Intermediate Classical Mechanics

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1 Intermediate Classical Mechanics TECHNICAL DETAILS Instructors: D. Mark Riffe Office: SER 222B Phone: Office Hours: to be determined Prerequisites: PHYS 2710, MATH 2210, 2250 Required Text: Newton, Lagrange, and Hamilton: a Course in Particle Mechanics by D. Mark Riffe. The text is available in the Physics Department Office, SER 250. Cost: $ Credits: 3 credit hours Lecture: MWF, Industrial Science 101A, 10:30 11:20 pm Course Website: on canvas.usu.edu OVERVIEW Subject matter. Classical mechanics is a general framework for describing and explaining motion of one or more objects. This framework forms the foundation for understanding much of contemporary physics, including classical field theory, quantum mechanics, and statistical physics. Classical mechanics lies at the heart of a huge variety of technology and natural phenomena; the topics in this course set the stage for applications in such diverse fields as mechanical and civil engineering, geology, atmospheric science, astronomy and astrophysics, and fluid mechanics. Specifically, we shall cover include Newton s, Lagrange s, and Hamilton s formulations as applied to single or multiple-particle systems. The three big conservation laws energy, momentum, and angular momentum will be discussed in detail. Although many physical situations will be discussed, we shall specifically focus on harmonic motion and the two-body problem, as these are perhaps the two most important problems in classical (as well as quantum) physics. While you have already studied some of the topics in this course such as Newton s second law the level at which we shall discuss the material is at a much higher conceptual level than in previous courses. At times, the word abstract may be an appropriate term to use, especially when we get to the Lagrangian and Hamiltonian descriptions of mechanics. In many ways this is 1

2 just the beginning of your foray into theoretical physics. It will likely not be easy, but I hope it will be fun! Math proficiency. While math is not physics, math is the language of physics. If one is not able to efficiently work with the necessary math, then physics cannot really be understood. In order to develop math proficiency, the homework assignment for each chapter begins with a set of exercises that specifically focus on mathematical manipulations that are independent of any physical situation, but which are necessary for the physics of that chapter. In part, we shall work on math skills during class. The level of mathematics you will be required to master is far above that in any of your previous physics courses. This course and its companion Foundations of Wave Phenomena (PHYS 3750) are designed to give you extensive experience in using vector calculus, linear algebra, and differential equations in physics settings. By mastering the mathematical tools used in these two courses, you should be well prepared for studying the more advanced topics of electrodynamics and quantum mechanics. COURSE GOALS (Students should be able to...) Connection between math and physics. Students should be able to translate a physical description of a classical-mechanics problem into the mathematical equations necessary to solve it. Students should be able to explain the physical meaning of the mathematical formulation of a classicalmechanics physics problem and/or its solution. Students should be able to achieve physical insight through the mathematics associated with a problem. Problem visualization. Students should be able to sketch an appropriate illustration of a physical problem, including any relevant coordinates. Graphical representation Students should be able to construct a graph appropriate to a particular problem or its solution, including the use of normalized variables on the axes of the graph. Knowledge organization. Students should be able to articulate the big ideas from each chapter, section, and/or lecture, thus indicating that they have organized their content knowledge. Students should be able to filter this knowledge to access the information they need to for a particular physical problem, and make connections between different concepts. Problem-solving techniques. Students should be able to choose and apply a problem-solving technique appropriate to a particular problem. Students should be able to justify their approach for solving a particular problem. 2

3 Problem-solving strategy Students should be able to (i) draw upon an organized set of content knowledge and (ii) apply problem-solving techniques relevant to that content in order to organize and carry out long analyses of physical problems. Students should be able to connect the pieces of a problem to reach the final solution. Students should recognize that mistakes are valuable in learning the material, be able to recover from such mistakes, and persist in working to the solution even though they may not necessarily see the path to the solution when they begin the problem. Students should be able to articulate what needs to be solved in a particular problem and know when they have solved it. Approximations. Students should be able to recognize when approximations are useful and use them effectively. For example, students should be able to recognize when a truncated series expansion is an appropriate approximation to an exact solution. Students should become facile with Taylor series expansion of functions, including (i) being able to identify the small parameter of the expansion, and (ii) knowing how many terms in the expansion to keep when using the series to approximate an exact expression. Expecting and checking solution. When appropriate for a given problem, students should be able to articulate their expectations for the solution, such as direction of a force, dependence on coordinate variables, and behavior at small or large distances and/or times. For all problems, students should be able to assess the reasonableness of a solution they have reached, by methods such as checking the symmetry of the solution, looking at limiting or special cases, relating the result to cases with analogous solutions, checking units, using dimensional analysis, and/or checking the scale/order of magnitude of the answer. Communication. Students should be able to justify and explain their thinking and/or approach to a problem or physical situation, in either written or oral form. Students should be able to write up problem solutions that are well-organized, clear, and easy to read. Intellectual maturity. Students should accept responsibility for their own learning. They should be aware of what they do and do not understand about physical phenomena and classes of problem. This is evidenced by asking sophisticated and specific questions, being able to articulate where in a problem they experienced difficulty, and taking action to move beyond that difficulty. SCHEDULE We shall start at the beginning and finish at the end. Along the way we will have 3 midterm exams. The first will take place after Chapter 3; the 3

4 second will take place after Chapter 5; the third will take place after we study two-body, central-force motion. READING QUIZZES There will be online reading quizzes, administered through Canvas. Generally, there will be a quiz before each class period. Each quiz will contain on the order of 5 questions, most of which should be readily answerable after reading the associated material in the text. The primary deadline for each quiz is the night before the associated lecture, at 1 AM. For full credit, each quiz must be completed before the primary deadline. A secondary deadline occurs 2 days after the primary deadline. The scores on quizzes completed between these two deadlines are worth 50% of their full value. No quizzes may be completed after the secondary deadline. HOMEWORK NOTEBOOK Assignments. There is a homework assignment at the end each chapter in the text. Each assignment comprises both mathematical exercises and physics problems, all of which you should work out. You should first work out the problems on scratch paper. Subsequently, you should enter clear solutions into your homework notebook (see below). Each solution should contain sufficient detail that anyone (with sufficient knowledge of mechanics) could read through the solution and readily follow its contents. As a scientist it is important to develop the habit of keeping a well organized notebook. Here you get the chance to do this. The Notebook. For recording your homework solutions, you should purchase a spiral bound, 11 9 notebook with at least 100 college-ruled pages. The notebook shall be used solely for writing up your homework solutions. Homework that is not in a spiral bound notebook will not be accepted for evaluation. Notebook Assessment. The notebooks will be collected at the beginning of each exam and evaluated for (i) completeness, (ii) clarity, and (iii) organization. They will not be graded for the correctness of the solutions; you will (in most cases) know whether you have a suitable solution, as the answers you are working towards are provided for each problem. Completeness will be assessed by tallying the number of homework problems that have been attempted. There must be a sincere attempt to do all parts of each problem. Sufficient detail must exist in order to convince the grader that you actually worked out the problem. Merely writing down the 4

5 answer is never sufficient. If you can t figure out a particular problem, then write up what you tried, and attempt to assess where things went wrong this is part of doing physics in the real world. The assessment of clarity will be based on two factors. First, the exposition of your solution is key. At the beginning of each solution the problem should be clearly stated; this should be a paraphrase of the key parts of the statement of the problem as it appears in the text. Following this statement, your solution should be written up in complete sentences using standard English. A bunch of equations will simply not cut it. The goal here to be able to have anyone (including yourself) read through your solutions and have the solution make immediate sense. Examples of ideal (and non-ideal) solutions will be provided on Canvas for your perusal. Second, the legibility of your handwriting will contribute to your clarity score. Additionally, you should use space wisely. That is, do not cram everything together. Cramming make for difficult reading and only engenders frustration on the part of the grader (which lowers your score). Full credit for organization will require the following: (i) a table of contents, (ii) numbered pages, (iii) the clear labeling of the problems, and (iv) entering the problems in the order that they appear in the text. Importance of Homework. The main point of doing homework is to have you actively engage with the material. Such engagement leads to the development of neural pathways associated with learning. To enhance the learning process it will be helpful to ask yourself, after having worked out each problem, What was the point of this problem; what should I have learned here? Most importantly, you should treat the homework as an opportunity to learn rather than some drudgery to simply slog through. You will be best served if you intentionally set time aside each week to work on the homework. The homework will likely take you many hours to complete, and so putting it off until a day or two before the exam will only produce stress, fatigue, and minimal learning from the experience; it will then simply be an unpleasant descent into paralyzing quicksand. Engaging with the homework can positively affect your exam scores. This is clearly illustrated in In Fig. 1, which plots exam scores vs the fraction of homework problems attempted (related to that exam) for a recent PHYS 3550 class. As the data show, If you want a high score on the homework, you must engage the homework. Conversely, if you want a low score, don t bother looking at the homework. The data also show that doing the homework is no guarantee of doing well on the exam. This is likely related to a couple of factors. First (as discussed above), one s approach to the homework has an impact on the learning process. Second, for most people effective preparation for an exam includes other modes of study, such as textbook reading and 5

6 Exam 1 Score HW Problems Attempted (fraction) 1.0 Figure 1: Scores on Exam 1 in PHYS 3550 (SP 2015) vs the fraction of homework problems attempted. reviewing, for example. COLLABORATION IS ENCOURAGED I strongly encourage collaboration, which is an essential skill in science (and highly valued by employers!) Social interaction is critical to the success of all scientists most good ideas grow out of discussions with colleagues; essentially all scientists work as part of a research team. Find a partner or two with whom you can discuss the homework. However, it is also important that you own the material. Limit yourself to verbal help; don t ever take written information from others, and don t take written notes when you talk to others. This practice will ensure that you think things through independently after you get help. If you complete the homework but do poorly on exams, then you are probably getting too much help. The point of the homework is not to just find the answer, but more importantly to discover how to obtain the answer. There will be time for peer discussion during classes where you will try to help your fellow students get over confusions by listening to them, asking questions, critiquing answers, and teaching each other. You will learn a lot this way! While collaboration is the rule in technical work, the evaluation of each individual also plays an important role. Exams will be done without help from others. The homework you write up and turn in must be your own work in your own words, reflecting your own understanding of the material. The reading quizzes are to be done by yourself. 6

7 EXAMS There will be three midterm exams and a comprehensive final exam. The midterm exams shall take place during the regularly scheduled class time; see the schedule below. The comprehensive final exam is on 11:30 AM - 1:20 PM, Wednesday, May 4, The final must be taken at this time. HOW TO SUCCEED IN THIS COURSE You can perform very well in this class if you adhere to the following set of recommendations. Read the relevant sections in the text before each class. By reading before class, the time spent during the class will be much more beneficial. The reading quizzes are (obviously) designed to encourage this activity Take detailed notes on your reading of the text and write down questions so you can ask them in class. Come to class and stay involved. Come to office hours with questions. Keep up with the homework. Schedule time to work and internalize the material. No one is smart enough to do the homework in the last hours before each exam, and no one is smart enough to learn the material without working the homework problems. Work together when necessary. Do your own thinking, but talking to others is a great way to get unstuck. Don t get behind. It s very hard to catch up. GRADING Scores on reading quizzes and exams as well as evaluations of your homework notebook all contribute to your final grade. The percentage that each contributes is as follows. Reading quizzes 5% Homework notebook 20% Midterm exams 50% (16.67% each) Final exam 25% The nominal grading scale is listed below. Some adjustments to this scale may be made if deemed necessary by the instructor. 7

8 A 93%, A 90%, B+ 87%, B 83%, B 80%, C+ 77%, C 73%, C 70%, D+ 67%, D 60% DISABILITY Students with ADA-Documented physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations. Veterans may also be eligible for services. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn. (435) voice, (435) TTY, (435) VP, or toll free at Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice. HONOR CODE The honor code will be strictly enforced in this course. Any suspected violations of the honor code will be promptly reported to the honor system. For more information please visit: Integrity.pdf POSSIBLE ERRORS The instructors reserve the right to correct any possible errors to this syllabus. 8

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221 Math 155. Calculus for Biological Scientists Fall 2017 Website https://csumath155.wordpress.com Please review the course website for details on the schedule, extra resources, alternate exam request forms,