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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. The links to over 600 problems and their solutions, as well as links to more advanced sections, interactive problems, simulations and videos may be made by typing in the URL’s which are noted throughout the text or by scanning the micro QR codes given alongside the URL’s, see:

This new edition of this essential text:

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. The links to over 600 problems and their solutions, as well as links to more advanced sections, interactive problems, simulations and videos may be made by typing in the URL’s which are noted throughout the text or by scanning the micro QR codes given alongside the URL’s, see:

This new edition of this essential text:

- Offers an introduction to the principles for each topic presented - Presents a comprehensive yet concise introduction to physics covering a wide range of material - Features a revised treatment of electromagnetism, specifically the more detailed treatment of electric and magnetic materials - Puts emphasis on the relationship between microscopic and macroscopic perspectives - Is structured as a foundation course for undergraduate students in physics, materials science and engineering - Has been rewritten to conform with the revised definitions of SI base units which came into force in May 2019

Note: Product cover images may vary from those shown

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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 ??-, ??- and ??-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

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 ??-, ??- and ??-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

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Michael M. Mansfield

Colm O'Sullivan University College Cork.

Colm O'Sullivan University College Cork.

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