Mechanics for Scientists and Engineers

University e-Prep Course

by NTU



These are Mechanics for Scientists and Engineers ePrep course topics by NTU meant for NSFs and NSMen to better prepare for university studies, but now it is open to all. It is based on the textbook “Physics for Scientists and Engineers” by Serway. The textbook comes free with the course. The detils of the topics covered are given below.


1 Physics and Measurement.

1.1 Standards of Length, Mass, and Time

1.2 Modeling and Alternative Representations

1.3 Dimensional Analysis

1.4 Conversion of Units

1.5 Estimates and Order-of-Magnitude Calculations

1.6 Significant Figures

2 Motion in One Dimension.

2.1 Position, Velocity, and Speed of a Particle

2.2 Instantaneous Velocity and Speed

2.3 Analysis Model: Particle Under Constant Velocity

2.4 The Analysis Model Approach to Problem Solving

2.5 Acceleration

2.6 Motion Diagrams

2.7 Analysis Model: Particle Under Constant Acceleration

2.8 Freely Falling Objects

2.9 Kinematic Equations Derived from Calculus

3 Vectors.

3.1 Coordinate Systems

3.2 Vector and Scalar Quantities

3.3 Basic Vector Arithmetic

3.4 Components of a Vector and Unit Vectors

4 Motion in Two Dimensions.

4.1 The Position, Velocity, and Acceleration Vectors

4.2 Two-Dimensional Motion with Constant Acceleration

4.3 Projectile Motion

4.4 Analysis Model: Particle in Uniform Circular Motion

4.5 Tangential and Radial Acceleration 4.6 Relative Velocity and Relative Acceleration

5 The Laws of Motion.

5.1 The Concept of Force

5.2 Newton’s First Law and Inertial Frames

5.3 Mass

5.4 Newton’s Second Law

5.5 The Gravitational Force and Weight

5.6 Newton’s Third Law

5.7 Analysis Models Using Newton’s Second Law

5.8 Forces of Friction

6 Circular Motion and Other Applications of Newton’s Laws.

6.1 Extending the Particle in Uniform Circular Motion Model

6.2 Nonuniform Circular Motion

6.3 Motion in Accelerated Frames

6.4 Motion in the Presence of Resistive Forces

7 Energy of a System.

7.1 Systems and Environments

7.2 Work Done by a Constant Force

7.3 The Scalar Product of Two Vectors

7.4 Work Done by a Varying Force

7.5 Kinetic Energy and the Work-Kinetic Energy Theorem

7.6 Potential Energy of a System

7.7 Conservative and Nonconservative Forces

7.8 Relationship Between Conservative Forces and Potential Energy

7.9 Energy Diagrams and Equilibrium of a System

8 Conservation of Energy.

8.1 Analysis Model: Nonisolated System (Energy)

8.2 Analysis Model: Isolated System (Energy)

8.3 Situations Involving Kinetic Friction

8.4 Changes in Mechanical Energy for Nonconservative Forces

8.5 Power

9 Linear Momentum and Collisions.

9.1 Linear Momentum

9.2 Analysis Model: Isolated System (Momentum)

9.3 Analysis Model: Nonisolated System (Momentum)

9.4 Collisions in One Dimension

9.5 Collisions in Two Dimensions

9.6 The Center of Mass

9.7 Systems of Many Particles

9.8 Deformable Systems

9.9 Rocket Propulsion

10 Rotation of a Rigid Object About a Fixed Axis

10.1 Angular Position, Velocity, and Acceleration

10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration

10.3 Angular and Translational Quantities

10.4 Torque

10.5 Analysis Model: Rigid Object Under a Net Torque

10.6 Calculation of Moments of Inertia

10.7 Rotational Kinetic Energy

10.8 Energy Considerations in Rotational Motion

10.9 Rolling Motion of a Rigid Object

11 Angular Momentum

11.1 The Vector Product and Torque

11.2 Analysis Model: Nonisolated System (Angular Momentum)

11.3 Angular Momentum of a Rotating Rigid Object

11.4 Analysis Model: Isolated System (Angular Momentum)

11.5 The Motion of Gyroscopes and Tops.

12 Static Equilibrium and Elasticity.

12.1 Analysis Model: Rigid Object in Equilibrium

12.2 More on the Center of Gravity

12.3 Examples of Rigid Objects in Static Equilibrium

12.4 Elastic Properties of Solids

13 Universal Gravitation.

13.1 Newton’s Law of Universal Gravitation

13.2 Free-Fall Acceleration and the Gravitational Force

13.3 Analysis Model: Particle in a Field (Gravitational)

13.4 Kepler’s Laws and the Motion of Planets

13.5 Gravitational Potential Energy

13.6 Energy Considerations in Planetary and Satellite Motion

14 Fluid Mechanics.

14.1 Pressure

14.2 Variation of Pressure with Depth

14.3 Pressure Measurements

14.4 Buoyant Forces and Archimedes’s Principle

14.5 Fluid Dynamics

14.6 Bernoulli’s Equation

14.7 Flow of Viscous Fluids in Pipes

14.8 Other Applications of Fluid Dynamics

15 Oscillatory Motion.

15.1 Motion of an Object Attached to a Spring

15.2 Analysis Model: Particle in Simple Harmonic Motion

15.3 Energy of the Simple Harmonic Oscillator

15.4 Comparing Simple Harmonic Motion with Uniform Circular Motion

15.5 The Pendulum

15.6 Damped Oscillations

15.7 Forced Oscillations

16 Wave Motion.

16.1 Propagation of a Disturbance

16.2 Analysis Model: Traveling Wave

16.3 The Speed of Transverse Waves on Strings

16.4 Rate of Energy Transfer by Sinusoidal Waves on Strings

16.5 The Linear Wave Equation

16.6 Sound Waves

16.7 Speed of Sound Waves

16.8 Intensity of Sound Waves

16.9 The Doppler Effect

17 Superposition and Standing Waves.

17.1 Analysis Model: Waves in Interference

17.2 Standing Waves

17.3 Boundary Effects: Reflection and Transmission

17.4 Analysis Model: Waves Under Boundary Conditions

17.5 Resonance

17.6 Standing Waves in Air Columns

17.7 Beats: Interference in Time

17.8 Nonsinusoidal Wave Patterns

18 Temperature.

18.1 Temperature and the Zeroth Law of Thermodynamics

18.2 Thermometers and the Celsius Temperature Scale

18.3 The Constant-Volume Gas Thermometer and the Absolute Temperature Scale

18.4 Thermal Expansion of Solids and Liquids

18.5 Macroscopic Description of an Ideal Gas

19 Heat and the First Law of Thermodynamics.

19.1 Heat and Internal Energy

19.2 Specific Heat and Calorimetry

19.3 Latent Heat

19.4 Work and Heat in Thermodynamic Processes

19.5 The First Law of Thermodynamics

19.6 Energy Transfer Mechanisms in Thermal Processes

20 The Kinetic Theory of Gases.

20.1 Molecular Model of an Ideal Gas

20.2 Molar Specific Heat of an Ideal Gas

20.3 The Equipartition of Energy

20.4 Adiabatic Processes for an Ideal Gas

20.5 Distribution of Molecular Speeds

21 Heat Engines, Entropy, and the Second Law of Thermodynamics.

21.1 Heat Engines and the Second Law of Thermodynamics

21.2 Heat Pumps and Refrigerators

21.3 Reversible and Irreversible Processes

21.4 The Carnot Engine

21.5 Gasoline and Diesel Engines

21.6 Entropy

21.7 Entropy in Thermodynamic Systems

21.8 Entropy and the Second Law

22 Electric Fields.

22.1 Properties of Electric Charges

22.2 Charging Objects by Induction

22.3 Coulomb’s Law

22.4 Analysis Model: Particle in a Field (Electric)

22.5 Electric Field of a Continuous Charge Distribution

22.6 Electric Field Lines

22.7 Motion of a Charged Particle in a Uniform Electric Field

23 Continuous Charge Distributions and Gauss’s Law.

23.1 Electric Field of a Continuous Charge Distribution

23.2 Electric Flux

23.3 Gauss’s Law

23.4 Applications of Gauss’s Law to Various Charge Distributions

24 Electric Potential.

24.1 Electric Potential and Potential Difference

24.2 Potential Difference in a Uniform Electric Field

24.3 Electric Potential and Potential Energy Due to Point Charges

24.4 Obtaining the Value of the Electric Field from the Electric Potential

24.5 Electric Potential Due to Continuous Charge Distributions

24.6 Conductors in Electrostatic Equilibrium

25 Capacitance and Dielectrics.

25.1 Definition of Capacitance

25.2 Calculating Capacitance

25.3 Combinations of Capacitors

25.4 Energy Stored in a Charged Capacitor

25.5 Capacitors with Dielectrics

25.6 Electric Dipole in an Electric Field

25.7 An Atomic Description of Dielectrics

26 Current and Resistance.

26.1 Electric Current

26.2 Resistance

26.3 A Model for Electrical Conduction

26.4 Resistance and Temperature

26.5 Superconductors

26.6 Electrical Power

27 Direct Current Circuits.

27.1 Electromotive Force

27.2 Resistors in Series and Parallel

27.3 Kirchhoff’s Rules

27.4 RC Circuits

27.5 Household Wiring and Electrical Safety

28 Magnetic Fields.

28.1 Analysis Model: Particle in a Field (Magnetic)

28.2 Motion of a Charged Particle in a Uniform Magnetic Field

28.3 Applications Involving Charged Particles Moving in a Magnetic Field

28.4 Magnetic Force Acting on a Current-Carrying Conductor

28.5 Torque on a Current Loop in a Uniform Magnetic Field

28.6 The Hall Effect

29 Sources of the Magnetic Field.

29.1 The Biot–Savart Law

29.2 The Magnetic Force Between Two Parallel Conductors

29.3 Ampère’s Law

29.4 The Magnetic Field of a Solenoid

29.5 Gauss’s Law in Magnetism

29.6 Magnetism in Matter

30 Faraday’s Law.

30.1 Faraday’s Law of Induction

30.2 Motional emf

30.3 Lenz’s Law

30.4 The General Form of Faraday’s Law

30.5 Generators and Motors

30.6 Eddy Currents

31 Inductance.

31.1 Self-Induction and Inductance

31.2 RL Circuits

31.3 Energy in a Magnetic Field

31.4 Mutual Inductance

31.5 Oscillations in an LC Circuit

31.6 The RLC Circuit

32 Alternating Current Circuits.

32.1 AC Sources

32.2 Resistors in an AC Circuit

32.3 Inductors in an AC Circuit

32.4 Capacitors in an AC Circuit

32.5 The RLC Series Circuit

32.6 Power in an AC Circuit

32.7 Resonance in a Series RLC Circuit

32.8 The Transformer and Power Transmission

33 Electromagnetic Waves.

33.1 Displacement Current and the General Form of Ampère’s Law

33.2 Maxwell’s Equations and Hertz’s Discoveries

33.3 Plane Electromagnetic Waves

33.4 Energy Carried by Electromagnetic Waves

33.5 Momentum and Radiation Pressure

33.6 Production of Electromagnetic Waves by an Antenna

33.7 The Spectrum of Electromagnetic Waves

34 The Nature of Light and the Laws of Geometric Optics.

34.1 The Nature of Light

34.2 The Ray Approximation in Ray Optics

34.3 Analysis Model: Wave Under Reflection

34.4 Analysis Model: Wave Under Refraction

34.5 Huygens’s Principle

34.6 Dispersion

34.7 Total Internal Reflection

35 Image Formation.

35.1 Images Formed by Flat Mirrors

35.2 Images Formed by Spherical Mirrors

35.3 Images Formed by Refraction

35.4 Images Formed by Thin Lenses

35.5 Lens Aberrations

35.6 Optical Instruments

36 Interference of Light Waves.

36.1 Young’s Double-Slit Experiment

36.2 Analysis Model: Waves in Interference

36.3 Intensity Distribution of the Double-Slit Interference Pattern

36.4 Change of Phase Due to Reflection

36.5 Interference in Thin Films

36.6 The Michelson Interferometer

37 Diffraction Patterns and Polarization.

37.1 Introduction to Diffraction Patterns

37.2 Diffraction Patterns from Narrow Slits

37.3 Resolution of Single-Slit and Circular Apertures

37.4 The Diffraction Grating

37.5 Diffraction of X-Rays by Crystals

37.6 Polarization of Light Waves

38 Relativity.

38.1 The Principle of Galilean Relativity

38.2 The Michelson-Morley Experiment

38.3 Einstein’s Principle of Relativity

38.4 Consequences of the Special Theory of Relativity

38.5 The Lorentz Transformation Equations

38.6 The Lorentz Velocity Transformation Equations

38.7 Relativistic Linear Momentum

38.8 Relativistic Energy

38.9 The General Theory of Relativity

39 Introduction to Quantum Physics.

39.1 Blackbody Radiation and Planck’s Hypothesis

39.2 The Photoelectric Effect

39.3 The Compton Effect

39.4 The Nature of Electromagnetic Waves

39.5 The Wave Properties of Particles

39.6 A New Model: The Quantum Particle

39.7 The Double-Slit Experiment Revisited

39.8 The Uncertainty Principle

40 Quantum Mechanics.

40.1 The Wave Function

40.2 Analysis Model: Quantum Particle Under Boundary Conditions

40.3 The Schrödinger Equation

40.4 A Particle in a Well of Finite Height

40.5 Tunneling Through a Potential Energy Barrier

40.6 Applications of Tunneling

40.7 The Simple Harmonic Oscillator

41 Atomic Physics.

41.1 Atomic Spectra of Gases

41.2 Early Models of the Atom

41.3 Bohr’s Model of the Hydrogen Atom

41.4 The Quantum Model of the Hydrogen Atom

41.5 The Wave Functions for Hydrogen

41.6 Physical Interpretation of the Quantum Numbers

41.7 The Exclusion Principle and the Periodic Table

41.8 More on Atomic Spectra: Visible and X-Ray

41.9 Spontaneous and Stimulated Transitions

41.10 Lasers

42 Molecules and Solids.

42.1 Molecular Bonds

42.2 Energy States and Spectra of Molecules

42.3 Bonding in Solids

42.4 Free-Electron Theory of Metals

42.5 Electrical Conduction in Metals, Insulators, and Semiconductors

42.6 Semiconductor Devices

43 Nuclear Physics.

43.1 Some Properties of Nuclei

43.2 Nuclear Binding Energy

43.3 Nuclear Models

43.4 Radioactivity

43.5 The Decay Processes

43.6 Natural Radioactivity

43.7 Nuclear Reactions

43.8 Nuclear Fission

43.9 Nuclear Reactors

43.10 Nuclear Fusion

43.11 Biological Radiation Damage

43.12 Uses of Radiation from the Nucleus

43.13 Nuclear Magnetic Resonance and Magnetic Resonance Imaging

44 Particle Physics and Cosmology.

44.1 Field Particles for the Fundamental Forces in Nature

44.2 Positrons and Other Antiparticles

44.3 Mesons and the Beginning of Particle Physics

44.4 Classification of Particles

44.5 Conservation Laws

44.6 Strange Particles and Strangeness

44.7 Finding Patterns in the Particles

44.8 Quarks

44.9 Multicolored Quarks

44.10 The Standard Model

44.11 The Cosmic Connection

44.12 Problems and Perspectives


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