Physics
10th Edition
ISBN: 9781118486894
Author: David Young, Shane Stadler
Publisher: WILEY
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Chapter 1, Problem 12FC
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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?
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 1 Solutions
Physics
Ch. 1.3 - 1. (a) Is it possible for two quantities to have...Ch. 1.3 - 2. You can always add two numbers that have the...Ch. 1.3 - 3. The following table lists four variables, along...Ch. 1.3 - Prob. 4CYUCh. 1.5 - 5. Which of the following statements, if any,...Ch. 1.6 - 6. Two vectors and are added together to give a...Ch. 1.6 - 7. Can two nonzero perpendicular vectors be added...Ch. 1.6 - 8. Can three or more vectors with unequal...Ch. 1.6 - 9. In preparation for this question, review...Ch. 1.6 - 10. Vectors , , and satisfy the vector equation ,...
Ch. 1.6 - Prob. 11CYUCh. 1.7 - Prob. 12CYUCh. 1.7 - Prob. 13CYUCh. 1.7 - Prob. 14CYUCh. 1.7 - Prob. 15CYUCh. 1.7 - Prob. 16CYUCh. 1.7 - Prob. 17CYUCh. 1.8 - Prob. 18CYUCh. 1 - Prob. 1FCCh. 1 - 2. How is the magnitude R of the resultant vector ...Ch. 1 - 5. The first drawing shows three displacement...Ch. 1 - 6. The first drawing shows the sum of three...Ch. 1 - 8. A person is jogging along a straight line, and...Ch. 1 - 11. A person drives a car for a distance of 450.0...Ch. 1 - Prob. 12FCCh. 1 - Prob. 15FCCh. 1 - Prob. 17FCCh. 1 - Prob. 18FCCh. 1 - 1. A student sees a newspaper ad for an apartment...Ch. 1 - 2. Bicyclists in the Tour de France reach speeds...Ch. 1 - 3. Vesna Vulovic survived the longest fall on...Ch. 1 - 4. Suppose a man’s scalp hair grows at a rate of...Ch. 1 - Prob. 5PCh. 1 - Prob. 6PCh. 1 - Prob. 7PCh. 1 - 8. The CGS unit for measuring the viscosity of a...Ch. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - 13. A highway is to be built between two towns,...Ch. 1 - Prob. 14PCh. 1 - Prob. 15PCh. 1 - 16. The drawing shows a person looking at a...Ch. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Prob. 19PCh. 1 - Prob. 20PCh. 1 - 21. Three deer, A, B, and C, are grazing in a...Ch. 1 - 22. An aerialist on a high platform holds on to a...Ch. 1 - Prob. 23PCh. 1 - Prob. 24PCh. 1 - 25. Consider the following four force...Ch. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Prob. 30PCh. 1 - Prob. 31PCh. 1 - 32. A jogger travels a route that has two parts....Ch. 1 - Prob. 33PCh. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - Prob. 36PCh. 1 - Prob. 37PCh. 1 - Prob. 38PCh. 1 - Prob. 39PCh. 1 - Prob. 40PCh. 1 - Prob. 41PCh. 1 - Prob. 42PCh. 1 - Prob. 43PCh. 1 - Prob. 44PCh. 1 - Prob. 45PCh. 1 - Prob. 46PCh. 1 - Prob. 47PCh. 1 - Prob. 48PCh. 1 - Prob. 49PCh. 1 - Prob. 50PCh. 1 - Prob. 51PCh. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 54PCh. 1 - Prob. 55PCh. 1 - Prob. 56PCh. 1 - Prob. 57APCh. 1 - Prob. 58APCh. 1 - Prob. 59APCh. 1 - Prob. 60APCh. 1 - Prob. 61APCh. 1 - Prob. 62APCh. 1 - Prob. 63APCh. 1 - Prob. 64APCh. 1 - Prob. 65APCh. 1 - Prob. 66APCh. 1 - Prob. 67APCh. 1 - Prob. 68APCh. 1 - Prob. 69AP
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