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Classical Mechanics Homework Assignment #14, due by 9 am Friday November 18 to Krishna’s office Lab 2 3255.

1. 9.16. (see Notes for hint and “optional” extension)
2. 9.19 (see Notes)
3. 9.29 (see Notes)
4. 11.6
5. 11.9
6. 11.25 (see Notes)

Notes

• For problem 9.16, you should find x(t) = Ae^Ωt + Be^-Ωt where A and B are arbitrary constants. For an optional extension to this problem that would make for a very nice quiz or exam problem, try this: Assume the distance from the center of the rod out to its edge is L. Assume that at t = 0, x = 0 (the bead is at the pivot point) and v = v0. Determine the amount of time it takes for the bead to reach the end of the rod from its starting point. Consider (though not necessary to actually carry out!) how you might do this from the inertial frame.
• For problem 9.19, the answer in the back is too brief to be useful, as it completely omits adequate discussion of the centrifugal and Coriolis forces.
• For problem 9.29, you may use Eq. (9.73) without deriving it. If you have time, it’s a good opportunity to practice the method used in section 9.8.
• For problem 11.25, you may need to look up the formula for the determinant of a 3×3 matrix. If you do need to look it up, pay attention to its structure. It should look very familiar – does anything cross your mind (hope this is a productive question)? To solve for the eigenvalues, you will wind up with an equation that is cubic in ω². There are a number of cool ways to solve a cubic equation – see if you have time to learn one that is relevant to solving this problem. Otherwise, you can use MMA to solve this for you.

The Equity & Inclusion Council will have a Community Forum for its recommendations for a Strategic Equity Plan on Wednesday November 16 from 3:15 – 5 pm in Purce Hall Lecture Hall 1.

From our Syllabus, our first Program Learning Goal is to “Interrogate how issues of power, identity, privilege, and equity intersect with the teaching, learning, and practice of math and science.” Several of the themes in the Equity Council’s Plan will sound familiar to themes we have discussed in our program.

Please note the following changes for Monday November 14:

• No changes to Multivariable & Vector Calculus: class still meets at 9 in Sem 2 D3105.
• Krishna will be available for regular open hours in Sem 2 D3105 from 11 – 12:20.
• Classical Mechanics meets at 12:30 in CAL West, not in Sem 2 D3105.

You can access the Week 8 Classical Mechanics Reading Response below.

• Part 1 due Mon. Nov. 14 by 9am
• Part 2 due Thu. Nov. 17 by 9am

• CM: Taylor 9.6-9.10, 11.1-11.3; 11.4-11.7
• DE: Check WAMAP
• MVVC: Check WAMAP
• Seminar: Why Race Matters in Physics Class

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.

As mentioned in class, you can find the Academic Statement Workshop completed on Wed. Nov. 9 below. For completeness, the first Academic Statement Workshop is also posted.

• Academic Statement Workshop 1 (10/26/16)
• Academic Statement Workshop 2 (11/9/16)

Here is the quiz that was give in Week 7 on Tue. Nov. 8.

Classical Mechanics Homework Assignment #12, due by 6 pm Thursday November 10 to Krishna’s office Lab 2 3255 (note that campus is closed on Fri. Nov. 11 in honor of Veteran’s Day). All problems from Taylor except as indicated.

1. 8.7
2. 8.9
3. 8.18
4. 8.20
5. 8.29
6. 8.30

Notes

• 8.29 seems unphysical, and perhaps in the given context it is. However, radioactive decay can result in the sudden loss of one charged particle (proton) from a nucleus, which amounts (classically) to the same problem.