
Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 15.4, Problem 1bTH
To determine
The change in velocity vector,
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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?
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 15 Solutions
Tutorials in Introductory Physics
Ch. 15.1 - Describe the motion. During which periods of time,...Ch. 15.1 - Find the object’s instantaneous velocity at each...Ch. 15.1 - For each of the following intervals, find the...Ch. 15.1 - In which of the cased from part c, if any, is the...Ch. 15.1 - In the interval from t=0s to t=6s , does the...Ch. 15.1 - In the small box on the graph above is a portion...Ch. 15.1 - Next, we expand the section of the previous graph...Ch. 15.1 - All three graphs are representations of the same...Ch. 15.1 - Suppose that the object is speeding up. Which of...Ch. 15.1 - Suppose that the object is slowing down. Which of...
Ch. 15.1 - Describe how you could use these devices to...Ch. 15.1 - Describe how you could use these devices to...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - In each of the following exercises, a motion will...Ch. 15.2 - There are several answers for most of the...Ch. 15.2 - There are several answers for most of the...Ch. 15.2 - There are several answers for most of the...Ch. 15.3 - A ball rolls up, then down an incline. Sketch an...Ch. 15.3 - Sketch x versus t, v versus t, and a versus t...Ch. 15.3 - Sketch x versus t, v versus t, and a versus t...Ch. 15.3 - Sketch x versus t, v versus t, and a versus t...Ch. 15.3 - Describe the motion of an object: For which the...Ch. 15.3 - Describe the motion of an object: b. For which the...Ch. 15.3 - Describe the motion of an object: c. For which the...Ch. 15.3 - Describe the motion of an object: d. For which the...Ch. 15.3 - Two carts roll toward each other on a level table....Ch. 15.3 - Two carts roll toward each other on a level table....Ch. 15.3 - Two carts roll toward each other on a level table....Ch. 15.3 - In this problem, a Cart moves in various ways on a...Ch. 15.3 - In this problem, a Cart moves in various ways on a...Ch. 15.3 - In this problem, a Cart moves in various ways on a...Ch. 15.3 - Carts A and B move along a horizontal track. The...Ch. 15.3 - Carts A and B move along a horizontal track. The...Ch. 15.3 - Carts A and B move along a horizontal track. The...Ch. 15.3 - Carts A and B move along a horizontal track. The...Ch. 15.3 - Two cars, C and D, travel in the same direction on...Ch. 15.3 - Two cars, P and Q, travel in the same direction on...Ch. 15.3 - Two cars, P and Q, travel in the same direction on...Ch. 15.4 - Prob. 1aTHCh. 15.4 - Prob. 1bTHCh. 15.4 - Describe how you would determine the acceleration...Ch. 15.4 - Copy vG and vH (placed “tailtotail”) in the space...Ch. 15.4 - Generalize your results above and from tutorial to...Ch. 15.4 - For each instant, state whether the object is...Ch. 15.4 - The diagram at right illustrates how the...Ch. 15.4 - For each of the instants 14, compare your...Ch. 15.4 - Choose a point about 1/8th of the way around the...Ch. 15.4 - Prob. 3bTHCh. 15.4 - How would you characterize the direction of v as...Ch. 15.4 - Each of the following statements in incorrect....Ch. 15.4 - On the diagram at right, draw vectors that...Ch. 15.4 - On the diagram at right, draw vectors that...Ch. 15.4 - Draw arrows on the diagram at points AG to...Ch. 15.4 - Next to each of the labeled points, state whether...Ch. 15.4 - Draw arrows on the diagram below to show the...Ch. 15.4 - On the diagram at right, draw velocity vectors for...Ch. 15.4 - On the diagram at right, draw the acceleration...Ch. 15.4 - How does the magnitude of the acceleration at E...Ch. 15.5 - Reference frame of boat B: Complete the upper...Ch. 15.5 - Reference frame of boat A: Complete the diagram at...Ch. 15.5 - Is the speed of the kayak in the frame of boat A...Ch. 15.5 - Rank the following quantities in order of...Ch. 15.5 - A third riverboat, boat C, moves downstream so as...Ch. 15.5 - Prob. 2aTHCh. 15.5 - A car, a truck, and a traffic cone are on a...Ch. 15.5 - The relationship vcar,cone=vcar,truck+vtruck,cone...Ch. 15.5 - Car P moves to the west with constant speed v0...Ch. 15.5 - Car P moves to the west with constant speed v0...Ch. 15.5 - Car P moves to the west with constant speed v0...Ch. 15.5 - Car P moves to the west with constant speed v0...Ch. 15.5 - Car P moves to the west with constant speed v0...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...Ch. 15.5 - A bicycle coasts up a hill while a car drives up...
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