Understanding Physics

Preface The Understanding Physics website Problems 1 Understanding the physical universe 1.1 The programme of physics 1.2 The building blocks of matter 1.3 Matter in bulk 1.4 The fundamental interactions 1.5 Exploring the physical universe: the scientific method 1.6 The role of physics: its scope and applications 2 Using mathematical tools in physics 2.1 Applying the scientific method 2.2 The use of variables to represent displacement and time 2.3 Representation of data 2.4 The use of differentiation in analysis: velocity and acceleration in linear motion 2.5 The use of integration in analysis 2.6 Maximum and minimum values of physical quantities: general linear motion 2.7 Angular motion: the radian 2.8 The role of mathematics in physics Worked examples Chapter 2 problems (up.ucc.ie/2/) 3 The causes of motion: dynamics 3.1 The concept of force 3.2 The first law of dynamics (Newton's first law) 3.3 The fundamental dynamical principle (Newton's second law) 3.4 Systems of units: SI 3.5 Time dependent forces: oscillatory motion 3.6 Simple harmonic motion 3.7 Mechanical work and energy 3.8 Plots of potential energy functions 3.9 Power 3.10 Energy in simple harmonic motion 3.11 Dissipative forces: damped harmonic motion 3.11.1 Trial solution technique for solving the damped harmonic motion equation (up.ucc.ie/3/11/) 3.12 Forced oscillations (up.ucc.ie/3/12/) 3.13 Non-linear dynamics: chaos (up.ucc.ie/3/13/) 3.14 Phase space representation of dynamical systems (up.ucc.ie/3/14/) Worked examples Chapter 3 problems (up.ucc.ie/3/) 4 Motion in two and three dimensions 4.1 Vector physical quantities 4.2 Vector algebra 4.3 Velocity and acceleration vectors 4.4 Force as a vector quantity: vector form of the laws of dynamics 4.5 Constraint forces 4.6 Friction 4.7 Motion in a circle: centripetal force 4.8 Motion in a circle at constant speed 4.9 Tangential and radial components of acceleration 4.10 Hybrid motion: the simple pendulum 4.10.1 Large angle corrections for the simple pendulum (up.ucc.ie/4/10/) 4.11 Angular quantities as vectors: the cross product Worked examples Chapter 4 problems (up.ucc.ie/4/) 5 Force fields 5.1 Newton's law of universal gravitation 5.2 Force fields 5.3 The concept of flux 5.4 Gauss' law for gravitation 5.5 Applications of Gauss' law 5.6 Motion in a constant uniform field: projectiles 5.7 Mechanical work and energy 5.8 Power 5.9 Energy in a constant uniform field 5.10 Energy in an inverse square law field 5.11 Moment of a force: angular momentum 5.12 Planetary motion: circular orbits 5.13 Planetary motion: elliptical orbits and Kepler's laws 5.13.1 Conservation of the Runge-Lens vector (up.ucc.ie/5/13/) Worked examples Chapter 5 problems (up.ucc.ie/5/) 6 Many-body interactions 6.1 Newton's third law 6.2 The principle of conservation of momentum 6.3 Mechanical energy of systems of particles 6.4 Particle decay 6.5 Particle collisions 6.6 The centre of mass of a system 6.7 The two-body problem: reduced mass 6.8 Angular momentum of systems of particles 6.9 Conservation principles in physics Worked examples Chapter 6 problems (up.ucc.ie/6/) 7 Rigid body dynamics 7.1 Rigid bodies 7.2 Rigid bodies in equilibrium: statics 7.3 Torque 7.4 Dynamics of rigid bodies 7.5 Measurement of torque: the torsion balance 7.6 Rotation of a rigid body about a fixed axis: moment of inertia 7.7 Calculation of moments of inertia: the parallel axis theorem 7.8 Conservation of angular momentum of rigid bodies 7.9 Conservation of mechanical energy in rigid body systems 7.10 Work done by a torque: torsional oscillations: rotational power 7.11 Gyroscopic motion 7.11.1 Precessional angular velocity of a top (up.ucc.ie/7/11/) 7.12 Summary- connection between rotational and translational motions Worked examples Chapter 7 problems (up.ucc.ie/7/) 8 Relative motion 8.1 Applicability of Newton's laws of motion: inertial reference frames 8.2 The Galilean transformation 8.3 The CM (centre-of-mass) reference frame 8.4 Example of a non-inertial frame: centrifugal force 8.5 Motion in a rotating frame: the Coriolis force 8.6 The Foucault pendulum 8.6.1 Precession of a Foucault pendulum (up.ucc.ie/8/6/) 8.7 Practical criteria for inertial frames: the local view Worked examples Chapter 8 problems (up.ucc.ie/8/) 9 Special relativity 9.1 The velocity of light 9.1.1 The Michelson-Morley experiment (up.ucc.ie/9/1/) 9.2 The Principle of Relativity 9.3 Consequences of the Principle of Relativity 9.4 The Lorentz transformation 9.5 The Fitzgerald-Lorentz contraction 9.6 Time dilation 9.7 Paradoxes in special relativity 9.7.1 Simultaneity: quantitative analysis of the twin paradox (up.ucc.ie/9/7/) 9.8 Relativistic transformation of velocity 9.9 Momentum in relativistic mechanics 9.10 Four-vectors: the energy-momentum 4-vector 9.11 Energy-momentum transformations: relativistic energy conservation 9.11.1 The force transformations (up.ucc.ie/9/11/) 9.12 Relativistic energy: mass-energy equivalence 9.13 Units in relativistic mechanics 9.14 Mass-energy equivalence in practice 9.15 General relativity Worked examples Chapter 9 problems (up.ucc.ie/9/) 10 Continuum mechanics: mechanical properties of materials: microscopic models of matter 10.1 Dynamics of continuous media 10.2 Elastic properties of solids 10.3 Fluids at rest 10.4 Elastic properties of fluids 10.5 Pressure in gases 10.6 Archimedes' principle 10.7 Fluid dynamics; the Bernoulli equation 10.8 Viscosity 10.9 Surface properties of liquids 10.10 Boyle's law (Mariotte's law) 10.11 A microscopic theory of gases 10.12 The SI unit of amount of matter; the mole 10.13 Interatomic forces: modifications to the kinetic theory of gases 10.14 Microscopic models of condensed matter systems Worked examples Chapter 10 problems (up.ucc.ie/10/) 11 Thermal physics 11.1 Friction and heating 11.2 The SI unit of thermodynamic temperature; the kelvin 11.3 Heat capacities of thermal systems 11.4 Comparison of specific heat capacities: calorimetry 11.5 Thermal conductivity 11.6 Convection 11.7 Thermal radiation 11.8 Thermal expansion 11.9 The first law of thermodynamics 11.10 Change of phase: latent heat 11.11 The equation of state of an ideal gas 11.12 Isothermal, isobaric and adiabatic processes: free expansion 11.13 The Carnot cycle 11.14 Entropy and the second law of thermodynamics 11.15 The Helmholtz and Gibbs functions Worked examples Chapter 11 problems (up.ucc.ie/11/) 12 Microscopic models of thermal systems: kinetic theory of matter 12.1 Microscopic interpretation of temperature 12.2 Polyatomic molecules: principle of equipartition of energy 12.3 Ideal gas in a gravitational field: the 'law of atmospheres' 12.4 Ensemble averages and distribution functions 12.5 The distribution of molecular velocities in an ideal gas 12.6 Distribution of molecular speeds 12.7 Distribution of molecular energies; Maxwell-Boltzmann statistics 12.8 Microscopic interpretation of temperature and heat capacity in solids Worked examples Chapter 12 problems (up.ucc.ie/12/) 13 Wave Motion 13.1 Characteristics of wave motion 13.2 Representation of a wave which is travelling in one dimension 13.3 Energy and power in a wave motion 13.4 Plane and spherical waves 13.5 Huygen's principle: the laws of reflection and refraction 13.6 Interference between waves: 13.7 Interference of waves passing through openings: diffraction 13.8 Standing waves 13.8.1 Standing waves in three dimensional cavity (up.ucc.ie/13/8/) 13.9 The Doppler effect 13.10 The wave equation 13.11 Waves along a string 13.12 Waves in elastic media: longitudinal waves in a solid rod 13.13 Waves in elastic media: sound waves in gases 13.14 Superposition of two waves of slightly different frequencies: wave and group velocities 13.15 Other waveforms: Fourier analysis Worked examples Chapter 13 problems (up.ucc.ie/13/) 14 Introduction to quantum mechanics 14.1 Physics at the beginning of the twentieth century 14.2 The blackbody radiation problem; Planck's quantum hypothesis 14.3 The specific heat capacity of gases 14.4 The specific heat capacity of solids 14.5 The photoelectric effect 14.5.1 Example of an experiment to study the photoelectric effect (up.ucc.ie/14/5/) 14.4 The X-ray continuum 14.7 The Compton effect: the photon model 14.8 The de Broglie hypothesis: wave-particle duality 14.9 Interpretation of wave-particle duality 14.10 The Heisenberg uncertainty principle 14.11 The wavefunction: expectation values 14.12 The Schrödinger (wave mechanical) method 14.12.1 Expectation value of momentum (up.ucc.ie/14/12/) 14.13 The free particle 14.14 The time-independent Schrödinger equation: eigenfunctions and eigenvalues 14.14.1 Derivation of the Ehrenfest theorem (up.ucc.ie/14/14/) 14.15 The infinite square potential well 14.16 Potential steps 14.17 Other potential wells and barriers 14.18 The simple harmonic oscillator 14.18.1 Ground state of the simple harmonic oscillator (up.ucc.ie/14/18/) 14.19 Further implications of quantum mechanics Worked examples Chapter 14 problems (up.ucc.ie/14/) 15 Electric currents 15.1 Electric currents 15.2 The electric current model; electric charge 15.3 The unit of electric current; the ampere 15.4 Heating effect revisited: electrical resistance 15.5 Strength of a power supply: emf 15.6 Resistance of a circuit 15.7 Potential difference 15.8 Effect of internal resistance 15.9 Comparison of emfs: the potentiometer 15.10 Multiloop circuits 15.11 Kirchhoff's rules 15.12 Comparison of resistances: the Wheatstone bridge 15.13 Power supplies connected in parallel 15.14 Resistivity and conductivity 15.15 Variation of resistance with temperature Worked examples Chapter 15 problems (up.ucc.ie/15/) 16 Electric fields 16.1 Electric charge at rest 16.2 Electric fields: electric field strength 16.3 Force between point charges: Coulomb's law 16.4 Electric flux and electric flux density 16.5 Electric fields due to systems of charges 16.6 The electric dipole 16.7 Gauss' law for electrostatics 16.8 Applications of Gauss's law 16.9 Potential difference in electric fields 16.10 Electric potential 16.11 Equipotential surfaces 16.12 Determination of electric field strength from electric potential 16.13 Acceleration of charged particles 16.14 The laws of electrostatics in differential form (up.ucc.ie/16/14) Worked examples Chapter 16 problems (up.ucc.ie/16/) 17 Electric fields in materials 17.1 Conductors in electric fields 17.2 Insulators in electric fields; polarisation 17.3 Electric susceptibility 17.4 Boundaries between dielectric media 17.5 Ferroelectricity and paraelectricity; permanently polarised materials 17.6 Uniformly polarised rod; the 'bar electret' 17.7 Microscopic models of electric polarisation 17.8 Capacitors 17.9 Examples of capacitors with simple geometry 17.10 Energy stored in an electric field 17.11 Capacitors in series and in parallel 17.12 Charge and discharge of a capacitor through a resistance 17.13 Measurement of permittivity Worked examples Chapter 17 problems (up.ucc.ie/17/) 18 Magnetic fields 18.1 Magnetism 18.2 The work of Ampère, Biot and Savart 18.3 Magnetic pole strength 18.4 Magnetic field strength 18.5 Ampère's law 18.6 The Biot-Savart law 18.7 Applications of the Biot-Savart law 18.8 Magnetic flux and magnetic flux density 18.9 Magnetic fields of permanent magnets; magnetic dipoles 18.10 Forces between magnets; Gauss' law for magnetism 18.11 The laws of magnetostatics in differential form (up.ucc.ie/18/11/) Worked examples Chapter 18 problems (up.ucc.ie/18/) 19 Electric currents and moving charges in magnetic fields 19.1 Forces between currents magnets 19.2 The force between two long parallel wires 19.3 Current loop in a magnetic field 19.4 Magnetic fields due to moving charges 19.5 Force on a moving electric charge in a magnetic field 19.6 Applications of moving charges in uniform magnetic fields; the classical Hall effect 19.7 Charge in a combined electric and magnetic field; the Lorentz force 19.8 Magnetic dipole moments of charged particles in closed orbits 19.9 Polarisation of magnetic materials; magnetisation, magnetic susceptibility 19.10 Paramagnetism and diamagnetism 19.11 Boundaries between magnetic media 19.12 Ferromagnetism; the magnetic needle revisited 19.13 Moving coil meters and electric motors 19.14 Electric and magnetic fields in moving reference frames (up.ucc.ie/19/14/) Worked examples Chapter 19 problems (up.ucc.ie/19) 20 Electromagnetic induction: time-varying emfs 20.1 The principle of electromagnetic induction 20.2 Simple applications of electromagnetic induction 20.3 Self-inductance 20.4 The series L-R circuit 20.5 Discharge of a capacitor through an inductor and resistor 20.6 Time-varying emfs: mutual inductance: transformers 20.7 Alternating current (a.c.) 20.8 Alternating current transformers 20.9 Resistance, capacitance and inductance in a.c. circuits 20.10 The series L-C-R circuit: phasor diagrams 20.11 Power in an a.c. circuit Worked examples Chapter 20 problems (up.ucc.ie/20/) 21 Maxwell's equations; Electromagnetic radiation 21.1 Reconsideration of the laws of electromagnetism: Maxwell's equations 21.2 Plane electromagnetic waves 21.3 Experimental observation of electromagnetic radiation 21.4 The electromagnetic spectrum 21.5 Polarization of electromagnetic waves 21.6 Energy, momentum and angular momentum in electromagnetic waves 21.7 The photon model revisited 21.8 Reflection of electromagnetic waves at an interface between non-conducting media (up.ucc.ie/21/8/) 21.9 Electromagnetic waves in a conducting medium (up.ucc.ie/21/9/) 21.10 Invariance of electromagnetism under the Lorentz transformation (up.ucc.ie/21/10/) 21.11 Maxwell's equations in differential form (up.ucc.ie/21/11/) Worked examples Chapter 21 problems (up.ucc.ie/21/) 22 Wave optics 22.1 Electromagnetic nature of light 22.2 Coherence: the laser 22.3 Diffraction at a single slit 22.4 Two slit interference and diffraction: Young's double slit experiment 22.5 Multiple slit interference: the diffraction grating 22.6 Diffraction of X-rays: Bragg scattering 22.7 The SI unit of luminous intensity, the candela Worked examples Chapter 22 problems (up.ucc.ie/22/) 23 Geometrical optics 23.1 The ray model: geometric optics 23.2 Reflection of light 23.3 Image formation by spherical mirrors 23.4 Refraction of light 23.5 Refraction at successive plane interfaces 23.6 Image formation by spherical lenses 23.7 Image formation of extended objects: magnification 23.8 Dispersion of light Worked examples Chapter 23 problems (up.ucc.ie/23/) 24 Atomic Physics 24.1 Atomic models 24.2 The spectrum of hydrogen: the Rydberg formula 24.3 The Bohr postulates 24.4 The Bohr theory of the hydrogen atom 24.5 The quantum mechanical (Schrödinger) solution of the one-electron atom 24.5.1 The angular and radial equations for a one-electron atom (up.ucc.ie/24/5/1/) 24.5.2 The radial solutions of the lowest energy state of hydrogen (up.ucc.ie/24/5/2/) 24.6 Interpretation of the one-electron atom eigenfunctions 24.7 Intensities of spectral lines: selection rules 24.7.1 Radiation from an accelerated charge (up.ucc.ie/24/7/1/) 24.7.2 Expectation value of the electric dipole moment (up.ucc.ie/24/7/2/) 24.8 Quantisation of angular momentum 24.8.1 The angular momentum quantisation equations (up.ucc.ie/24/8/) 24.9 Magnetic effects in one-electron atoms: the Zeeman effect 24.10 The Stern-Gerlach experiment: electron spin 24.10.1 The Zeeman effect (up.ucc.ie/24/10) 24.11 The spin-orbit interaction 24.11.1 The Thomas precession (up.ucc.ie/24/11/) 24.12 Identical particles in quantum mechanics: the Pauli exclusion principle 24.13 The periodic table: multielectron atoms 24.14 The theory of multielectron atoms 24.15 Further uses of the solutions of the one-electron Worked examples Chapter 24 problems (up.ucc.ie/24/) 25 Electrons in solids: quantum statistics 25.1 Bonding in molecules and solids 25.2 The classical free electron model of solids 25.3 The quantum mechanical free electron model of solids: Fermi energy 25.4 The electron energy distribution at 0 K 25.5 Electron energy distributions at T > 0 K 25.5.1 The quantum distribution functions (up.ucc.ie/24/5/) 25.6 Specific heat and conductivity in the quantum free electron model 25.7 Quantum statistics: systems of bosons 25.8 Superconductivity Worked examples Chapter 25 problems (up.ucc.ie/25/) 26 Semiconductors 26.1 The band theory of solids 26.2 Conductors, insulators and semiconductors 26.3 Intrinsic and extrinsic (doped) semiconductors 26.4 Junctions in conductors 26.5 Junction in semiconductors; the p-n junction 26.6 Biased p-n junctions; the semiconductor diode 26.7 Photodiodes, particle detectors and solar cells 26.8 Light emitting diodes; semiconductor lasers 26. 9 The tunnel diode 26.10 Transistors Worked examples Chapter 26 problems (up.ucc.ie/26/) 27 Nuclear and particle physics 27.1 Properties of atomic nuclei 27.2 Nuclear binding energies 27.3 Nuclear models 27.4 Radioactivity 27.5 alpha-, beta- and gamma-decay 27.6 Detection of radiation: units of radioactivity 27.7 Nuclear reactions 27.8 Nuclear fission and nuclear fusion 27.9 Fission reactors 27.10 Thermonuclear fusion 27.11 Sub-nuclear particles 27.12 The quark model Worked examples Chapter 27 problems (up.ucc.ie/27/) Appendix A: Mathematical rules and formulas Appendix B: Some fundamental physical constants Appendix C: Some astrophysical and geophysical data Appendix D: The 2019 revision of SI Bibliography Index