PHYS105A, UCSB, 2009-01/03

Announcements

• [March 12] The information slides on the Final have been posted below.
• [March 11] There will be an additional review session (lead by RE) on Wednesday before the Final. It will be at 5:15 pm in the PSR (1st floor of Broida)
• [March 10] FAQ and their answers about the Final have been posted below, including a link to last year's final and its answers.
• [March 10] Extra exercises have been posted below as Imaginary Homework 7; the answers to which will be discussed in Friday's Discussion sessions.
• [March 9] Remaining schedule of Week X has been posted.
• [March 9] Solutions to Homework 6 have been posted.
• [March 2] Solutions to Homework 5 have been posted.
• [Feb 26] New homework 6 has been announced.
• [Feb 25] Important note regarding HW 5: In Problem 5.45 you should only consider the long term behavior of the system, i.e. after the transients have died out.
• [Feb 19] New Homework 5 has been announced.
• [Feb 13] The solutions to Homework 4 have been posted below.
• [Feb 12] There will be no new homework announcement this week. Also, remember that next Monday February 16 is Presidents' Day and there will be no class.
• [Feb 9] The Midterm has been graded and can be picked up from the TAs during their office hours.
• [Feb 9] Somebody left a black umbrella after the Discussion session of last Friday. You can pick it up at the office hours of MH this Tuesday.
• [Feb 5] Homework 4 has been posted, which is due Thursday, February 12 at 2 pm.
• [Feb 4] The solutions to the Midterm have been posted.
• [Feb 3] Homework 3 has been graded and can be picked up at MH's office hours today, between 1:30 and 3 pm.
• [Feb 2] Because too many students did not separate their answer to Problem 2.53 from their answers to the other problems, this homework 3 could not be graded in parallel by the TAs and therefore has not been graded yet.
• [Feb 2] The old graded Homeworks 1 and 2 can be picked up from WvD's office on Monday.
• [Feb 1] A Midterm FAQ has been posted below.
• [Jan 29] Solutions to Homework 3 have been posted.
• [Jan 28] The office hours of RE are as follows in the coming two weeks:

1. Week 4: Wednesday 12:00-1:30 pm and Thursday 10:30-12:00 pm and 3:30-5:00 pm
2. Week 5: Thursday 10:30-12:00 pm

• [Jan 24] Solutions to Homework 2 have been posted.
• [Jan 24] A brief note explaining how, by taking the origin to infinity, the angular momentum laws converge to the standard momentum laws has been posted below.
• [Jan 23] The Midterm on Chapters 1,2,3 will be on Wednesday, February 4 (Week 5)
• [Jan 22] The new Homework 3 has been posted. Note that Problem 2.53 should be handed in on a separate page. This homework is due on Thursday January 29 at 2 pm
• [Jan 19] The office hours of RE will be different in Week 3 (that week only): Tuesday 3:00-4:30 and the usual Thursday 10:30-12:00, both in the Physics Study Room.
• [Jan 19] Three remarks regarding the usage of computers for the homework problems:

1. Besides Maple, Mathematica and Matlab, you could also try using Sage: It is a powerful and free mathematics software system that can be installed on OS X and Linux systems. Note however that it also has all of the typical disadvantages of open source software: it's a bit clunky and takes some time getting used to.
2. You can use computers to verify your answers, but don't become too "Mathematica dependent" as its usage if of course not allowed during the Midterm and the Final.
3. Here is the Mathematica notebook that RE showed in the Discussion of Week 2.

• [Jan 19] The office hours of MH have been posted.
• [Jan 16] Correction: Problem 2.53 will be part of HW3 and is no longer part of HW2.
• [Jan 16] The solutions to HW1 have been posted below.
• [Jan 15] New Homework 2 is posted below (due Thursday Jan 22, 2 pm)
• [Jan 15] Note that HW1 is due today (Thursday) at 2 pm.
• [Jan 9] Slides with additional information on Homework 1 have been posted below.
• [Jan 8] Homework 1 has been announced in the"Schedule of Topics" section below. It is due on Thursday, January 15 at 2 pm. Please read the notes that go with this first assignment.
• [Jan 5] Introductory slides with "rules and regulations" posted below.
• [December 23, 2009] Installment of this website for Phys 105A, Winter 2009.

Schedule of Topics, Homework Assignements and Slides

Week I (Jan 5 - 11): "1. Newton's Laws of Motion"

• Monday, January 5: First class
• Topics: "rules and regulations"; real valued vector spaces, inner product, cross product, differentiation of time-dependent vectors; mass and force, Newton's First Law of Inertia, Newton's Second Law, reference frames, Newton's Third Law, Conservation of Momentum; coordinate systems
• "Rules and Regulations" slides: Introduction to Phys105A
• Homework 1: Problems 1.12, 1.26, 1.35 and 1.50 in Taylor's Classical Mechanics.
• This homework is due on Thursday, January 15 at 2 pm in the Phys105A homework box at "the usual spot", i.e. at the entrance of Broida. Each problem is worth 10 points (so, 40 points total). Please answer each question on a separate page. Mark Howard will be grading this assignment. Note that 1.50 requires the use of a computer program like Matlab, Maple or Mathematica. This software can be found on the computers in the Physics Study Room, which is on the first floor of Broida behind the elevators. You should print out both the plots and the the code you wrote to create them. If you already know how to use one of these computer programs, these problems should be easy. If you do not know them, you will have to spend some more time. (It is a very valuable thing to know how to use a computer to solve such problems, and it will be a skill that you will use many times in your scientific career.)
  • Additional slides on Homework 1
  • Solutions to HW1
• Discussion [MH]: new Homework 1

Week II (Jan 12 - 18): "2. Projectiles and Charged Particles"

• Topics: linear and quadratic drag forces, gravitational forces, describing linear air resistance with linear first-order differential equations, coupled versus uncoupled differential equations, complex exponential functions, general versus specific solutions, terminal speed; describing quadratic air resistance with quadratic first-order differential equations, separation of variables technique, numerical solutions to differential equations
• Monday and Wednesday: WvD will be away; instead prof. A. Cleland will be teaching those two days
• Thursday: Homework 1 due at 2 pm
• Homework 2: Problems 2.7, 2.31, and 2.43 and 2.53
  • This homework is due on Thursday January 22 at 2 pm in the Phys105A homework box.
  • Note that Problem 2.53 will be part of HW3 instead; as a result the total of points for HW2 is 30, not the usual 40.
• Solutions to HW2
• Discussion [RE]: new Homework 2

Week III (Jan 19 - 25): "3. Momentum and Angular Momentum"

• Monday January 19: No class (Martin Luther King, Jr.'s Birthday)
• Topics: cross product, movement of charged particles in a magnetic field, coupled differential equations; conservation of momentum, elastic versus inelastic collisions, center of mass; conservation of angular momentum for one and several particles, torque, Kepler's second law, moment of inertia
• Explanation how angular momentum laws converge to standard momentum laws by taking the origin to infinity
• Thursday: Homework 2 due at 2 pm
• Homework 3: Problem 2.53 (on separate page), and Problems 3.4, 3.27 and 3.37
• This homework is due on Thursday January 29 at 2 pm in the Phys105A homework box
• Solution to Problem 2.53 (HW3)
• Solutions to Problems 3.4, 3.27 and 3.37 (HW3)
• Discussion [MH]: old HW1 + new HW3

Week IV (Jan 26 - Feb 1): "4. Energy"

• Topics: kinetic energy, work, line integral, Work-KE theorem; conservative force, potential energy, mechanical energy, conservation of energy, nonconservative forces, conservative force as the gradient of potential energy, curl of a force
• Thursday: Homework 3 due at 2 pm
• Discussion [RE]: old HW2 + upcoming Midterm

Week V (Feb 2 - Feb 8): "4. Energy"

• Topics: spherical coordinates; stable and unstable equilibria, one-dimensional systems; energy of multiple particles, elastic collisions; central forces, symmetrical forces, time-dependent potential energy
• Wednesday, Feb 4: Midterm on Chapters 1-3
• Solutions to Midterm
• Homework 4: Problems 4.8, 4.12, 4.25, and 4.53
• This homework is due Thursday February 12 at 2 pm in the Phys105A homework box.
  • Problem 4.25b is indeed very easy; the real difficulty lies with the (c) question.
• Solutions to HW4
• Discussion [MH]: old HW3 + new HW4

Week VI (Feb 9 - Feb 15): "5. Oscillations"

• Thursday: Homework 4 due at 2 pm
• Midterm graded
• Discussion [MH]: Midterm

Week VII (Feb 16 - Feb 22): "5. Oscillations"

• Monday February 16: No class (Presidents' Day)
• Homework 4 graded + Homework 5 announced
• Homework 5: Problems 5.24, 5.27, 5.36 and 5.45
• When answering Problem 5.36 you should plot both the graph of Taylor's Example 5.3 and the one with the new initial conditions of 5.36 in order to be able to compare the two properly.
• Note regarding 5.45: "rate" is work per second, hence it equals Fv, with F the force and v the velocity (see also Problem 5.44)
  • Another important note regarding Problem 5.45: You should only consider the long term behavior of the system, i.e. after the transients have died out.
  • Problem 5.45 is difficult so give yourself plenty of time to solve it.
  • This homework is due Thursday February 26 at 2 pm in the Phys105A homework box.
• Solutions to Homework 5
• Discussion [MH]: old HW4 + new HW5

Week VIII (Feb 23 - March 1): "6. Calculus of Variations"

• Thursday: Homework 5 due at 2 pm
• Homework 6: Problems 6.3, 6.19, 6.20, 6.25
  • This homework is due Thursday March 5 at 2 pm in the Phys105A homework box.
• Solutions to Homework 6
• Discussion [MH]: new HW6

Week IX (March 2 - March 8): "7. Lagrange Equations"

• Homework 5 graded
• Thursday: Homework 6 due at 2 pm
• Discussion [RE]: old HW5 + upcoming Final

Week X (March 9 - March 13): "7. Lagrange Equations"

• Homework 6 graded
• Monday: Chapter 7: Lagrange Equations
• Imaginary Homework 7: Problems 7.14, 7.32, 7.41 and 7.46
• The answers to these problems will be discussed in Friday's Discussion session.
• Wednesday: Overview of material of final + Information on scores thus far
• Friday: Odds and Ends (requests are welcome)
• Discussion [WvD]: imaginary HW7 + upcoming Final

Finals Week (March 16 - March 21):

• Wednesday March 18: Final review session (by RE)
  • time: 5:15 pm
  • place: PSR (1st floor Broida)
• Information on Final(rules, material, tips)
• Friday, March 20: Final on all covered material of Chapters 1-7
• time: 12:00-3:00 pm
• place: Buchanan 1920

General Course Information

• Course number: Phys 105A
• Course title: Classical Mechanics
• Total credits: 3

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

Course Information for Winter 2009

Professor:

• Wim van Dam
  • vandam@cs.____.___
  • Harold Frank Hall, Room 2151

Teaching Assistants:

• Mark Howard
  • mhoward@physics.____.___
• Richard Eager
  • reager@physics.____.___

Required Textbook:

• Classical Mechanics by John R. Taylor, University Science Books (2005)
  • The material for the Winter 2009 course will be Chapters 1 through 7.

Grading/Exams:

The course grade is determined by: Homework + Midterm + Final = 60% + 10% + 30%

Mark Howard will be grading Homeworks 1, 3, 4 and 6.

Richard Eager will be grading Homeworks 2 and 5,

Both MH and RE will be grading the Midterm and the Final.

(Typical) Weekly Schedule:

Class and Discussions:

• Monday, 11:00-11:50: Class in Phelps 1425
• Wednesday, 11:00-11:50: Class in Phelps 1425
• Friday, 11:00-11:50: Class in Phelps 1425
• Friday, 1:00-1:50: Discussion in Ellison Hall 2816
• Friday, 2:00-2:50: Discussion in North Hall 1105

Homework:

• Thursday: Announcement of new homework on this site
• Thursday: Homework due at 2 pm in Phys105A homework box at the entrance of Broida

Office hours:

(Note though that the office hours of RE are slightly different in Week 4 and 5.)

• Monday, 1:00-3:00: Office hours of WvD in Harold Frank Hall, Room 2151
• Tuesday, 1:30-3:00: Office hours of MH in the Physics Study Room (Broida Hall, Room 1019)
• Thursday, 10:30-12:00: Office hours of RE in the Physics Study Room (Broida Hall, Room 1019)
• Thursday, 3:30-5:00: Office hours of RE in the Physics Study Room (Broida Hall, Room 1019)
• Friday 3:30-5:00: Office hours of MH in the Physics Study Room (Broida Hall, Room 1019)

Academic Honesty:

The following applies to every course you attend at UC Santa Barbara (from UCSB Campus Regulations, Chapter VII: "Student Conduct and Discipline"):

It is expected that students attending the University of California understand and subscribe to the ideal of academic integrity, and are willing to bear individual responsibility for their work. Any work (written or otherwise) submitted to fulfill an academic requirement must represent a student’s original work. Any act of academic dishonesty, such as cheating or plagiarism, will subject a person to University disciplinary action. Using or attempting to use materials, information, study aids, or commercial “research” services not authorized by the instructor of the course constitutes cheating. Representing the words, ideas, or concepts of another person without appropriate attribution is plagiarism. Whenever another person’s written work is utilized, whether it be a single phrase or longer, quotation marks must be used and sources cited. Paraphrasing another’s work, i.e., borrowing the ideas or concepts and putting them into one’s “own” words, must also be acknowledged. Although a person’s state of mind and intention will be considered in determining the University response to an act of academic dishonesty, this in no way lessens the responsibility of the student.

Specifically for the current Phys105A course this means that

• You are not allowed to copy or transcribe answers to homework assignments from others or other sources.
• Although you are allowed to discuss homework assignments with others, you should write down your answers independently. You should always be able to argue and explain your answers when asked for clarifications.
• During the Midterm and Final Examination no electronics are allowed, additional notes are only allowed to the extent described prior to the test.
• When in doubt, ask.
• Students violating the rules of Academic Honesty will receive an "F" for the course and will be reported to the Office of Judicial Affairs.

Frequently Asked Questions about the Phys105A Midterm (Winter 2009)

• When, where is the Midterm?
• The Midterm is on Wednesday, February 4, 2009, between 11:00 and 11:50 am. Please show up on time as we will also have to end on time. The Midterm will be in Phelps 1425, the regular class room.
• What is the material?
  • Chapters 1, 2 and 3 of Taylor, i.e. the material that we covered in Weeks I through IV. More specifically you can expect the questions to focus on the material that was covered by the homework assignments 1, 2 and 3. You can look at the "topics" of Weeks I-IV for a summary.
• What am I allowed to take with me, what not?
• Please take with you a pen and scrap paper and a double-sided page of self-made notes.
• No calculator, no blue book, no scantron?
  • No, no and no. Calculators are not allowed and the final answers are to be written on the pages of the Midterm.
• What should I write on my page of notes?
• Anything you want, but the "Principal Definitions and Equations" of Chapters 1-3 are probably a good start.
• How many questions will there be?
• This is not known yet.
• But what can I expect?
• That's a better question. For starters, have a look at last year's Midterm here and its solutions here. The Midterm of 2008 took more time and covered more material, so you should think of having to answer questions 1-4 in 50 minutes.

Frequently Asked Questions about the Phys105A Final (Winter 2009)

• When, where is the Final?
• The Final is on Friday, March 20, 2009, between 12:00 and 3:00 pm. Please show up on time as we will also have to end on time. The Final will be in Buchanan 1920, so not the regular class room.
• Friday, March 20: Final on all covered material of Chapters 1-7
• time: 12:00-3:00 pm
• place: Buchanan 1920
• What is the material?
  • Chapters 1 through 7 of Taylor, i.e. the material that we covered during the whole quarter. More specifically you can expect the questions to focus on the material that was covered by the homework. A more detailed list of topics and non-topics will be posted soon.
• What am I allowed to take with me, what not?
• Please take with you a pen and scrap paper and a double-sided page of self-made notes.
• No calculator, no blue book, no scantron?
  • No, no and no. Calculators are not allowed and the final answers are to be written on the pages of the Final.
• What should I write on my page of notes?
• Anything you want, but the "Principal Definitions and Equations" of Chapters 1-7 are probably a good start.
• How many questions will there be?
• This is not known yet.
• But what can I expect?
• For starters, you can have a look at last year's Final here and its solutions here. (Note however that we did not really do rocket science this year, hence Question 1 is somewhat out of bounds.)