Advanced Classical Mechanics PHYS 331 Fall 2007
Homework Assignment #1
(due: Wednesday, August 29, 9 am)
1. Inertial Frames: Taylor 1.26 (5P)
2. Angular Momentum: Taylor 1.34 (5P)
3. Newton’s Second Law: Taylor 1.40 (6P)
Additional Hint: To ensure that r2is monotonically increasing look at d
dtr2.
4. Mathematica Lab: Finish the mathematica lab from Friday, Aug. 24. Hand in
a print out of your saved session. (6P)
5. Skateboard: Taylor problems 1.50 and 1.51
Notice that the DE (1.51) is equivalent to the pendulum. You might remember from
PHYS 211 Lab that you compared the approximate period Twith the numerical Tfor
two different starting angles. In this problem you compare the complete motion. Notice
also if the nonlinearity makes Tsmaller or larger. (6P)
Hint: Use for Taylor 1.50 phi0 = 20 Pi / 180
6. Air Resistance: Use mathematica to make your own Fig. (2.10) (6P)
Hint: You will need ParametricPlot and NDSolve. To get information on these com-
mands click on the Help-button on the right of the menue bar. Using HelpBrowser search
for NDSolve and expand the “Further Examples” at the end of the page by clicking on
the triangle. Then expand the examples for the “Ordinary Differential Equations” by
double clicking on the right blue square bracket. In there you find even how to get the
parametric plot for a numerical solution of NDSolve.
7. Ball in Glycerin Taylor problem 2.10 (5P)
Hint: The buoyant force of the ball bearing is ρglycVball g.
8. Rocket Taylor problem 3.11 (6P)
9. Center of Mass: Taylor problems 3.18 & 3.20 (5P)