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Physics 8.012: Mechanics I Problem Set 8, Exercises of Classical Physics

University of AllahabadClassical Physics

A problem set from the mit physics 8.012: mechanics i course, fall term 2008. It includes collaboration policies, reading assignments, and ten problems with solutions not to be copied. The problems cover topics such as moments of inertia, rectangular symmetry, and euler's disk. Students are encouraged to discuss problems with each other but must write up their own solutions. Violations of the collaboration policy may result in disciplinary action.

Typology: Exercises

2011/2012

Uploaded on 08/12/2012

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Physics 8.012: Physics (Mechanics) I Fall Term 2008
PROBLEM SET 8
Collaboration policy: You are encouraged to freely discuss homework problems with other 8.012
students and teaching staff. However, you must write up your solutions completely on your
own—do not simply copy solutions from other students. You are forbidden from consulting
solutions from previous years or from the web. Violations of this policy may result in
disciplinary action.
Reading: Kleppner & Kolenkow, Chapter 7
0. Collaboration and discussion. Please list the names of all the students with whom you
discussed these homework problems. Also be sure to write down your name and recitation
section clearly on the first page.
1. Kleppner & Kolenkow, Problem 6.33 [10 points]
2. Kleppner & Kolenkow, Problem 6.39 [10 points]
3. Kleppner & Kolenkow, Problem 6.40 [10 points]
4. Kleppner & Kolenkow, Problem 6.41 [10 points]
5. Kleppner & Kolenkow, Problem 7.2 [10 points]
6. Kleppner & Kolenkow, Problem 7.3 [10 points]
7. Kleppner & Kolenkow, Problem 7.4 [10 points]
Continued on next page...
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Physics 8.012: Physics (Mechanics) I Fall Term 2008 PROBLEM SET 8 Collaboration policy: You are encouraged to freely discuss homework problems with other 8. students and teaching staff. However, you must write up your solutions completely on your own—do not simply copy solutions from other students. You are forbidden from consulting solutions from previous years or from the web. Violations of this policy may result in disciplinary action. Reading: Kleppner & Kolenkow, Chapter 7

  1. Collaboration and discussion. Please list the names of all the students with whom you discussed these homework problems. Also be sure to write down your name and recitation section clearly on the first page.
  2. Kleppner & Kolenkow, Problem 6.33 [10 points]
  3. Kleppner & Kolenkow, Problem 6.39 [10 points]
  4. Kleppner & Kolenkow, Problem 6.40 [10 points]
  5. Kleppner & Kolenkow, Problem 6.41 [10 points]
  6. Kleppner & Kolenkow, Problem 7.2 [10 points]
  7. Kleppner & Kolenkow, Problem 7.3 [10 points]
  8. Kleppner & Kolenkow, Problem 7.4 [10 points] Continued on next page...
  1. Rectangular Symmetry. [15 points] A flat, uniform rectangle with sides of length a and b is at rest in free space (there are initially no external forces acting). You strike two opposite corners with equal and opposite forces F� as indicated for a short time period Δt. (a) [5 pts] Calculate the moments of inertia of the rectangle about horizontal (ˆx) and vertical (ˆy) axes passing through its center of mass. Note that this does not require calculating the moment of inertia tensor. Verify your answers by showing that these moments of inertia satisfy the perpendicular axis theorem, Ix + Iy = Iz , where Iz is the moment of inertia about an axis coming out of the page (ˆz) through the center of mass (which you should also calculate). (b) [10 pts] Calculate the spin vector (ω� ) and angular momentum vector (L�^ ) immediately after the strike. Show that these are not parallel, and that the spin vector points along the opposite diagonal from where the forces were applied if a =� b. Continued on next page...