Physics 116B Homework Assignment 3 - Mathematical Methods in Physics, Assignments of Physics

Download Physics 116B Homework Assignment 3 - Mathematical Methods in Physics and more Assignments Physics in PDF only on Docsity! Physics 116B Mathematical Methods in Physics Spring 2005 Homework Assignment #3 Due in Class or Office Hours, Friday, April 22 Please show your work, neatly, on all problems. Please refer to my printed guidelines on presentation of homework solutions. My solutions will be posted on the course web site, http://scipp.ucsc.edu/~johnson/phys116b/phys116b.htm, within a day after the due date. 1. 10.6-3 2. 10.6-5 3. 10.6-7 4. A mass m is located at )0,0,(),,( azyx = . A second mass m is located at )0,,0( a . A third mass m2 is located at )0,,( aa −− . A forth mass m is located at ),0,0( a . a. Find the inertia tensor I from Equation 14 of Section 10.6. b. Diagonalize it to find the principal moments of inertia and the principal axes. 5. Suppose that the uncertainty on a measurement of position is distributed according to ( )2221 53278),( yxyxeyxf ++−⋅= π a. Evaluate the integral ∫ ∫ ∞ ∞− ∞ ∞− ⋅= dxdyyxfxyM xy ),( explicitly by making a transformation of variables to a coordinate system aligned with the error ellipse. Do the work; don’t just use a formula from the textbook. b. Find the measurement uncertainties along the major and minor axes of the error ellipse. c. What angle does the major axis of the ellipse make with the x axis? 6. 12.1-7 7. 12.1-10 8. 12.1-13 9. 12.1-14 10. 12.1-17 11. 12.2-5, 7 and 8 12. 12.2-10 and 11