Classical Mechanics Homework Assignment #13

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Classical Mechanics Homework Assignment #13, due by 5 pm Monday November 14 to Krishna’s office Lab 2 3255.

  1. 9.2
  2. 9.3
  3. 9.5
  4. 9.8 (see Notes)
  5. 9.9 (see Notes)
  6. 9.10 (see Notes)

Notes

  • For problems 9.8 and 9.9, recall that the Coriolis and centrifugal forces are given by Eqs. (9.35) and (9.36). I think you will find Figure 9.15 very useful. In that figure, x (which points east) is into the page at point O. The angle θ is the colatitude. Problem 9.8 gives you practice with directions as described in Figure 9.15 and using the cross product (and right hand rule). For problem 9.9, make sure you can use Figure 9.15 to justify why the angle between v0 and Ω is π/2 – θ. Finally, recall that for vectors A and B, the magnitude of the vector cross product of A and B is given by |A||B| sin α, where α is the (smaller) angle between A and B.
  • Problem 9.10 offers an opportunity to study the derivation of Eq. (9.34) starting from Eq. (9.31) and using Eq. (9.30). For the situation described in problem 9.10, nothing changes in the steps between (9.31) and (9.32). In Eq. (9.32), however, is where the non-constant nature of Ω matters because of the d/dt.