Due Friday, September 10, 12:50 pm in class.
Reading: Before you start doing this homework set, read the relevant sections from chapter
1 of Marion and Thornton which we covered in class, namely: 1.9
, 1.10
, 1.11
, 1.12
, 1.13
,
1.14
, 1.15
, 1.16
and 1.17
. Skip any formulas which involve the rotation matrices λ ij discussed in the earlier sections 1.3-1.8.
Please make a note on your homework how long it took you to complete the homework.
Problem 1. Velocity and acceleration.
Problem 1-10 from Marion&Thornton. Derive also the equation of the particle’s trajectory. What kind of a curve is this?
Problem 2. Solving vector equations.
Problem 1-13 from Marion&Thornton.
Problem 3. Proving vector identities.
Problem 1-23 from Marion&Thornton.
Hint: use any method you like, not necessarily ǫ ijk notation. For example, you are allowed to make use of (1.82) which we proved in class.
Problem 4. Simple integration.
Problem 1-34 from Marion&Thornton.
Problem 5. Gauss’ law.
(Note added 09/09: I will accept solutions for this problem until
Monday 09/13.) Problem 1-36 from Marion&Thornton. Obtain the result in two different ways: by direct integration and by applying Gauss’ law.
Problem 6. Stokes’s theorem.
(Note added 09/09: I will accept solutions for this problem until Monday 09/13.) Problem 1-38 from Marion&Thornton. Obtain the result in two different ways: by direct integration and by applying Stokes’s theorem.
Problem 7. Analytic geometry.
Problem 1-39 from Marion&Thornton.
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