Matter and Interactions
4th Edition
ISBN: 9781118875865
Author: Ruth W. Chabay, Bruce A. Sherwood
Publisher: WILEY
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Chapter 3, Problem 26P
To determine
The speed of the sun after one day.
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Question 3 of 17
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L
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0.5/
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
45
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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 3 Solutions
Matter and Interactions
Ch. 3.2 - A star exerts a gravitational force of magnitude 4...Ch. 3.2 - At a particular instant Ganymede and Europa, two...Ch. 3.3 - A moving electron passes near the nucleus of a...Ch. 3.4 - A 60 kg person stands on the Earth’s surface. (a)...Ch. 3.5 - Prob. 5CPCh. 3.7 - A moving electron passes near the nucleus of a...Ch. 3.8 - Look at the periodic table on the inside front...Ch. 3.11 - A system consists of a 2 kg block moving with...Ch. 3.12 - You and a friend each hold a lump of wet clay....Ch. 3.14 - Suppose you have four stars with given initial...
Ch. 3 - Prob. 1QCh. 3 - Why is the value of the constant g different on...Ch. 3 - You hold a tennis ball above your head, then open...Ch. 3 - Suppose that you are going to program a computer...Ch. 3 - A bullet traveling horizontally at a very high...Ch. 3 - You hang from a tree branch, then let go and fall...Ch. 3 - One kind of radioactivity is called “alpha decay.”...Ch. 3 - A bowling ball is initially at rest. A Ping-Pong...Ch. 3 - The windshield of a speeding car hits a hovering...Ch. 3 - At a particular instant the magnitude of the...Ch. 3 - Masses M and m attract each other with a...Ch. 3 - A 3 kg ball and a 5 kg ball are 2 m apart, center...Ch. 3 - The mass of the Earth is 6 × 1024 kg, and the mass...Ch. 3 - A star exerts a gravitational force of magnitude...Ch. 3 - A planet exerts a gravitational force of magnitude...Ch. 3 - A moon orbits a planet in the xy plane, as shown...Ch. 3 - The mass of the Sun is 2 × 1030 kg, and the mass...Ch. 3 - Measurements show that Jupiter’s gravitational...Ch. 3 - Prob. 19PCh. 3 - A planet of mass 4 × 1024 kg is at location...Ch. 3 - The mass of Mars is 6.4 × 1023 kg and its radius...Ch. 3 - At what height above the surface of the Earth is...Ch. 3 - Calculate the approximate gravitational force...Ch. 3 - A steel ball of mass m falls from a height h onto...Ch. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - (a) In outer space, far from other objects, block...Ch. 3 - In June 1997 the NEAR spacecraft (“Near Earth...Ch. 3 - Figure 3.60 shows two positively charged objects...Ch. 3 - Figure 3.61 shows two negatively charged objects...Ch. 3 - The left side of Figure 3.62 shows a proton and an...Ch. 3 - An alpha particle contains two protons and two...Ch. 3 - A proton and an electron are separated by 1 ×...Ch. 3 - Prob. 38PCh. 3 - Use data from the inside back cover to calculate...Ch. 3 - At a particular instant a proton exerts an...Ch. 3 - Prob. 41PCh. 3 - At a certain instant object 1 is at location ⟨10,...Ch. 3 - The mass of the Earth is 6 × 1024 kg, the mass of...Ch. 3 - The mass of the Sun is 2 × 1030 kg, the mass of...Ch. 3 - Two rocks are tied together with a string of...Ch. 3 - A tennis ball of mass 0.06 kg traveling at a...Ch. 3 - In outer space, far from other objects, two rocks...Ch. 3 - When they are far apart, the momentum of a proton...Ch. 3 - You and a friend each hold a lump of wet clay....Ch. 3 - A car of mass 2800 kg collides with a truck of...Ch. 3 - A bullet of mass 0.105 kg traveling horizontally...Ch. 3 - In outer space a small rock with mass 5 kg...Ch. 3 - Two rocks collide in outer space. Before the...Ch. 3 - In outer space two rocks collide and stick...Ch. 3 - Prob. 58PCh. 3 - Prob. 60PCh. 3 - A space station has the form of a hoop of radius...
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