical coordinates (slides)
    Thursday Feb 8: energy of two particles, elastic collisions, energy of several particles (slides)
    no homework this week, instead prepare for the Midterm of Thursday, February 15

  • Week 6 [February 12 - February 18]
    Tuesday Feb 13: Midterm overview (slides)
    Thursday Feb 15: Midterm on Chapters 1-4 (Midterm)
    Homework 5, due Friday February 23, 11:30 am
    Midterm/Homework 5 solutions

  • Week 7 [February 19 - February 25]
    Monday Feb 19: President's Day
    Tuesday Feb 20: simple harmonic oscillations, damped oscillations, linear differential operators
    Thursday Feb 22: weak, strong and critical damping , driven oscillations (slides of both Tuesday and Thursday)
    Homework 6, due Monday March 5, 11:30 am
    Homework Solutions 6

  • Week 8 [February 26 - March 4]
    Tuesday Feb 27: driven osciallations, resonance, LRC circuits, a bit of Fourier analysis (slides)
    Thursday Feb 29: Calculus of variations (slides)
    Homework 7 (reduced version), due Monday March 12, 11:30 am
    Homework Solutions 7

  • Week 9 [March 5 - March 11]
    Monday March 5: Homework 6 due at 11:30 am
    Tuesday March 6: brachistochrone solutions, Lagrange's equations and Newton's second law (slides)
    Thursday March 8: Hamilton's principle, generalized coordinates, constrained systems (slides)

  • Week 10 [March 12 - March 18]
    Monday March 12: Homework 7 due at 11:30 am
    Tuesday March 13: pendulum in accelerating frame, Midterm versus Homework statistics (slides)
    Thursday March 15: review, rules and regulations, Q&A (slides)

  • Finals Week [March 19 - March 24]
    Wednesday March 21, 8:00 - 11:00 am: Final Examination on all material in Broida 1640.

PHYS 522 Mechanics

Current semester class files are listed here.  Past semester files are listed here.  Schedule can be found below.

PHYS522 – Mechanics – Spring 2009

Textbook:   Classical Mechanics, John R. Taylor

Suggested References:Analytic Mechanics, Fowles; Classical Mechanics, Goldstein; Wave Physics, Nettel; Mathematical Methods for Physicists, Arfken and Weber; Classical Dynamics of Particles and Systems, Fifth Edition, Thorton and Marion

Instructor: Dr. Brian R. Washburn CW 36B, (785) 532-2263  Office hours: M/W/F 9:30-10:30 PM or by appt.

Purpose and Goals:  The purpose of this course is to expose you to advanced formalisms of classical mechanics, thus introducing the foundation for other areas of physics.  Another important purpose is to for you to develop a strong conceptual understanding of mechanics, and to develop the problem-solving techniques needed to handle sophisticated problems in classical mechanics.

The overall goals of this class are:

·    Introducing “new” formalisms of classical mechanics and how these formalisms are related to other areas of physics.

·    Expanding your current knowledge of mechanics.

·    Introducing the concept of symmetry and its relationship to conservation principles.

·    Developing essential mathematical and numerical methods and tools.

·    Improving your writing and problem-solving skills

·    Improving your conceptual understanding of mechanics, and your ability to communicate your knowledge.



Exams:  There will be two exams plus a cumulative final exam.  The exams will either be in-class or a take home exam, to be agreed upon by the class and instructor. 

In-Class Quizzes:  Surprise quizzes on the reading material may be given during the lecture or recitation.  The purpose of the quiz is the make you read the book before attending class.

Homework:  It is expected that you will learn the course material mostly by completing the homework.  Note that the course material will be challenging, so you will need to work hard on the homework to be successful.  Homework assignments will be given approximately once per week and will take about 10 hours.  Discussing the homework with your classmates is encouraged but you should be able to write up the assignment on your own.  In the case when you get stuck on a problem, credit will be given for a statement indicating how your solution is incorrect.

Guidelines for the homework:

·    Read the textbook before doing the homework

·    Draw a detailed diagram, write down the given variables, and write out what is to be found.

·    Think about the solution beforehand, and then see if the guess corresponds to your solution. 

·    Discuss the homework with your classmates but write the homework out on your own.

·    Ask thoughtful questions if you get stuck.

·    It is important for you, the scientist in-training, to learn how to communicate scientific information in a clear and precise manner.  It is your responsibility to present the homework solutions in a readable and logical manner.  If this is not done there will be a grade penalty.

Tentative Course Schedule, Mechanics PHYS 522, Spring 2008

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