EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 10, Problem 3CC
To determine
Whether every world, with a liquid-rich iron core, contain a magnetic dynamo or not.
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Question 3 of 17
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L
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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?
xcom
L
2
(b) What is the y coordinate of the system's center of mass?
Ycom
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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 10 Solutions
EBK LOOSE-LEAF VERSION OF UNIVERSE
Ch. 10 - Prob. 1CCCh. 10 - Prob. 2CCCh. 10 - Prob. 3CCCh. 10 - Prob. 4CCCh. 10 - Prob. 5CCCh. 10 - Prob. 1CLCCh. 10 - Prob. 1QCh. 10 - Prob. 2QCh. 10 - Prob. 3QCh. 10 - Prob. 4Q
Ch. 10 - Prob. 5QCh. 10 - Prob. 6QCh. 10 - Prob. 7QCh. 10 - Prob. 8QCh. 10 - Prob. 9QCh. 10 - Prob. 10QCh. 10 - Prob. 11QCh. 10 - Prob. 12QCh. 10 - Prob. 13QCh. 10 - Prob. 14QCh. 10 - Prob. 15QCh. 10 - Prob. 16QCh. 10 - Prob. 17QCh. 10 - Prob. 18QCh. 10 - Prob. 19QCh. 10 - Prob. 20QCh. 10 - Prob. 21QCh. 10 - Prob. 22QCh. 10 - Prob. 23QCh. 10 - Prob. 24QCh. 10 - Prob. 25QCh. 10 - Prob. 26QCh. 10 - Prob. 27QCh. 10 - Prob. 28QCh. 10 - Prob. 29QCh. 10 - Prob. 30QCh. 10 - Prob. 31QCh. 10 - Prob. 32QCh. 10 - Prob. 33QCh. 10 - Prob. 34QCh. 10 - Prob. 35QCh. 10 - Prob. 36QCh. 10 - Prob. 37QCh. 10 - Prob. 38QCh. 10 - Prob. 39QCh. 10 - Prob. 40QCh. 10 - Prob. 41QCh. 10 - Prob. 42QCh. 10 - Prob. 43Q
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