University Physics Volume 1

Citation

Moebs, W., Ling, S. J., & Sanny, J. (2016). University Physics Volume 1. OpenStax. Free official edition: https://openstax.org/details/books/university-physics-volume-1

Chapter Summary

Chapter 1: Units and Measurement

Opening with the Whirlpool Galaxy as an example of how scale needs units, the chapter surveys the scope and scale of physics and introduces SI units and standards, unit conversion, dimensional analysis, order-of-magnitude (Fermi) estimates and significant figures. It ends with a general problem-solving method that the rest of the book follows.

Chapter 2: Vectors

This chapter builds the vector algebra used throughout mechanics and later electromagnetism: scalars and vectors, components in two- and three-dimensional coordinate systems, graphical and analytical addition, unit vectors, and the scalar (dot) and vector (cross) products, which later define work, torque and angular momentum.

Chapter 3: Motion Along a Straight Line

Using a maglev train as its opening example, the chapter defines position, displacement, average and instantaneous velocity and acceleration, using derivatives from the start. It derives the constant-acceleration equations, treats free fall, and closes by integrating acceleration to find velocity and displacement.

Chapter 4: Motion in Two and Three Dimensions

Kinematics is extended to vectors in two and three dimensions: displacement, velocity and acceleration vectors, projectile motion, uniform and nonuniform circular motion (centripetal and tangential acceleration), and relative motion between reference frames.

Chapter 5: Newton's Laws of Motion

The chapter turns from describing motion to its causes. It defines force, states Newton's three laws (with inertial frames and the second law in momentum form), distinguishes mass and weight, surveys common forces—normal force, tension, spring force—and teaches free-body diagrams as the central tool.

Chapter 6: Applications of Newton's Laws

Building on Chapter 5, this chapter solves more complex problems with several forces and connected objects, adds static and kinetic friction, applies Newton's laws to circular motion (including banked curves, as the racing-car opening suggests), and introduces drag forces and terminal speed, using calculus for velocity-dependent forces.

Chapter 7: Work and Kinetic Energy

Work is defined as the integral of force along a path (via the dot product), kinetic energy is introduced, and the work-energy theorem is derived as a tool that avoids solving Newton's equations directly. Power completes the chapter.

Chapter 8: Potential Energy and Conservation of Energy

The chapter defines potential energy for a system, distinguishes conservative from non-conservative forces, and develops conservation of mechanical energy. Potential-energy diagrams are used to discuss turning points and stability, and a final section on sources of energy places the general law of conservation of energy in a wider context.

Chapter 9: Linear Momentum and Collisions

Momentum, impulse and the impulse-momentum theorem lead to conservation of momentum for closed systems. The chapter classifies elastic and inelastic collisions, treats collisions in two dimensions, develops the center of mass for discrete and continuous systems, and ends with rocket propulsion.

Chapter 10: Fixed-Axis Rotation

Rotational kinematics is developed by analogy with linear motion: angular variables, constant angular acceleration, and links between angular and tangential quantities. The chapter then introduces moment of inertia and rotational kinetic energy, calculates moments of inertia by integration and the parallel-axis theorem, and defines torque, Newton's second law for rotation, and rotational work and power.

Chapter 11: Angular Momentum

Rolling motion with and without slipping, angular momentum of particles and rigid bodies, conservation of angular momentum (illustrated by the helicopter tail rotor) and the precession of a gyroscope make up this chapter.

Chapter 12: Static Equilibrium and Elasticity

Combining the force and torque conditions, the chapter solves equilibrium problems typical of construction and the human body, then introduces stress, strain and the elastic moduli (Young's, bulk and shear) and the distinction between elastic and plastic behaviour.

Chapter 13: Gravitation

Newton's law of universal gravitation is applied near Earth's surface and on astronomical scales: gravitational potential energy and escape velocity, satellite orbits and their energy, Kepler's laws, tidal forces, and a brief qualitative introduction to Einstein's theory of gravity, including black holes.

Chapter 14: Fluid Mechanics

The chapter covers density and pressure, pressure measurement, Pascal's principle and hydraulics, Archimedes' principle and buoyancy, then moves to fluid dynamics: flow rate and continuity, Bernoulli's equation and its applications, and viscosity, Poiseuille's law and turbulence.

Chapter 15: Oscillations

Unit 2, Waves and Acoustics, begins with simple harmonic motion of a mass on a spring, its energy, its relation to uniform circular motion, simple and physical pendulums, and damped and forced oscillations with resonance, motivated by the tuned-mass damper in a tall building.

Chapter 16: Waves

Mechanical waves are described mathematically through the wave function and the wave equation; the chapter derives wave speed on a stretched string, computes energy and power carried by a wave, and treats superposition, interference, standing waves and resonance on strings.

Chapter 17: Sound

The final chapter applies wave ideas to sound: pressure and displacement descriptions, the speed of sound in different media, intensity and the decibel scale, normal modes in pipes, sources of musical sound, beats, the Doppler effect and shock waves.

Key Concepts

Chapter 1: Units and Measurement

• SI base units: the meter, kilogram and second (with other base units) from which all mechanical units are derived.
• Dimensional analysis: checking that every term in an equation has the same dimensions.

Chapter 2: Vectors

• Vector components: describing a vector by its projections on coordinate axes, which turns vector addition into addition of components.
• Scalar and vector products: the dot product, which gives a scalar, and the cross product, which gives a vector perpendicular to both factors.

Chapter 3: Motion Along a Straight Line

• Instantaneous velocity and acceleration: the first and second time derivatives of position.
• Constant-acceleration kinematics: the set of equations relating position, velocity, acceleration and time when acceleration is constant.

Chapter 4: Motion in Two and Three Dimensions

• Projectile motion: independent horizontal motion at constant velocity and vertical motion with constant acceleration.
• Centripetal acceleration: acceleration toward the centre of a circular path, of magnitude v²/r.

Chapter 5: Newton's Laws of Motion

• Newton's second law: the net external force equals mass times acceleration, or the rate of change of momentum.
• Free-body diagram: a sketch of all external forces on one object, the starting point for applying Newton's laws.

Chapter 6: Applications of Newton's Laws

• Friction: static and kinetic contact forces proportional to the normal force through coefficients that depend on the surfaces.
• Terminal speed: the constant speed reached when drag balances the driving force.

Chapter 7: Work and Kinetic Energy

• Work: the line integral of force along a displacement.
• Work-energy theorem: the net work done on a particle equals its change in kinetic energy.

Chapter 8: Potential Energy and Conservation of Energy

• Conservative force: a force whose work is independent of path, allowing a potential energy to be defined.
• Conservation of mechanical energy: with only conservative forces doing work, kinetic plus potential energy stays constant.

Chapter 9: Linear Momentum and Collisions

• Impulse-momentum theorem: the impulse of the net force equals the change in momentum.
• Center of mass: the mass-weighted average position, which moves as if all external forces acted there.

Chapter 10: Fixed-Axis Rotation

• Moment of inertia: the rotational analogue of mass, depending on how mass is distributed about the axis.
• Torque: the cross product of position and force, which causes angular acceleration.

Chapter 11: Angular Momentum

• Conservation of angular momentum: with zero net external torque, a system's angular momentum is constant.
• Precession: the slow rotation of a spinning top's axis caused by gravitational torque.

Chapter 12: Static Equilibrium and Elasticity

• Conditions for equilibrium: zero net external force and zero net external torque.
• Stress, strain and elastic modulus: force per area, fractional deformation, and their ratio in the elastic range.

Chapter 13: Gravitation

• Universal gravitation: every pair of masses attracts with a force proportional to their masses and inversely proportional to the square of their separation.
• Kepler's laws: elliptical orbits, equal areas in equal times, and the period-radius relation, derived from Newton's law.

Chapter 14: Fluid Mechanics

• Archimedes' principle: the buoyant force equals the weight of fluid displaced.
• Bernoulli's equation: energy conservation along a streamline relating pressure, speed and height.

Chapter 15: Oscillations

• Simple harmonic motion: oscillation under a restoring force proportional to displacement, with sinusoidal position.
• Resonance: large-amplitude response when a driving frequency is near the natural frequency.

Chapter 16: Waves

• Wave equation: the partial differential equation whose solutions describe waves travelling at speed v.
• Standing waves: superposed waves forming fixed nodes and antinodes at particular resonant frequencies.

Chapter 17: Sound

• Sound intensity level: intensity measured on the logarithmic decibel scale.
• Doppler effect: the shift in observed frequency caused by motion of the source or observer.

Critical Analysis

Strengths

• Designed for calculus-based courses. The preface states that the book is written for the two- or three-semester calculus-based sequence, and derivatives and integrals are used from Chapter 3 onward—for instantaneous velocity, work as a line integral, moments of inertia and the wave equation—rather than being added as optional boxes.
• Consistent worked-example format. Examples follow a Strategy, Solution, Significance pattern; by a count of the PDF there are over 200 examples and about 150 "Check Your Understanding" questions, along with Problem-Solving Strategy boxes that break methods into steps.
• Rich end-of-chapter material. Each chapter review gives key terms, key equations and a section-by-section summary, followed by conceptual questions, problems by section, additional problems and challenge problems. The answer key gives all Check Your Understanding answers and odd-numbered answers to the end-of-chapter questions and problems.
• Contemporary contexts. Chapter openings use applications such as a maglev train, wind farms, a helicopter rotor, a tuned-mass damper in a skyscraper and hurricane pressure, which suits engineering students as well as physics majors.

Limitations

• Particle-physics viewpoint rather than engineering mechanics. Statics appears only in one chapter (Chapter 12), with no trusses, frames, distributed loads, shear and moment diagrams, or systematic treatment of rigid-body dynamics in the plane; students in a statics-and-dynamics course still need an engineering mechanics text.
• Limited depth in some topics. Fluid dynamics, elasticity and oscillations receive one chapter each, with no Lagrangian methods, matrix vibration analysis or multi-degree-of-freedom systems.
• Breadth makes it long. At about 950 pages including appendices, the volume covers more than one semester for many courses, and instructors must select sections.
• Answers rather than solutions. The printed answer key gives final answers for odd-numbered items only; worked solutions are in a separate Student Solution Guide referred to in the preface, so self-learners must check their reasoning there or elsewhere.

Where It Fits in the Course

In the Statics and Dynamics list, University Physics Volume 1 is the calculus-based physics foundation. Bird and Ross's Mechanical Engineering Principles, by its description, addresses mechanical engineering principles for early engineering students; the OpenStax book gives the calculus-based physics behind those principles. Hibbeler's Engineering Mechanics: Statics and Meriam and Kraige's Engineering Mechanics: Dynamics are the standard engineering texts for the course itself; read Chapters 2, 5, 6 and 9–12 of this volume first, or alongside them, to secure vectors, free-body diagrams, momentum and rotational dynamics.

Williams's Fundamentals of Applied Dynamics and Rao's Mechanical Vibrations are specialised texts that go well beyond this book. Chapter 15 (oscillations) is a useful preparation for Rao, and Chapters 9–11 for Williams, but neither topic is treated here at the level those courses require.

How to Use This Book

The book is aimed at first-year science and engineering students taking calculus concurrently or beforehand; algebra, trigonometry and basic differentiation and integration are needed. For a statics and dynamics course, the core chapters are 1–2 (units and vectors), 3–6 (kinematics and Newton's laws), 7–9 (energy and momentum), 10–12 (rotation, angular momentum and equilibrium); Chapter 13 is optional for orbital mechanics, Chapter 14 for fluids, and Chapters 15–17 for vibrations and waves.

Work through the examples by covering the Solution and attempting the Strategy yourself, answer the Check Your Understanding questions, and then do problems from the section lists before the Additional and Challenge Problems. Use the chapter review's key equations as a revision sheet. The web version on OpenStax.org has the same content and links between sections, which helps when a later chapter refers back.

Edition and Sources

This guide is based on the free PDF of University Physics Volume 1 (original publication 2016; current PDF © 2026 Rice University, licensed CC BY-NC-SA 4.0; senior contributing authors William Moebs, Samuel J. Ling and Jeff Sanny) downloaded from the official OpenStax page, https://openstax.org/details/books/university-physics-volume-1. It draws on the preface, the full table of contents, and for all seventeen chapters the opening figure and introduction, the chapter outline of sections, and the end-of-chapter summary, with counts of examples and pedagogical features.