Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 17, Problem 18QAP
To determine
Reason why dark matter does not collapse.
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Question 3 of 17
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In the figure above, three uniform thin rods, each of length L, form
an inverted U. The vertical rods each have a mass m; the horizontal
rod has a mass 3m.
NOTE: Express your answer in terms of the variables given.
(a) What is the x coordinate of the system's center of mass?
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(b) What is the y coordinate of the system's center of mass?
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Chapter 17 Solutions
Understanding Our Universe
Ch. 17.1 - Prob. 17.1CYUCh. 17.2 - Prob. 17.2CYUCh. 17.3 - Prob. 17.3CYUCh. 17.4 - Prob. 17.4CYUCh. 17.5 - Prob. 17.5CYUCh. 17 - Prob. 1QAPCh. 17 - Prob. 2QAPCh. 17 - Prob. 3QAPCh. 17 - Prob. 4QAPCh. 17 - Prob. 5QAP
Ch. 17 - Prob. 6QAPCh. 17 - Prob. 7QAPCh. 17 - Prob. 8QAPCh. 17 - Prob. 9QAPCh. 17 - Prob. 10QAPCh. 17 - Prob. 11QAPCh. 17 - Prob. 12QAPCh. 17 - Prob. 13QAPCh. 17 - Prob. 14QAPCh. 17 - Prob. 15QAPCh. 17 - Prob. 16QAPCh. 17 - Prob. 17QAPCh. 17 - Prob. 18QAPCh. 17 - Prob. 19QAPCh. 17 - Prob. 20QAPCh. 17 - Prob. 21QAPCh. 17 - Prob. 22QAPCh. 17 - Prob. 23QAPCh. 17 - Prob. 24QAPCh. 17 - Prob. 25QAPCh. 17 - Prob. 26QAPCh. 17 - Prob. 27QAPCh. 17 - Prob. 28QAPCh. 17 - Prob. 29QAPCh. 17 - Prob. 30QAPCh. 17 - Prob. 31QAPCh. 17 - Prob. 32QAPCh. 17 - Prob. 33QAPCh. 17 - Prob. 34QAPCh. 17 - Prob. 35QAPCh. 17 - Prob. 36QAPCh. 17 - Prob. 37QAPCh. 17 - Prob. 38QAPCh. 17 - Prob. 39QAPCh. 17 - Prob. 40QAPCh. 17 - Prob. 41QAPCh. 17 - Prob. 42QAPCh. 17 - Prob. 43QAPCh. 17 - Prob. 44QAPCh. 17 - Prob. 45QAP
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