Classical Mechanics Exam 1

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In case you would like to get started on exam revisions early, here is Classical Mechanics Exam 1.

Guidelines:

  • Revisions due within one week of receiving back exam.
  • Revisions should be presented in the form of a Public Solution: either typeset or narrative. Typeset solutions should be printed out for submission; links to narrative solutions should be sent to Krishna
  • Students may choose to revise any exam questions they like, but must revise the entire question, with the exception of bonus/challenge parts (though you are encouraged to do those as well).
  • Revisions to multiple choice/matching/ranking/fill in the blank type questions must include a full explanation (simply choosing the correct response is insufficient).
  • Revised solutions must be perfectly clear, complete, and correct to be considered.
  • You may use any resource to prepare your revised solution. HOWEVER…
    • …Revised solutions must display your personal understanding of the material. This means that you must personally understand every step that you write down, and individually produce the content of your final submitted revised solution.

Classical Mechanics Homework Assignment #9

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Classical Mechanics Homework Assignment #9, due by 5 pm Monday October 31 to Krishna’s office Lab 2 3255. If you attend the guest lecture on Mon. 10/31 from 3 – 5, assignment can be submitted directly to Krishna Tuesday morning. All problems from Taylor except as indicated. * indicates problem where MMA might be helpful.

  1. 7.8
  2. 7.11
  3. 7.14
  4. 7.15
  5. 7.16
  6. 7.18

Notes: Answering the “main” question in problems 7.14, 7.15, 7.16, and 7.18 can be done using methods from Newtonian mechanics. The point of using Lagrangian mechanics is to give you practice with this new method on familiar systems. If have enough time, you might find it valuable to solve these problems using both Lagrangian mechanics and Newtonian mechanics.

Feynman Lectures on Principle of Least Action

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A PSAM student asked for some further resources on the variational principle. One of my go to sources for alternative explanations are the Feynman Lectures on Physics, which can be read freely online. There is a discussion of the least action principle: Lecture 19 The Principle of Least Action. Given what you are likely to have studied, I recommend stopping when the discussion turns to least action for the relativistic case. I’m not sure the discussion will help you solve problems, but I think it could enhance your conceptual understanding.

Classical Mechanics Homework Assignment #8

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Classical Mechanics Homework Assignment #8, due by 5 pm Monday October 24 to Krishna’s office Lab 2 3255. All problems from Taylor except as indicated. * indicates problem where MMA might be helpful.

  1. 6.4
  2. 6.12
  3. 6.15
  4. 6.17
  5. 6.19
  6. 6.26

Notes:

  • For 6.4, review the discussion on p. 217. This is a famous problem with a famous result; you might already have done a version of this proof in Calculus I as an example of optimization. You won’t use variational methods (other than what is built into Fermat’s Principle already) but you may find yourself using multivariable calculus (specifically partial derivatives). 
  • For 6.12, make sure to find the actual arsinh function in terms of y and arbitrary integration constants.
  • For 6.15, you could use the result of example 6.2 and some cleverness, or you could use this is an opportunity to practice the calculations associated with that famous example. Your choice, or both.
  • For 6.19, the area A of the surface of revolution formed by y = y(x) as described is given by the integral of 2πy ds (you can find the explanation of this in a calculus text).
  • In problem 6.26, take advantage of this opportunity to solidify your understanding of the steps that take you from equation (6.10) through (6.13).