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244 Chapter 3 Conservation of Momentum
Chapter 4Conservation of Angular Momentum4.1 Angular Momentum In Two Dimensions4.1.1 Angular momentum“Sure, and maybe the sun won’t come up tomorrow.” Of course,the sun only appears to go up and down because the earth spins,so the cliche should really refer to the unlikelihood of the earth’sstopping its rotation abruptly during the night. Why can’t it stop?It wouldn’t violate conservation of momentum, because the earth’srotation doesn’t add anything to its momentum. While Californiaspins in one direction, some equally massive part of India goes theopposite way, canceling its momentum. A halt to Earth’s rotationwould entail a drop in kinetic energy, but that energy could simplybe converted into some other form, such as heat.a / The jumper can’t move hislegs counterclockwise withoutmoving his arms clockwise.(Thomas Eakins.)Other examples along these lines are not hard to find. An atomspins at the same rate for billions of years. A high-diver who isrotating when he comes off the board does not need to make anyphysical effort to continue rotating, and indeed would be unable tostop rotating before he hit the water.These observations have the hallmarks of a conservation law:A closed system is involved. Nothing is making an effort to twistthe earth, the hydrogen atom, or the high-diver. They are isolatedfrom rotation-changing influences, i.e., they are closed systems.Something remains unchanged. There appears to be a numericalquantity for measuring rotational motion such that the total amountof that quantity remains constant in a closed system.245
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Fullerton, Californiawww.lightandma
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Contents0 Introduction and Review0.
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5.5 More About Heat Engines . . . .
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669.11.3 Magnetic Fields by Ampère
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The Mars Climate Orbiter is prepare
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temperatures and with many combinat
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idence that quarks have smaller par
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give clearer explanations.Finally,
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It can also be handy to have a rela
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The prefix centi-, meaning 10 −2
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goes like this:V = 1 3 Ah[1]A = πr
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the notation 10 0 to stand for one,
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calculation, 5.04 cm, was really no
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0.2 Scaling and Order-of-Magnitude
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to many times your own height. The
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g / 1. This plank is as long as it
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the front panels of the three violi
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Correct solution #4: The area of a
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here?” The scientific Mr. Spock w
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1. Don’t even attempt more than o
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Problem 10.mean, however, is define
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(d) Find the person’s acceleratio
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Albert Einstein, and his moustache,
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54 Chapter 0 Introduction and Revie
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a / Portrait of Monsieur Lavoisiera
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1.1.1 Problem-solving techniquesHow
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∆m = 0, where m is the total mass
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different substances will have diff
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c / Left: In a frame of referenceth
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f / Discussion question B.(discusse
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Self-check D.since the derivative o
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ProblemsThe symbols √ , , etc. ar
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difficult? ⊲ Solution, p. 932Key
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Heat energy can be convertedto ligh
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a new form of invisible “mystery
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f / A realistic drawing of Joule’
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numbers. With a purely numerical ap
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of gravity doesn’t change much if
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field. If the plane can start from
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m / Discussion question C.n / A hyd
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88 Chapter 2 Conservation of Energy
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A car drives over a cliff.new frame
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How long does it take to move 1 met
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a / Approximations to thebrachistoc
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a / An ellipse is circle that hasbe
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to deduce the general equation for
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to the mass of the object that inte
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The minimum velocity required for t
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and since sin θ dθ occurs in the
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that is deeper than r. Under the as
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2.3.6 ⋆ Evidence for repulsive gr
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a / A vivid demonstration thatheat
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ture. This is a very good question,
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Three functions with thesame curvat
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This looks like a cosine function,
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Problem 16.13 Anya and Ivan lean ov
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Problem 27.then we’d have U/m =
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37 Two springs with spring constant
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ExercisesExercise 2A: Reasoning wit
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128 Chapter 2 Conservation of Energ
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3.1 Momentum In One Dimensiona / Sy
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eing to the right. The initial mome
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3.1.3 Momentum compared to kinetic
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3.1.4 Collisions in one dimensiong
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could never do that again in a mill
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i / The highjumper’s body passeso
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where x 1 is the mass of the first
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3.1.6 The center of mass frame of r
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The airbag increases ∆tso as to r
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d / Two magnets exert forceson each
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x (m) t (s)10 1.8420 2.8630 3.8040
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3.2.4 Forces between solidsConserva
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Maximum acceleration of a car examp
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Discussion QuestionA Criticize the
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C A pool ball is rebounding from th
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forces, as if the hand were a pair
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This may not sound like an impressi
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stroke are both executed in straigh
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Accelerating a cart example 35If yo
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w / A wedge.x / Archimedes’ screw
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As in the preceding example, we hav
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that have the same frequency is a s
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around until I got this result, sin
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quality factor, Q, is defined as Q
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ight direction to add energy to the
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i / Example 45: a viola withouta mu
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Collapse of the Nimitz Freeway exam
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end up canceling out, however:Q =
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186 Chapter 3 Conservation of Momen
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c / Bullets are dropped and shot at
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the asteroid’s energy and boostin
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coordinate axes. Even though ∆x,
Page 194 and 195: of the three components,∆p x = 0
Page 196 and 197: A useless vector operation example
Page 198 and 199: Solving for the unknowns gives∆x
Page 200 and 201: o / Example 64.p / Adding vectors g
Page 202 and 203: How to generalize one-dimensional e
Page 204 and 205: needed to support the object in fig
Page 206 and 207: The easiest method is the one demon
Page 208 and 209: Incorrect solution #4:(same notatio
Page 210 and 211: The magnitude of the acceleration i
Page 212 and 213: dropped out like a trap door, showi
Page 214 and 215: af / Breaking trail, by WalterE. Bo
Page 216 and 217: know how to integrate with respect
Page 218 and 219: ProblemsThe symbols √ , , etc. ar
Page 220 and 221: Problem 16.Problem 19.resistance.)1
Page 222 and 223: of gravity on Mars.(a) Find the tim
Page 224 and 225: partner force. (a) A swimmer speeds
Page 226 and 227: Problem 45the 0.4-gram masses would
Page 228 and 229: 53 If you walk 35 km at an angle 25
Page 230 and 231: (b) Interpret this equation in the
Page 232 and 233: Problem 71.232 Chapter 3 Conservati
Page 234 and 235: 77 A car accelerates from rest. At
Page 236 and 237: Problem 81.81 Complete example 71 o
Page 238 and 239: ExercisesExercise 3A: Force and Mot
Page 240 and 241: Exercise 3C: Worksheet on Resonance
Page 242 and 243: Exercise 3D: Vectors and MotionEach
Page 246 and 247: An overhead view of apiece of putty
Page 248 and 249: inward toward the hinge will have n
Page 250 and 251: special case, we can choose to visu
Page 252 and 253: j / Two asteroids collide.k / Every
Page 254 and 255: Note that although the factors of 2
Page 256 and 257: Relationship between force and torq
Page 258 and 259: is straight down, which is perpendi
Page 260 and 261: ⊲ All three objects in the figure
Page 262 and 263: aa / Example 10.to either side of e
Page 264 and 265: momentum tells us that L = mrv sin
Page 266 and 267: In the absence of any torque, a rig
Page 268 and 269: Radial acceleration at the surface
Page 270 and 271: The parallel axis theorem example 1
Page 272 and 273: differential. The result isarea ===
Page 274 and 275: of inertia as if the object was smo
Page 276 and 277: h / Moments of inertia of somegeome
Page 278 and 279: 4.3 Angular Momentum In Three Dimen
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Page 282 and 283: manner like this, then the definiti
Page 284 and 285: k / Example 27.torque to the left w
Page 286 and 287: We can also generalize the plane-ro
Page 288 and 289: Problem 1.Problem 6.Problem 8.Probl
Page 290 and 291: 14 (a) The bar of mass m is attache
Page 292 and 293: Problem 22.22 The sun turns on its
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35 The nucleus 168 Er (erbium-168)
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ExercisesExercise 4A: TorqueEquipme
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pesky set of constraints on heat en
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mit more air into the cavity behind
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Pressure of lava underneath a volca
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h / A simplified version of anideal
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for us to construct a simple connec
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For the first time we have an inter
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a / 1. The temperature differencebe
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Carnot engines operating between a
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from A to B, he lets it by, but whe
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B When we run the Carnot engine in
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f / A phase space for a singleatom
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time, the energy sharing is very un
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will the the one that maximizes the
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If the gas is monoatomic, then we k
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5.4.4 The arrow of time, or “this
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5.4.6 Summary of the laws of thermo
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may be in the form of microscopic d
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significant amount of heat to flow
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while the smaller area under the bo
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7 (a) Determine the ratio between t
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338 Chapter 5 Thermodynamics
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end of this book, we’ll even see
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c / As the wave pattern passes the
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the wave move ahead faster and get
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k / Hitting a key on a pianocauses
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Our final result for the speed of t
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care, because the delay is the same
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An easy way to visualize this is in
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can be constructed as a superpositi
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⊲ Looking up the speed of light i
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scientists, to speak of the Big Ban
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6.2 Bounded WavesSpeech is what sep
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d / An uninverted reflection. There
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our intuitive expectation of strong
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valid solutions. In the following s
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j / In the mirror image, theareas o
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m / A pulse bounces backand forth.i
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q / Graphs of loudness versusfreque
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s / Standing waves on a rope. (PSSC
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“cavity” and “neck” parts o
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Problem 5.Problem 8.5 The figure sh
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Problem 16.16 A Fabry-Perot interfe
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c / Newton’s laws do not distingu
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f / The correspondence principlereq
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d / A Galilean version of therelati
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g / Three types of transformations
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system, velocities are always unitl
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p / Apparatus used for the testof r
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sumption, the assumption that it ma
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at rest relative to the water. But
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7.2.4 No action at a distanceThe Ne
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so that Alice can complete her moti
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time into different regions accordi
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position relative to the sun at exa
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7.2.7 ⋆ Four-vectors and the inne
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would depend on the relative veloci
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7.3 DynamicsSo far we have said not
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In this frame, as expected, the sma
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But this whole argument was based o
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meters per second, so converting to
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Expressing γ as ( 1 − v 2 /c 2)
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7.3.4 ⋆ ProofsThis optional secti
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these lines. For example, a car sit
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An Einstein’s ring. Thedistant ob
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two-dimensional universe as if it w
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h / 1. A ray of light is emittedupw
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object that that isn’t influenced
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it impossible for any observer to b
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a variant on the Penrose singularit
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in it. Instead, it is currently spe
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2 Astronauts in three different spa
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(d) Simplify your answer to part c
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Problem 25b. Redrawn fromVan Baak,
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ExercisesExercise 7A: The Michelson
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Exercise 7B: Sports in Slowlightlan
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448 Chapter 7 Relativity
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Exercise 7D: Misconceptions about R
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452 Chapter 7 Relativity
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sun, moon, stars, and planets were
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Two types of chargeWe can easily co
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the other acquires an equal amount
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to get the beam up to speed in the
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telling us that we know about matte
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the muddle. The row-and-column sche
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the force of air friction canceled
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ectly evaluate the implications of
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that they were indeed electrically
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C Thomson found that the m/q of an
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the object with a net positive char
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thickness of material the radioacti
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It was already known that although
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particle. It turned out that it was
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For example they could easily strip
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cording to Mosely, the atomic numbe
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that fly off to see what was inside
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solution was found by measuring the
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o / A nuclear power plant at Catten
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neutrons. In a nuclear fission bomb
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We can now list all four of the kno
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1. Our sun’s source of energy is
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a / The known nuclei, represented o
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killed, because the DNA becomes una
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e / Wild Przewalski’s horsesprosp
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Problem 1. Top: A realisticpicture
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12 The subatomic particles called m
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ExercisesExercise 8A: Nuclear decay
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saxophone, every technological tool
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Example 1Ions moving across a cell
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ut the original meaning was to trav
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Force depends only on position. Sin
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Here are a few questions and answer
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flow through it.For many substances
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superconductivity in metals that wo
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j / Example 9. In 1 and 2,charges t
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look like the usual resistor. The f
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9.1.5 Current-conducting properties
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attery acid becomes depleted of hyd
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9.2 Parallel and Series CircuitsIn
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to each resistance, resulting inI t
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where “...” means that the sum
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the two resistors in figure h/3.We
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Choice of high voltage for power li
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A complicated circuit example 20⊲
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Problem 2.ProblemsThe symbols √ ,
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Problem 16.only count that as one u
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knob turned all the way clockwise,
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A printed circuit board, likethe ki
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ExercisesExercise 9A: Voltage and C
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Exercise 9C: Reasoning About Circui
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556 Chapter 9 Circuits
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a / A bar magnet’s atoms are(part
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defined. The ship’s captain can m
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Reduction in gravity on Io due to J
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j / Example 3.self-check AFind an e
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a dipole moment — they are define
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10.2.1 One dimensionVoltage is elec
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The interpretation is that if you b
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Figure c shows some examples of way
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For large values of d, this express
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where Q is the total charge of the
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g / Example 12: variation of the fi
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corners to the disk and transform i
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10.4 Energy In Fieldsa / Two opposi
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self-check DWe can think of the qua
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of the inward field contributed by
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space, 2 while charge doesn’t, we
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a / The symbol for a capacitor.b /
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ounding each capacitor will be half
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in time:x ↔ qv ↔ Iself-check GH
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due to its own momentum. It perform
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or|V | =∣ LdIdt ∣ ,which in man
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the inductor resists such a sudden
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Example 26.Death by solenoid; spark
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ordering.( 1 √2+√ i ) 2 = √ 1
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x / The complex number e iφlies on
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Figure aa shows a useful way to vis
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Inductors tend to be big, heavy, ex
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The reason for using the trig ident
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a purely inductive or capacitive lo
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Resonance with damping example 33
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orE outward, on side 1 A + E outwar
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|E| = kq totalr 2 ,where r is the r
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y considering its point charges ind
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Discussion Questionsg / Discussion
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with charge, change the Coulomb con
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The symmetry between the two sides
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where dv is the volume of the cube.
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The three terms in the divergence a
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Problem 19.Problem 20.proton, for e
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the lightning strike.(b) Based on y
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units.(b) Verify that RC has units
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lating freely (without any driving
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ExercisesExercise 10A: Field Vector
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5. Now hook up the two solenoids in
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A large current is createdby shorti
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time I used it implicitly was in fi
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f / A standard dipole madefrom a sq
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and substituting q = λh and v = m/
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o / Magnetic forces cause abeam of
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electric field, a magnetic one, can
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u / In this scene from SwanLake, th
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so the total field in the z directi
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For the y component, we havee / A s
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We can pin down the result even mor
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i / The field of a dipole.where r i
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circulates around the y axis, so at
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to be, not where it is now. Coulomb
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We have found one specific example
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to a flagpole, we can cancel out a
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11.4 Ampère’s Law In Differentia
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y evaluating the field at the midpo
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i.e.,F = axˆx + byˆx + cˆx + dx
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k / A summary of the derivative, gr
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c / Detail from Ascending andDescen
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the magnet. Are these atomic curren
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field in her region of space has be
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A changing magnetic flux makes a cu
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nearly zero. By Faraday’s law, th
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c / An Ampèrian surface superimpos
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and Maxwell’s equations becomeΦ
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k / Red and blue light travelat the
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second, the zero-point is located a
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is the magnitude of the momentum ve
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Discussion question A.Discussion qu
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only penetrates to a very small dep
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elationship D = ɛE would actually
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esulting in cancellation.The opposi
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a low permeability, while the other
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n / A fluxgate compass.is externall
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6 Two parallel wires of length L ca
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an instant at the upper right, but
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Problem 25.20 Four long wires are a
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Problem 35.Problem 37.32 Verify Amp
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Problem 42.beam of light usually co
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(c) Discuss the relationship betwee
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(f) Use conservation of energy to r
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5. Now position yourself with your
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12.1.1 The nature of lightThe cause
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An image of Jupiter andits moon Io
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d / Two self-portraits of theauthor
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ultimate truth about light, but the
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• There is a tendency to conceptu
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self-check AEach of these diagrams
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m / Discussion question B.Discussio
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12.2 Images by ReflectionInfants ar
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Discussion QuestionA The figure sho
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down magnification is AB/DE. A repe
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i / A Newtonian telescopebeing used
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B Locate the images formed by two p
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12.3 Images, QuantitativelyIt sound
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⊲ The object and image angles are
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12.3.2 Other cases with curved mirr
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signs also have to be memorized for
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h / A diverging mirror in the shape
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j / Spherical mirrors are thecheape
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general type of eye that we share w
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shown on this graph and then attemp
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the mechanical model would predict
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that your calculator will flash an
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D Classify the examples shown in fi
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12.4.6 ⋆ Microscopic description
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12.5 Wave OpticsElectron microscope
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of a crystal? Sound waves are used
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j / Thomas Youngk / Double-slit dif
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object that diffracts it, so the tr
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Although the equation λ/d = sin θ
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things we’ve learned about diffra
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apidly changing distances; on reuni
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6 The figure on the next page shows
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14 Here’s a game my kids like to
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27 Suppose a converging lens is con
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same depth, but not quite. [Check:
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Problem 42.42 Panel 1 of the figure
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46 The figure below shows two diffr
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53 The beam of a laser passes throu
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Problem 59.the ancient problem of i
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3. Now imagine the following new si
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Exercise 12B: Object and Image Dist
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Exercise 12D: Double-Source Interfe
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Exercise 12E: Single-slit diffracti
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Exercise 12F: Diffraction of LightE
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energy, instead of being spread out
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correlated. If they have been playi
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small.The statement that the rule f
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But the y axis can no longer be a u
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for a long time once it gets there,
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j / Calibration of the 14 C dating
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given by(probability of a ≤ x ≤
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k / In recent decades, a huge hole
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A wave is partially absorbed.c / A
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f / The hamster in her hamsterball
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How would you extract h from the gr
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F Does E = hf imply that a photon c
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of approaching this issue.)j / Bull
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We assume v is small enough so that
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the probability distribution will b
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trons that we have already used for
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equations of general validity are t
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wave carries high probability and w
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An infinite sine wave can only tell
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momentum implies a definite kinetic
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of snapshots would amount to a desc
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close are the electrons to the limi
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dimensional particle in a box, and
Page 868 and 869:
Applying this to conservation of en
Page 870 and 871:
the probability of making it throug
Page 872 and 873:
Three dimensionsFor simplicity, we
Page 874 and 875:
1. Oscillations can go backand fort
Page 876 and 877:
C The figure shows a skateboarder t
Page 878 and 879:
a / Eight wavelengths fit aroundthi
Page 880 and 881:
As shown by these examples, the unc
Page 882 and 883:
e / The three states of the hydroge
Page 884 and 885:
f / The energy levels of a particle
Page 886 and 887:
∂r/∂x = x/r comes in handy. Com
Page 888 and 889:
50% of its time in each atom. It’
Page 890 and 891:
tus to the z axis) and more memorab
Page 892 and 893:
ut why does that have anything to d
Page 894 and 895:
the data are only inaccurate due to
Page 896 and 897:
14 The photoelectric effect can occ
Page 898 and 899:
Problem 25.(b) Sketch a graph showi
Page 900 and 901:
conservation of energy and momentum
Page 902 and 903:
Problem 43.43 On pp. 884-885 of sub
Page 904 and 905:
ExercisesExercise 13A: Quantum Vers
Page 906 and 907:
⊲ First we convert the equation i
Page 908 and 909:
Programming With PythonThe purpose
Page 910 and 911:
Appendix 2: MiscellanyUnphysical
Page 912 and 913:
18 bestt = t19 c1 = bestc120 c2 = b
Page 914 and 915:
p i + ∑ iThe spin theoremTheorem:
Page 916 and 917:
Appendix 3: Photo CreditsExcept as
Page 918 and 919:
Appendix 4: Hints and SolutionsHint
Page 920 and 921:
Hints for Chapter 6Page 377, proble
Page 922 and 923:
Answers to Self-Checks for Chapter
Page 924 and 925:
Page 301: (1) Not valid. The equati
Page 926 and 927:
Page 584:N −1 m −2 C 2 V 2 m
Page 928 and 929:
the dashed ray.Page 748: You should
Page 930 and 931:
direction it was initially going (i
Page 932 and 933:
Page 52, problem 38: The cone of mi
Page 934 and 935:
Page 224, problem 37: (a) Spring co
Page 936 and 937:
object, we have static friction, wh
Page 938 and 939:
Page 549, problem 29:(a) Conservati
Page 940 and 941:
Page 798, problem 19: (a) The objec
Page 942 and 943:
.0.8 Notation and unitsquantity uni
Page 944 and 945:
surfaces. For comparison, a typical
Page 946 and 947:
elations:a = ∆v∆tx = 1 2 at2 +
Page 948 and 949:
we are moving along with the projec
Page 950 and 951:
the number of oscillations required
Page 952 and 953:
In general, the cross product of ve
Page 954 and 955:
Sound waves consist of increases an
Page 956 and 957:
signs for charge is that with this
Page 958 and 959:
know that there is a delay in time
Page 960 and 961:
is related byΦ = 4πkq into the ch
Page 962 and 963:
to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
Page 966 and 967:
oth position and momentum, the Heis
Page 968 and 969:
Schrödinger’s, 864cathode rays,
Page 970 and 971:
unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
Page 974 and 975:
Einstein’s early theory, 838energ
Page 976 and 977:
Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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