Skip to main content Skip to local navigation
Christopher Bergevin
Home » Classical Mechanics (PHYS 2010)

Classical Mechanics (PHYS 2010)

York University 

Winter 2020 - Course Website

Basic Information

  • Course Description:  Newtonian mechanics of mass points and rigid bodies. Accelerated reference frames and rotational motion, centrifugal and Coriolis forces. Central force motion in celestial mechanics. Euler's equations: precession and nutation in the gyroscope. Three credits. Prerequisites: SC/PHYS 1010 6.00, or SC/PHYS 1800 3.00 and SC/PHYS 1801 3.00, or SC/ISCI 1310 6.0 or a minimum grade of C in SC/PHYS 1410 6.00 or SC/PHYS 1420 6.00; SC/MATH 1014 3.00 or equivalent; SC/MATH 1025 3.00 or equivalent; SC/MATH 2015 3.00 or equivalent. Corequisite: SC/MATH 2271 3.00. PRIOR TO FALL 2010: Prerequisites: SC/PHYS 1010 6.00, or a minimum grade of C in SC/PHYS 1410 6.00 or SC/PHYS 1420 6.00; SC/MATH 1014 3.00 or equivalent; SC/MATH 1025 3.00 or equivalent; Co-requisite: SC/MATH 2015 3.00. 
  • Location & Time:  TTh 10-11:30 (DB 0014) AND Recitation F 9:30-10:30 (DB 0014) 
  • Course Syllabus (includes course logistics):  here (pdf) 
  • Instructor: Christopher Bergevin
    Office: Petrie 240 
    Email: cberge [AT] yorku.ca 
    Office Hours: T 12-1 & Th 2-3, and by appointment  
    Phone: 416-736-2100 ext.33730 
  • Text: Elements of Newtonian Mechanics, (2000, 3rd Ed.) JM Knudsen & PG Hjorth (Springer) 

Updates and Useful Bits

  • [2020.04.14] A few reminders as we work towards wrapping things up. There are several options, each of which requests you to contact us before noon on 4/20 (if you have not already) expressing your choice:
    • If you aim to take the final exam on 4/21, you need to email Gehrig (gehrigmic@yahoo.ca) by noon on 4/20 to let him know. You will be added to an email list that we will use to communicate w/ test-takers. The specific time of day for the exam is still TBD (I'd like to make it earlier than the current 7 PM start time).
    • Any requests for deferred status, either in terms of taking the final exam at a later date (TBD) and/or a delay in turning in the project, should be made to Gehrig (gehrigmic@yahoo.ca) by noon on 4/20 at the absolute latest. Please note that at present, dates are uncertain as to when a deferred exam will take place or how a delayed project submission will affect timing of assigning a final grade for the course.
    • If you aim to request an assessed grade, please contact me by noon on 4/20 to be added to a list. For determining the assessed grade, the x/70 is directly scaled to X/100 so to determine a letter grade. But this requires the project to be submitted on time. And also is a bit of a gamble in that regard: A poor project grade could bring you down.
    • If we do not hear from you by noon on 4/20, we will assume you are aiming to take a deferred final exam. 
    • The project (in its revised form as detailed below) should be submitted electronically in the form of pdfs and sent to Reuben (nebuer@my.yorku.ca). They must be submitted by 11:59 PM on April 25. 
  • [2020.04.10]
    • Streamlining website content to improve clarity.
    • Students who would like more direct/individual interactions, I and the TAs are happy to help. There are several approaches we can take on this. First is via email. I will do my best to respond as quickly as possible from here on out, as we move towards wrapping up the semester. Also, feel free to try to contact Gehrig (gehrigmic@yahoo.ca) and/or Reuben (nebuer@my.yorku.ca). Second is via phone or possibly skype (so to have more direct interaction in real-time). If interested, please send me an email request to set up a time and I will nail something down w/ you ASAP. Third, if interested, we may be able to set up some form of a review session w/ the TAs for an upcoming date. Please email Reuben (nebuer@my.yorku.ca) ASAP if interested.
    • Final grades will be determined chiefly in accordance with what is outlined in the syllabus. Specifically, homework grades (i.e., average of HWs 1-5) will count for 25%, the project for 15% (see revised details below re 2020.04.05 update), the midterm for 25%, and the final exam for 35%. Given the extenuating circumstances, if you have a strong preference NOT to take a final exam and instead receive an assessed grade, that may be an option (but does require the project component to be completed on-time, and that it'd count for 20% of your final grade, not 15%). Please email me (cberge@yorku.ca) expressing such a desire.
    • For students who wish to take it, the final exam for 2010 to scheduled take place on Tuesday April 21. There are two options at this point: Take it on 4/21 or request a deferred exam. Again, given the extenuating circumstances, I am happy to support student decisions either way. Please email Gehrig (gehrigmic@yahoo.ca) ASAP to voice your decision. Given the circumstances, if we don't hear from you, we will assume you desire a deferred exam (for a future date TBD).
    • Given the disruption of the course, here are some details for the format and content on the final exam:
      • Any detailed quantitative/analytic questions will be confined to material covered on or before the cessation of lectures on 3/13. This includes motion in higher dimensions, (non-)conservative forces, oscillations (incl. basics of Fourier analysis), and nonlinear dynamics. Tutorial and HW problems are the general "flavor" you want to prepare for. There will likely be three problems of this sort.
      • For material posted since 3/13 (which has been chiefly reading and/or review slides in nature), there will be several short conceptual/qualitative questions (e.g., short answer, multiple choice) to test your coverage of the material. This includes rotational motion, non-inertial reference frames, and central forces (e.g., gravitational motion). If you have been reading the assigned book chapters from K&H (ideally supplemented by F&C), you should be in good shape. I stress here that such will be well within the realm of fairness, given the disruptions to the course. You are encouraged to get in touch w/ me or the TAs w/ any questions or concerns in this regard.
      • The exam will be designed to be taken over the course of three hours, but you will be given out over a 5 hour window, thereby allowing you ample time to download/take/scan/upload in the allotted time. Specific details will be provided ahead of 4/21. You will be expected to take the exam individually without any form of interaction with one another, but it will be open-book/note.
      • For students with Letters of Accommodation on file, no problem. Please just make sure to let Gehrig know of your accommodations when responding. 
    • In light of the fact that delays have pushed things well into the exam period, it is understandable if more time is needed to complete the project. If you would like deferred status, so to submit the project at a later date, that could be acceptable. Please discuss with your group and if there is consensus, please send Gehrig (gehrigmic@yahoo.ca) ASAP a note indicating such and we can proceed from there. Please note that for grading the project, the goal is to have a flexible metric so to be as (liberally) fair as possible.
  • [2020.04.05] Project-centric update. This details key updates w/ regard to how the format of the project has been streamlined to factor in current circumstances: 
    • The "group project" has been redesignated as "Final Exam Part 2". It will still count for 15% of your final grade, but the way the project is graded will deviate from what was laid out in the project overview (https://www.yorku.ca/cberge/2010images/PHYS2010W20projectOverview.pdf). What is stated here supercedes that document. The intention is help students out given the present circumstances.
    • There are now only two things that you are required to submit, as detailed below. All submissions should be electronic in the form of pdfs and sent to Reuben (nebuer@my.yorku.ca). They must be submitted by 11:59 PM on April 25. 
      • 1. Group Poster - This should be a single pdf (no larger than 15 MB), as detailed in the project overview. Specifically, consider the sections starting off with "You and your group will make a digital poster..." and "When creating the poster...", as well as the Fig.1 ("Guidleines for poster presentation") and the provided URLs. Even though you won't be orally presenting it, the poster should be able to "stand on its own". Only one poster file needs to be submitted by the group.
      • 2. Description of your role/contribution - Every student in the class is expected to submit this. It should be ~1/2 page in length, and clearly lay out what and how you contributed. Further, please indicate what fraction of the work (as a percentage ranging from 0-100) you believe you did in terms of the final poster submission, as well as the percentage you feel other members contributed (all totaling to 100%). You are requested NOT to describe the role (or lack thereof) that others in your group played, but merely just indicate a percentage. Focus solely on describing your specific efforts and contribution.
    • You are also encouraged to submit a short report/"appendix" (at the time of poster submission), containing relevant code and whatnot. This is NOT REQUIRED, but is suggested as a means to help you focus your collective efforts and provide a useful reference.
    • With regard to grading, a final project grade will be determined primarily based upon the instructor and TAs collectively evaluating the group poster. Your individual grade may differ from that of the group based upon the contents of your submitted description of your role. The intention is to ensure that grades are fairly assigned for all members in the group. And just to make clear: Your grade will be based upon the poster (as there is no longer a presentation component, nor a report as previously required).
    • Lastly, I understand there is a lot of variability in how the pandemic has affected people's lives, and thus led to disrupting the "group" nature of the project. We will do our best to strive to be fair and transparent, so to help students who need to wrap up PHYS 2010 get finished, while also allow for some "breathing room" for those who are unable to perform/contribute as they would under more normal circumstances. As stated before, we really do want to provide ALL students w/ a chance to succeed, but also need to do our best to be fair. 

[2020.03.17] I realize how disruptive current circumstances are for all. We all have a lot on our plates, and the last thing we need is to worry about school. So for the moment, let me assure you that you do not need to worry about class/grades. First and foremost, take care of yourself. Only then can you help take care of those around you. And follow the guidelines out there: respect the communal need for "social distancing", so to limit exposure for all. 

For the moment, consider any course-related deadline suspended (incl. HW5). We all need a bit of time for things to settle a bit further before we collectively figure out how to proceed. I am greatly heartened that York is showing strong leadership w/ setting a solid foundation looking ahead, while not ignoring the gravity of circumstances. I will follow their lead and help us move forward in a positive way. 

Let me highlight some text-related focal points, as well as some problems to keep you (pleasantly) occupied: 

  • Review your 1st year text re "systems of particles": center-of-mass, momentum, collisions
  • Review your 1st year text re rotational motion: angular kinematics, associated vectors, torque, angular momentum
  • Knudsen & Hjorth ch.3.1-3.4: Gravitational vs Inertial Mass
  • Knudsen & Hjorth ch.4.1-4.2: Galilei Transformations
  • Knudsen & Hjorth ch.5.1: Rotational Motions
  • Problems: see Knudsen & Hjorth ch.2.2 (try setting these up and solving through, independent of the text/solution)

As for HW5, a lot of of folks asked about 7B. First, make sure you see the updated pdf (as the problem was retooled a bit from what was initially posted). Second, see your book (specifically Knudsen & Hjorth 15.10). That should give you the needed boost... 

Class Notes

  • 2020.01.07 - Introduction and review 
    • Book reading: Knudsen & Hjorth ch.1.1-1.5
    • Slides
  • 2020.01.09 - 1-D to 3-D motion, Projectiles 
    • Book reading: Knudsen & Hjorth Appendix
    • Slides
  • 2020.01.10 - Tutorial I 
  • 2020.01.14 - Newton's Laws (Revisited) 
    • Book reading: Knudsen & Hjorth 2.1-2.2, 
    • Slides
  • 2020.01.16 - Conservative Forces 
    • Book reading: Knudsen & Hjorth 8.1-8.2
    • Slides
  • 2020.01.17 - Tutorial II 
  • 2020.01.21 - Drag (1-D), Higher Dimensions 
    • Book reading: Knudsen & Hjorth 7.1, 8.3-8.5
    • Slides
  • 2020.01.23 - Vector Calc Review
    • Book reading: Knudsen & Hjorth N/A
    • Slides
  • 2020.01.24 - Tutorial III 
  • 2020.01.28 - Higher Dimensions: Work-Energy Theorem Revisited
    • Book reading: Knudsen & Hjorth 8.4-8.8
    • Slides
  • 2020.01.30 - Wrapping up Projectile Motion; (Intro to) Oscillations I
  • 2020.01.31 - Tutorial IV 
  • 2020.02.04 - Oscillations II
    • Book reading: Knudsen & Hjorth 15.4-15.5, 15.11
    • Slides
  • 2020.02.06 - Oscillations III
    • Book reading: Knudsen & Hjorth 15.6-15.10
    • Slides
  • 2020.02.07 - Tutorial V 
  • 2020.02.11 - Oscillations IV
  • 2020.02.13 - MIDTERM
    • See notes above for tips re preparing
  • 2020.02.14 - Tutorial VI 
    • Discussion of problems/solutions to the midterm exam
  • 2020.02.18 & 20 (and 21) - NO CLASS (Reading Week) 
  • 2020.02.25 - CLASS CANCELLED (instructor sick) 
  • 2020.02.27 - Oscillations V
  • 2020.02.28 - Tutorial VII 
  • 2020.03.03 - Oscillations VI - Damped driven HO, Resonance
    • Book reading: 15.ff, 16.2
    • Slides
  • 2020.03.05 - Oscillations VII - Fourier
  • 2020.03.06 - Tutorial VIII 
    • Focus on discussing the last 1/3 of the 3/5 lecture (i.e., slides 31ff from here), along with the associated code EXspecREP3.m (all the essential bits can be downloaded here as a zipped file)
  • 2020.03.10 - Fourier
  • 2020.03.10 - Pendula, Nonlinear Oscillations, and Bifurcations
    • Book reading: Ex.1.8, 9.1, 11.1
    • Slides
  • 2020.03.13 - Tutorial IX 
    • Friday the 13th!! (Come visit me at office hours! Or come watch me grade 2010 exams!)
    • Discussion of HW5 problems
    • Discussion of "massive springs" (see notes)
  • 2020.03.23 - Gravitational vs Inertial Mass, Galilei Transformations
    • Book reading: 3.1-3.4, 4.1-4.2
  • 2020.03.31 - Major Update Purpose here is to provide some (very delayed!) materials, as well as some additional materials relevant to the course. Several of these pdfs (i.e. F&C chapters) are relevant to the Knudsen & Hjorth (K&H) book. They are intended as useful reference, with the caveat that they are a bit beyond the scope of 2010 math-wise (but very useful for 3010). Think of them as complementing K&H, and useful references to be familiar with. 
    • HW5 solutions
    • Review slides dealing with some 1st year-level background on a variety of relevant topics (e.g., systems, momentum, rotation of a rigid body) [Note: This is a large download, ~50 MB]
    • Notes on massive springs
    • Book reading: K&H ch.4 (inertial reference frames)
    • Book reading: K&H ch.6 (non-inertial reference frames) --> This material is complemented by Fowles & Cassidy (2005) ch.5 (focus chiefly on their 5.1-5.3)
    • Book reading: K&H ch.3 and 14 (gravity) --> This material is complemented by F&C ch.6 (focus chiefly on their 6.1-6.5)
    • Book reading: K&H 2.2, 12.1-12.2 (dynamics of systems) --> " complemented by F&C ch.7 (see 7.1; later bits contain more detailed investigations into classical gravity)
    • Book reading: K&H 9-11, 12.3 (planar rotational motion of rigid bodies) --> " complemented by F&C ch.8 (focus chiefly on their 8.1-6.3)In the near future, I will aim to provide some problems to solve that are tied to the concepts/material noted above. I realize that many students are under a lot of strain. So don't worry about the deluge of information posted here. Try to do your best to digest as you can. More updates will be provided here to help guide you along as we try to wrap up the course for those you need an end point sooner rather than later.

HW Assignments

Homework should be handed in as a hard copy before the start of class. 

Computer Codes(Matlab) 

Matlab codes relevant to topics covered in lecture