An updated and thoroughly revised third edition of the foundational text offering an introduction to physics with a comprehensive interactive website
The revised and updated third edition of Understanding Physics presents a comprehensive introduction to college-level physics. Written with today's students in mind, this compact text covers the core material required within an introductory course in a clear and engaging way. The authors - noted experts on the topic - offer an understanding of the physical universe and present the mathematical tools used in physics.
The book covers all the material required in an introductory physics course. Each topic is introduced from first principles so that the text is suitable for students without a prior background in physics. At the same time the book is designed to enable students to proceed easily to subsequent courses in physics and may be used to support such courses. Relativity and quantum mechanics are introduced at an earlier stage than is usually found in introductory textbooks and are integrated with the more 'classical' material from which they have evolved.
Worked examples and links to problems, designed to be both illustrative and challenging, are included throughout.
Table of Contents
Preface to third edition xv
1 Understanding the physical universe 1
1.1 The programme of physics 1
1.2 The building blocks of matter 2
1.3 Matter in bulk 4
1.4 The fundamental interactions 5
1.5 Exploring the physical universe: the scientific method 5
1.6 The role of physics; its scope and applications 7
2 Using mathematical tools in physics 9
2.1 Applying the scientific method 9
2.2 The use of variables to represent displacement and time 9
2.3 Representation of data 10
2.4 The use of differentiation in analysis: velocity and acceleration in linear motion 13
2.5 The use of integration in analysis 16
2.6 Maximum and minimum values of physical variables: general linear motion 21
2.7 Angular motion: the radian 22
2.8 The role of mathematics in physics 24
Worked examples 25
Chapter 2 problems (up.ucc.ie/2/) 27
3 The causes of motion: dynamics 29
3.1 The concept of force 29
3.2 The First law of Dynamics (Newton's first law) 30
3.3 The fundamental dynamical principle (Newton's second law) 31
3.4 Systems of units: SI 33
3.5 Time dependent forces: oscillatory motion 37
3.6 Simple harmonic motion 39
3.7 Mechanical work and energy 42
3.8 Plots of potential energy functions 45
3.9 Power 46
3.10 Energy in simple harmonic motion 47
3.11 Dissipative forces: damped harmonic motion 48
3.11.1 Trial solution technique for solving the damped harmonic motion equation (up.ucc.ie/3/11/1/) 50
3.12 Forced oscillations (up.ucc.ie/3/12/) 51
3.13 Non-linear dynamics: chaos (up.ucc.ie/3/13/) 52
3.14 Phase space representation of dynamical systems (up.ucc.ie/3/14/) 52
Worked examples 52
Chapter 3 problems (up.ucc.ie/3/) 56
4 Motion in two and three dimensions 57
4.1 Vector physical quantities 57
4.2 Vector algebra 58
4.3 Velocity and acceleration vectors 62
4.4 Force as a vector quantity: vector form of the laws of dynamics 63
4.5 Constraint forces 64
4.6 Friction 66
4.7 Motion in a circle: centripetal force 68
4.8 Motion in a circle at constant speed 69
4.9 Tangential and radial components of acceleration 71
4.10 Hybrid motion: the simple pendulum 71
4.10.1 Large angle corrections for the simple pendulum (up.ucc.ie/4/10/1/) 72
4.11 Angular quantities as vector: the cross product 72
Worked examples 75
Chapter 4 problems (up.ucc.ie/4/) 78
5 Force fields 79
5.1 Newton's law of universal gravitation 79
5.2 Force fields 80
5.3 The concept of flux 81
5.4 Gauss's law for gravitation 82
5.5 Applications of Gauss's law 84
5.6 Motion in a constant uniform field: projectiles 86
5.7 Mechanical work and energy 88
5.8 Power 93
5.9 Energy in a constant uniform field 94
5.10 Energy in an inverse square law field 94
5.11 Moment of a force: angular momentum 97
5.12 Planetary motion: circular orbits 98
5.13 Planetary motion: elliptical orbits and Kepler's laws 99
5.13.1 Conservation of the Runge-Lens vector (up.ucc.ie/5/13/1/) 100
Worked examples 101
Chapter 5 problems (up.ucc.ie/5/) 104
6 Many-body interactions 105
6.1 Newton's third law 105
6.2 The principle of conservation of momentum 108
6.3 Mechanical energy of systems of particles 109
6.4 Particle decay 110
6.5 Particle collisions 111
6.6 The centre of mass of a system of particles 115
6.7 The two-body problem: reduced mass 116
6.8 Angular momentum of a system of particles 119
6.9 Conservation principles in physics 120
Worked examples 121
Chapter 6 problems (up.ucc.ie/6/) 125
7 Rigid body dynamics 127
7.1 Rigid bodies 127
7.2 Rigid bodies in equilibrium: statics 128
7.3 Torque 129
7.4 Dynamics of rigid bodies 130
7.5 Measurement of torque: the torsion balance 131
7.6 Rotation of a rigid body about a fixed axis: moment of inertia 132
7.7 Calculation of moments of inertia: the parallel axis theorem 133
7.8 Conservation of angular momentum of rigid bodies 135
7.9 Conservation of mechanical energy in rigid body systems 136
7.10 Work done by a torque: torsional oscillations: rotational power 138
7.11 Gyroscopic motion 140
7.11.1 Precessional angular velocity of a top (up.ucc.ie/7/11/1/) 141
7.12 Summary: connection between rotational and translational motions 141
Worked examples 141
Chapter 7 problems (up.ucc.ie/7/) 144
8 Relative motion 145
8.1 Applicability of Newton's laws of motion: inertial reference frames 145
8.2 The Galilean transformation 146
8.3 The CM (centre-of-mass) reference frame 149
8.4 Example of a non-inertial frame: centrifugal force 153
8.5 Motion in a rotating frame: the Coriolis force 155
8.6 The Foucault pendulum 158
8.6.1 Precession of a Foucault pendulum (up.ucc.ie/8/6/1/) 158
8.7 Practical criteria for inertial frames: the local view 158
Worked examples 159
Chapter 8 problems (up.ucc.ie/8/) 163
9 Special relativity 165
9.1 The velocity of light 165
9.1.1 The Michelson-Morley experiment (up.ucc.ie/9/1/1/) 165
9.2 The principle of relativity 166
9.3 Consequences of the principle of relativity 166
9.4 The Lorentz transformation 168
9.5 The Fitzgerald-Lorentz contraction 171
9.6 Time dilation 172
9.7 Paradoxes in special relativity 173
9.7.1 Simultaneity: quantitative analysis of the twin paradox (up.ucc.ie/9/7/1/) 174
9.8 Relativistic transformation of velocity 174
9.9 Momentum in relativistic mechanics 176
9.10 Four-vectors: the energy-momentum 4-vector 177
9.11 Energy-momentum transformations: relativistic energy conservation 179
9.11.1 The force transformations (up.ucc.ie/9/11/1/) 180
9.12 Relativistic energy: mass-energy equivalence 180
9.13 Units in relativistic mechanics 183
9.14 Mass-energy equivalence in practice 184
9.15 General relativity 185
Worked examples 185
Chapter 9 problems (up.ucc.ie/9/) 188
10 Continuum mechanics: mechanical properties of materials: microscopic models of matter 189
10.1 Dynamics of continuous media 189
10.2 Elastic properties of solids 190
10.3 Fluids at rest 193
10.4 Elastic properties of fluids 195
10.5 Pressure in gases 196
10.6 Archimedes' principle 196
10.7 Fluid dynamics; the Bernoulli equation 198
10.8 Viscosity 201
10.9 Surface properties of liquids 202
10.10 Boyle's law (or Mariotte's law) 204
10.11 A microscopic theory of gases 205
10.12 The SI unit of amount of substance; the mole 207
10.13 Interatomic forces: modifications to the kinetic theory of gases 208
10.14 Microscopic models of condensed matter systems 210
Worked examples 212
Chapter 10 problems (up.ucc.ie/10/) 214
11 Thermal physics 215
11.1 Friction and heating 215
11.2 The SI unit of thermodynamic temperature, the kelvin 216
11.3 Heat capacities of thermal systems 216
11.4 Comparison of specific heat capacities: calorimetry 218
11.5 Thermal conductivity 219
11.6 Convection 220
11.7 Thermal radiation 221
11.8 Thermal expansion 222
11.9 The first law of thermodynamics 224
11.10 Change of phase: latent heat 225
11.11 The equation of state of an ideal gas 226
11.12 Isothermal, isobaric and adiabatic processes: free expansion 227
11.13 The Carnot cycle 230
11.14 Entropy and the second law of thermodynamics 231
11.15 The Helmholtz and Gibbs functions 233
Worked examples 234
Chapter 11 problems (up.ucc.ie/11/) 236
12 Microscopic models of thermal systems: kinetic theory of matter 237
12.1 Microscopic interpretation of temperature 237
12.2 Polyatomic molecules: principle of equipartition of energy 239
12.3 Ideal gas in a gravitational field: the ‘law of atmospheres’ 241
12.4 Ensemble averages and distribution functions 242
12.5 The distribution of molecular velocities in an ideal gas 243
12.6 Distribution of molecular speeds 244
12.7 Distribution of molecular energies; Maxwell-Boltzmann statistics 246
12.8 Microscopic interpretation of temperature and heat capacity in solids 247
Worked examples 248
Chapter 12 problems (up.ucc.ie/12/) 249
13 Wave motion 251
13.1 Characteristics of wave motion 251
13.2 Representation of a wave which is travelling in one dimension 253
13.3 Energy and power in wave motion 255
13.4 Plane and spherical waves 256
13.5 Huygens' principle: the laws of reflection and refraction 257
13.6 Interference between waves 259
13.7 Interference of waves passing through openings: diffraction 263
13.8 Standing waves 265
13.8.1 Standing waves in a three dimensional cavity (up.ucc.ie/13/8/1/) 267
13.9 The Doppler effect 268
13.10 The wave equation 270
13.11 Waves along a string 270
13.12 Waves in elastic media: longitudinal waves in a solid rod 271
13.13 Waves in elastic media: sound waves in gases 272
13.14 Superposition of two waves of slightly different frequencies: wave and group velocities 274
13.15 Other wave forms: Fourier analysis 275
Worked examples 279
Chapter 13 problems (up.ucc.ie/13/) 280
14 Introduction to quantum mechanics 281
14.1 Physics at the beginning of the twentieth century 281
14.2 The blackbody radiation problem: Planck's quantum hypothesis 282
14.3 The specific heat capacity of gases 284
14.4 The specific heat capacity of solids 284
14.5 The photoelectric effect 285
14.5.1 Example of an experiment to study the photoelectric effect (up.ucc.ie/14/5/1/) 285
14.6 The X-ray continuum 287
14.7 The Compton effect: the photon model 287
14.8 The de Broglie hypothesis: wave-particle duality 290
14.9 Interpretation of wave particle duality 292
14.10 The Heisenberg uncertainty principle 293
14.11 The Schrödinger (wave mechanical) method 295
14.12 Probability density; expectation values 296
14.12.1 Expectation value of momentum (up.ucc.ie/14/12/1/) 297
14.13 The free particle 298
14.14 The time-independent Schrödinger equation: eigenfunctions and eigenvalues 300
14.14.1 Derivation of the Ehrenfest theorem (up.ucc.ie/14/14/1/) 301
14.15 The infinite square potential well 303
14.16 Potential steps 305
14.17 Other potential wells and barriers 311
14.18 The simple harmonic oscillator 313
14.18.1 Ground state of the simple harmonic oscillator (up.ucc.ie/14/18/1/) 313
14.19 Further implications of quantum mechanics 313
Worked examples 314
Chapter 14 problems (up.ucc.ie/14/) 316
15 Electric currents 317
15.1 Electric currents 317
15.2 The electric current model; electric charge 318
15.3 The SI unit of electric current; the ampere 320
15.4 Heating effect revisited; electrical resistance 321
15.5 Strength of a power supply; emf 323
15.6 Resistance of a circuit 324
15.7 Potential difference 324
15.8 Effect of internal resistance 326
15.9 Comparison of emfs; the potentiometer 328
15.10 Multiloop circuits 329
15.11 Kirchhoff's rules 330
15.12 Comparison of resistances; the Wheatstone bridge 331
15.13 Power supplies connected in parallel 332
15.14 Resistivity and conductivity 333
15.15 Variation of resistance with temperature 334
Worked examples 335
Chapter 15 problems (up.ucc.ie/15/) 338
16 Electric fields 339
16.1 Electric charges at rest 339
16.2 Electric fields: electric field strength 341
16.3 Forces between point charges: Coulomb's law 342
16.4 Electric flux and electric flux density 343
16.5 Electric fields due to systems of charges 344
16.6 The electric dipole 346
16.7 Gauss's law for electrostatics 349
16.8 Applications of Gauss's law 349
16.9 Potential difference in electric fields 352
16.10 Electric potential 353
16.11 Equipotential surfaces 355
16.12 Determination of electric field strength from electric potential 356
16.13 Acceleration of charged particles 357
16.14 The laws of electrostatics in differential form (up.ucc.ie/16/14) 358
Worked examples 359
Chapter 16 problems (up.ucc.ie/16/) 361
17 Electric fields in materials; the capacitor 363
17.1 Conductors in electric fields 363
17.2 Insulators in electric fields; polarization 364
17.3 Electric susceptibility 367
17.4 Boundaries between dielectric media 368
17.5 Ferroelectricity and paraelectricity; permanently polarised materials 369
17.6 Uniformly polarised rod; the ‘bar electret’ 370
17.7 Microscopic models of electric polarization 372
17.8 Capacitors 373
17.9 Examples of capacitors with simple geometry 374
17.10 Energy stored in an electric field 376
17.11 Capacitors in series and in parallel 377
17.12 Charge and discharge of a capacitor through a resistor 378
17.13 Measurement of permittivity 379
Worked examples 380
Chapter 17 problems (up.ucc.ie/17/) 382
18 Magnetic fields 383
18.1 Magnetism 383
18.2 The work of Ampère, Biot, and Savart 385
18.3 Magnetic pole strength 386
18.4 Magnetic field strength 387
18.5 Ampère's law 388
18.6 The Biot-Savart law 390
18.7 Applications of the Biot-Savart law 392
18.8 Magnetic flux and magnetic flux density 393
18.9 Magnetic fields of permanent magnets; magnetic dipoles 394
18.10 Forces between magnets; Gauss's law for magnetism 395
18.11 The laws of magnetostatics in differential form (up.ucc.ie/18/11/) 396
Worked examples 396
Chapter 18 problems (up.ucc.ie/18/) 397
19 Interactions between magnetic fields and electric currents; magnetic materials 399
19.1 Forces between currents and magnets 399
19.2 The force between two long parallel wires 400
19.3 Current loop in a magnetic field 401
19.4 Magnetic fields due to moving charges 403
19.5 Force on a moving electric charge in a magnetic field 403
19.6 Applications of moving charges in uniform magnetic fields; the classical Hall effect 404
19.7 Charge in a combined electric and magnetic field; the Lorentz force 407
19.8 Magnetic dipole moments of charged particles in closed orbits 407
19.9 Polarisation of magnetic materials; magnetisation, magnetic susceptibility 408
19.10 Paramagnetism and diamagnetism 409
19.11 Boundaries between magnetic media 411
19.12 Ferromagnetism; permanent magnets revisited 411
19.13 Moving coil meters and electric motors 412
19.14 Electric and magnetic fields in moving reference frames (up.ucc.ie/19/14/) 414
Worked examples 414
Chapter 19 problems (up.ucc.ie/19) 416
20 Electromagnetic induction: time-varying emfs 417
20.1 The principle of electromagnetic induction 417
20.2 Simple applications of electromagnetic induction 420
20.3 Self-inductance 421
20.4 The series L-R circuit 424
20.5 Discharge of a capacitor through an inductor and a resistor 425
20.6 Time-varying emfs: mutual inductance: transformers 427
20.7 Alternating current (a.c.) 429
20.8 Alternating current transformers 432
20.9 Resistance, capacitance, and inductance in a.c. circuits 433
20.10 The series L-C-R circuit: phasor diagrams 435
20.11 Power in an a.c. circuit 438
Worked examples 439
Chapter 20 problems (up.ucc.ie/20/) 441
21 Maxwell's equations: electromagnetic radiation 443
21.1 Reconsideration of the laws of electromagnetism: Maxwell's equations 443
21.2 Plane electromagnetic waves 446
21.3 Experimental observation of electromagnetic radiation 448
21.4 The electromagnetic spectrum 449
21.5 Polarisation of electromagnetic waves 451
21.6 Energy, momentum and angular momentum in electromagnetic waves 454
21.7 The photon model revisited 457
21.8 Reflection of electromagnetic waves at an interface between non-conducting media (up.ucc.ie/21/8/) 458
21.9 Electromagnetic waves in a conducting medium (up.ucc.ie/21/9/) 458
21.10 Invariance of electromagnetism under the Lorentz transformation (up.ucc.ie/21/10/) 458
21.11 Maxwell's equations in differential form (up.ucc.ie/21/11/) 458
Worked examples 459
Chapter 21 problems (up.ucc.ie/21/) 461
22 Wave optics 463
22.1 Electromagnetic nature of light 463
22.2 Coherence: the laser 465
22.3 Diffraction at a single slit 467
22.4 Two slit interference and diffraction: Young's double slit experiment 470
22.5 Multiple slit interference: the diffraction grating 472
22.6 Diffraction of X-rays: Bragg scattering 475
22.7 The SI unit of luminous intensity, the candela 478
Worked examples 479
Chapter 22 problems (up.ucc.ie/22/) 480
23 Geometrical optics 481
23.1 The ray model: geometrical optics 481
23.2 Reflection of light 481
23.3 Image formation by spherical mirrors 482
23.4 Refraction of light 485
23.5 Refraction at successive plane interfaces 489
23.6 Image formation by spherical lenses 491
23.7 Image formation of extended objects: magnification; telescopes and microscopes 495
23.8 Dispersion of light 497
Worked examples 498
Chapter 23 problems (up.ucc.ie/23/) 501
24 Atomic physics 503
24.1 Atomic models 503
24.2 The spectrum of hydrogen: the Rydberg formula 505
24.3 The Bohr postulates 506
24.4 The Bohr theory of the hydrogen atom 507
24.5 The quantum mechanical (Schrödinger) solution of the one-electron atom 510
24.5.1 The angular and radial equations for a one-electron atom (up.ucc.ie/24/5/1/) 513
24.5.2 The radial solutions of the lowest energy state of hydrogen (up.ucc.ie/24/5/2/) 513
24.6 Interpretation of the one-electron atom eigenfunctions 514
24.7 Intensities of spectral lines: selection rules 517
24.7.1 Radiation from an accelerated charge (up.ucc.ie/24/7/1/) 518
24.7.2 Expectation value of the electric dipole moment (up.ucc.ie/24/7/2/) 518
24.8 Quantisation of angular momentum 518
24.8.1 The angular momentum quantisation equations (up.ucc.ie/24/8/1/) 519
24.9 Magnetic effects in one-electron atoms: the Zeeman effect 520
24.10 The Stern-Gerlach experiment: electron spin 521
24.10.1 The Zeeman effect (up.ucc.ie/24/10/1/) 523
24.11 The spin-orbit interaction 523
24.11.1 The Thomas precession (up.ucc.ie/24/11/1/) 524
24.12 Identical particles in quantum mechanics: the Pauli exclusion principle 525
24.13 The periodic table: multielectron atoms 526
24.14 The theory of multielectron atoms 529
24.15 Further uses of the solutions of the one-electron atom 529
Worked examples 530
Chapter 24 problems (up.ucc.ie/24/) 532
25 Electrons in solids: quantum statistics 533
25.1 Bonding in molecules and solids 533
25.2 The classical free electron model of solids 537
25.3 The quantum mechanical free electron model: the Fermi energy 539
25.4 The electron energy distribution at 0 K 541
25.5 Electron energy distributions at T>0 K 544
25.5.1 The quantum distribution functions (up.ucc.ie/24/5/1/) 544
25.6 Specific heat capacity and conductivity in the quantum free electron model 544
25.7 Quantum statistics: systems of bosons 546
25.8 Superconductivity 547
Worked examples 548
Chapter 25 problems (up.ucc.ie/25/) 549
26 Semiconductors 551
26.1 The band theory of solids 551
26.2 Conductors, insulators and semiconductors 552
26.3 Intrinsic and extrinsic (doped) semiconductors 553
26.4 Junctions in conductors 555
26.5 Junctions in semiconductors; the p-n junction 556
26.6 Biased p-n junctions; the semiconductor diode 557
26.7 Photodiodes, particle detectors and solar cells 558
26.8 Light emitting diodes; semiconductor lasers 559
26.9 The tunnel diode 560
26.10 Transistors 560
Worked examples 563
Chapter 26 problems (up.ucc.ie/26/) 564
27 Nuclear and particle physics 565
27.1 Properties of atomic nuclei 565
27.2 Nuclear binding energies 567
27.3 Nuclear models 568
27.4 Radioactivity 571
27.5 𝛼-, 𝛽- and 𝛾-decay 572
27.6 Detection of radiation: units of radioactivity 575
27.7 Nuclear reactions 577
27.8 Nuclear fission and nuclear fusion 578
27.9 Fission reactors 579
27.10 Thermonuclear fusion 581
27.11 Sub-nuclear particles 584
27.12 The quark model 587
Worked examples 591
Chapter 27 problems (up.ucc.ie/27/) 592
Appendix A: Mathematical rules and formulas 593
Appendix B: Some fundamental physical constants 611
Appendix C: Some astrophysical and geophysical data 613
Appendix D: The international system of units - SI 615
Bibliography 619
Index 621
