Final Paper


The purpose of the Term Paper is to have you study one practical application of classical mechanics that was not discussed in the lectures . There are many novel topics that could be selected from science, engineering, bioengineering, fluid mechanics, sports, etc. Select a topic that most interests you.. It is strongly recommended that you select a topic that involves dynamics of the system, rather than statics which usually are of less interest. Check with me (Professor Wolfs) before you start in order to ensure that the relevance and scope of your project is appropriate to Physics 235W.

Examples of topics that have been submitted as Physics 235W term papers in recent years are:

  • Science
    Celestial mechanics, satellite orbits, spiral galaxies, comet orbits, asteroid orbits, Hohmann transfer, protostar, gravitational redshift.. Coulomb scattering. Mechanics of a scientific instrument, e.g. gravimeter. Historical aspect of classical mechanics. Charged particle motion in beam transport systems. Speed of sound in a three-dimensional crystalline lattice. Three--body motion. Hurricanes, tornados, and other weather phenomena
  • Engineering
    Dynamics in engineering such as bridge vibrations, automobile suspension system. Projectile motion, rockets, Space Shuttle. Kinematics of a roller coaster, mechanical toy, gyroscopes, trebucket, pinball machine.
  • Bioengineering
    Kinematics of biomedical systems such as the eardrum.
  • Music
    Mechanics of a musical instrument. Normal modes of coupled strings on a piano, a violin, a drum.
  • Sports
    Dynamics and stability of a bicycle, skate board, parachute, windsurfer etc. Dynamics of movement in a fluid, e.g., skydivers, flight, diving, bungee jumping, boomerang, frisbee. The dynamics of a sport such as rowing, baseball, billiards, skiing, snowboarding, tennis, soccer, gymnastics, juggling, karate, dance.
  • Other
    Applications of Euler-Lagrange equations to economics.


Writing requirement:
The Term Paper provides an excellent opportunity to combine a requirement of the Physics 235W course simultaneously with one unit of credit towards the College Upper-level Writing Requirement. The Departmental definition of the writing requirement is as follows: "The writing must be substantial and must receive appropriate oversight, i.e. attention by instructor or faculty supervisor to elements of writing itself in addition to scientific accuracy. Elements to be examined will normally include consistency of argument, adherence to accepted norms of language and format, and clarity of message, with no fewer than one thorough rewritten resubmission expected from the student when standards are not met". The term paper will be used to satisfy the College Writing Requirement. A description of these requirements plus links to the articles on scientific communication and writing of reports can be found on the College Writing Requirement link on the P235 website.

The term paper should be about 10 pages which is insufficient to give a comprehensive discussion of any of the topics listed. Therefore, restrict your paper to one very specific and localized aspect of the topic chosen. That is, it is much better to discuss, in detail, one specific aspect of the topic rather than presenting an overview. The discussion of the phenomenon chosen should include a schematic derivation starting from the basic equations of motion. If the mathematics is too complicated for an exact derivation, indicate the basic steps and assumptions in the derivation and reference the source of your final equations. Computer simulations of the classical equations of motion are especially illuminating in describing the behavior of many systems in classical mechanics. Performing such computer simulations as part of the term paper is encouraged, but great care must be taken not to waste too much of your valuable time since such computer simulations can be very time consuming. Put numbers in your equations to indicate the order of magnitude of the effects being studied. Minimize the engineering or biological aspects of your problem; it is the underlying physics of the problem, and how it relates to P235, that is of most interest to me. Please type the text but the equations may be hand written if you prefer since the equation editor for Word is primative and inconvenient to use.

This term paper will carry 15% of the grade for the course and IProf. Wolfs will grade all the term papers. Possible starting references for most of the topics mentioned are "Scientific American" or "Physics Today" and the web. The problem you will encounter is that such starting references are too elementary for Physics 235W, therefore you will need to look at advanced reference texts on your topic. Check with the Librarian in the POA Library if you need assistance in locating references. List the references that you used for your paper. The final version of this paper must be handed in by Wednesday November 25, 2020. Students must submit their first full draft of the Term Paper to a Writing Fellow at the College Writing center to evaluate the clarity of message, and adherance to accepted norms of language and format. The first draft, signed by the Writing Fellow who read this draft, must be submitted with the final paper.

In summary, the following steps must be taken:

  1. Discuss your proposed topic with Prof. Wolfs to ensure that the scope and topic are appropiate for Physics 235. You must submit a written proposal of the topic to be covered by Friday October 29, 2021, at noon.
  2. Meet with a Writing Fellow of College Writing Center to discuss your first draft of the term paper. The Writing Fellows will provide me with an email that they have talked with you and a summary of their comments.. The Writing and Speaking Center will be offering appointments through the Zoom platform for the fall semester. Students can view the schedule and make an appointment on the Writing Ceneter's scheduling website. If you have any questions related to the services offered by the writing center, you can email the office at
  3. Submit the revised final version of your final paper (in pdf format) by Wednesday November 24, 2021, at noon. The pdf file you submit should be named FinalPaperPhy235XXYYYYYYYY.pdf where XX is your last name and YYYYYYYY is your student id number. You must also submit your first draft (in pdf format). This pdf file should be named FirstDraftPhy235XXYYYYYYYY.pdf where XX is your last name and YYYYYYYY is your student id number. Both files must be submitted using this dropbox link.

The grading matrix that will be used to evaluate the final paper can be found on the Download section of the PHY 235W webpages or can be accessed via this link.

Term Paper.

Write about a topic related to classical mechanics.