
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Question
Chapter 12, Problem 76PQ
(a)
To determine
The time when the object is momentarily not rotating.
(b)
To determine
Whether the object will begin to turn clockwise or counterclockwise after briefly stopping.
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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
Sketch the harmonic.
Chapter 12 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 12.1 - Figure 12.5 shows two rotating objects. Indicate...Ch. 12.2 - Prob. 12.2CECh. 12.2 - Prob. 12.3CECh. 12.2 - Prob. 12.4CECh. 12.2 - Prob. 12.5CECh. 12.5 - For each exercise shown in Figure 12.22, how does...Ch. 12 - Often, we model the Moon as a particle in a...Ch. 12 - Suppose a satellite orbits the Earth such that it...Ch. 12 - Prob. 3PQCh. 12 - Prob. 4PQ
Ch. 12 - A ceiling fan is rotating counterclockwise with a...Ch. 12 - As seen from above the Earths North Pole, the...Ch. 12 - A rotating objects angular position is given by...Ch. 12 - A rotating objects angular position is given by...Ch. 12 - Jupiter rotates about its axis once every 9 hours...Ch. 12 - Prob. 10PQCh. 12 - Prob. 11PQCh. 12 - Prob. 12PQCh. 12 - Prob. 13PQCh. 12 - Prob. 14PQCh. 12 - Prob. 15PQCh. 12 - A disk rolls up an inclined plane as shown in...Ch. 12 - Jeff, running outside to play, pushes on a...Ch. 12 - A potters wheel rotating at 240 rev/min is...Ch. 12 - Friction in an old clock causes it to lose 1...Ch. 12 - A wheel starts from rest and in 12.65 s is...Ch. 12 - Prob. 21PQCh. 12 - Starting from rest, a wheel reaches an angular...Ch. 12 - A potters wheel is rotating with an angular...Ch. 12 - The angular speed of a wheel is given by (t) =...Ch. 12 - Prob. 25PQCh. 12 - Prob. 26PQCh. 12 - An electric food processor comes with many...Ch. 12 - Prob. 28PQCh. 12 - A bicyclist is testing a new racing bike on a...Ch. 12 - Prob. 30PQCh. 12 - A disk is initially at rest. A penny is placed on...Ch. 12 - Prob. 32PQCh. 12 - Consider again the two wind turbines in Problem...Ch. 12 - Consider again the two wind turbines in Problem...Ch. 12 - In testing an automobile tire for proper...Ch. 12 - Prob. 36PQCh. 12 - A merry-go-round at a childrens park begins at...Ch. 12 - A wheel rotating at a constant rate of 1850...Ch. 12 - Why are doorknobs placed on the edge opposite the...Ch. 12 - Prob. 40PQCh. 12 - Prob. 41PQCh. 12 - Prob. 42PQCh. 12 - A wheel of inner radius r1 = 15.0 cm and outer...Ch. 12 - A uniform plank 6.0 m long rests on two supports,...Ch. 12 - Prob. 45PQCh. 12 - Prob. 46PQCh. 12 - Prob. 47PQCh. 12 - Prob. 48PQCh. 12 - Prob. 49PQCh. 12 - Prob. 50PQCh. 12 - Prob. 51PQCh. 12 - Given a vector A=4.5+4.5j and a vector B=4.5+4.5j,...Ch. 12 - A square plate with sides 2.0 m in length can...Ch. 12 - Prob. 54PQCh. 12 - A disk with a radius of 4.5 m has a 100-N force...Ch. 12 - Disc jockeys (DJs) use a turntable in applying...Ch. 12 - Prob. 57PQCh. 12 - Prob. 58PQCh. 12 - A wheel initially rotating at 85.0 rev/min...Ch. 12 - Prob. 60PQCh. 12 - A centrifuge used for training astronauts rotating...Ch. 12 - Problems 62 and 63 are paired. 62. C A disk is...Ch. 12 - Prob. 63PQCh. 12 - A potters wheel rotates with an angular...Ch. 12 - Prob. 65PQCh. 12 - Prob. 66PQCh. 12 - Prob. 67PQCh. 12 - Lara is running just outside the circumference of...Ch. 12 - The propeller of an aircraft accelerates from rest...Ch. 12 - A ball rolls to the left along a horizontal...Ch. 12 - Three forces are exerted on the disk shown in...Ch. 12 - Consider the disk in Problem 71. The disks outer...Ch. 12 - Prob. 73PQCh. 12 - Prob. 74PQCh. 12 - Prob. 75PQCh. 12 - Prob. 76PQCh. 12 - Prob. 77PQCh. 12 - Prob. 78PQCh. 12 - Prob. 79PQCh. 12 - Prob. 80PQCh. 12 - If the rod in Problem 79 is in equilibrium, what...Ch. 12 - As a compact disc (CD) spins clockwise as seen...Ch. 12 - A disk-shaped machine part has a diameter of 40.0...Ch. 12 - Prob. 84PQ
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