University Physics Volume 1 PDF Download – OpenStax

Students taking University Physics I can download the complete textbook “University Physics Volume 1” by Samuel J. Ling, Jeff Sanny, William Moebs, and contributors, free as a PDF from OpenStax. It is a calculus-based, traditional example-and-exercise-driven physics text — every section works through several fully-solved examples before a large practice-problem set, and every chapter closes with a Key Terms, Key Equations, and Key Concepts review before its Chapter Review Exercises.

This is Volume 1 of OpenStax’s three-volume University Physics series, covering Mechanics (units and measurement through gravitation and fluids) and an introduction to Oscillations, Waves, and Sound. Volume 2 continues with Thermodynamics and Electricity & Magnetism, and Volume 3 covers Optics and Modern Physics — this volume is designed to stand alone as a complete first-semester course.

Book Overview

Chapter List

Chapter 1: Units and Measurement

Difficulty: Easy · University Physics I · Key topics: scope of physics, units and standards, unit conversion, dimensional analysis, significant figures

This opening chapter builds the measurement toolkit every later chapter assumes. It starts by framing physics as the single set of laws governing everything from galaxies to atoms, then moves quickly to practical skills: the SI system of units and standards, converting between unit systems, and dimensional analysis as a way to check whether an equation could possibly be correct before you trust its answer. It closes with estimation (Fermi calculations, for approximating a quantity you can’t measure directly), significant figures, and a general framework for approaching any physics problem systematically.

Key Points:

• The same physical laws apply across every scale physics studies, from subatomic particles to galaxies
• Dimensional analysis checks whether an equation’s units are even consistent, catching many algebra mistakes before you compute a wrong number
• A Fermi calculation estimates an unknown quantity using only reasonable assumptions and rough arithmetic, without needing exact data
• Significant figures communicate how precisely a measured (not calculated) quantity is actually known
• The chapter’s problem-solving framework — understand, set up, solve, check — is used implicitly in every worked example for the rest of the book

Practice Tip: Before trusting any formula you derive, check its units on both sides — if they don’t match, the formula is wrong, no matter how the algebra looked.

Common Mistake: Reporting a calculated answer with more significant figures than the least-precise measurement used to compute it. A calculator showing eight digits doesn’t mean your answer is known to eight digits of precision.

Important Questions:

• What is dimensional analysis used for, and why is it useful even before you plug in numbers? Dimensional analysis checks that the units on both sides of an equation match. It’s useful as an early error check — if the units don’t agree, the equation is definitely wrong, which catches mistakes before you waste time computing an incorrect numerical answer.
• What is a Fermi calculation, and when would you use one? A Fermi calculation is a rough order-of-magnitude estimate built from reasonable assumptions rather than exact data — used when you need an approximate answer to a question you can’t look up or measure directly, such as estimating how many piano tuners work in a city.

Chapter 2: Vectors

Difficulty: Easy · University Physics I · Key topics: scalars vs. vectors, coordinate systems and components, vector algebra, dot and cross products

Vectors are the mathematical language the rest of the book is written in, and this chapter builds that language from scratch. It starts with the core distinction between scalars (quantities with only magnitude, like mass) and vectors (quantities with magnitude and direction, like displacement and force) — a signpost only tells you distance, not displacement, without a direction attached. From there it covers coordinate systems and vector components, the algebra of adding and subtracting vectors, and finally the two ways of multiplying vectors: the dot product (giving a scalar, used for work) and the cross product (giving a vector, used for torque and angular momentum).

Key Points:

• A scalar has only magnitude (mass, temperature); a vector has both magnitude and direction (displacement, velocity, force)
• Any vector can be broken into components along coordinate axes, which is what makes vector algebra tractable
• Vector addition is done component-by-component — add the x-components together, the y-components together, and so on
• The dot product of two vectors produces a scalar and depends on the angle between them — it’s the tool behind the definition of work
• The cross product of two vectors produces a new vector perpendicular to both — it’s the tool behind torque and angular momentum, covered in later chapters

Memory Tip: Dot product gives a scalar (“dot” is a single point — like a scalar has no direction); cross product gives a vector (the “cross” shape hints at the two arms crossing into a new perpendicular direction).

Common Mistake: Adding vector magnitudes directly without accounting for direction — two 5-newton forces pulling in opposite directions do not add to 10 newtons of net force; they cancel to zero. Vectors must be added component-by-component, or geometrically head-to-tail.

Important Questions:

• What’s the difference between a scalar and a vector, with one example of each? A scalar has only magnitude, no direction — mass (5 kg) is a scalar. A vector has both magnitude and direction — a displacement of 5 km north is a vector; the same 5 km with no stated direction is not enough information to describe motion.
• What kind of quantity does a dot product produce, and what kind does a cross product produce? A dot product of two vectors produces a scalar (a single number, no direction) — used to define work. A cross product of two vectors produces a new vector, perpendicular to both original vectors — used to define torque and angular momentum.

Chapter 3: Motion Along a Straight Line

Difficulty: Easy · University Physics I · Key topics: position, displacement, velocity, acceleration, constant acceleration, free fall

This chapter introduces kinematics — describing motion without asking what causes it — restricted to one dimension so the concepts stay clean before Chapter 4 extends them to two and three dimensions. It works up carefully from position and displacement, to average and instantaneous velocity, to average and instantaneous acceleration, building each definition on the last. The chapter’s practical payoff is the set of constant-acceleration equations, applied immediately to free fall (motion under gravity alone) as the most common real-world example of constant acceleration, and closing with how to recover velocity and displacement from an acceleration function.

Key Points:

• Kinematics describes HOW something moves — position, velocity, acceleration — without asking WHY (that’s dynamics, covered starting Chapter 5)
• Displacement is the change in position; it can be zero even after a long, winding trip that returns to the start
• Instantaneous velocity is the limit of average velocity over a shrinking time interval — conceptually, it’s a derivative
• The constant-acceleration equations (the “kinematic equations”) only apply when acceleration is truly constant — check this assumption before using them
• Free fall is simply motion under constant gravitational acceleration (g ≈ 9.8 m/s² near Earth’s surface), a specific case of the general constant-acceleration equations

Practice Tip: Before reaching for a kinematic equation, list what you know and what you’re solving for, then pick the ONE equation that contains exactly those variables and no others — this avoids solving two equations simultaneously by accident.

Common Mistake: Confusing average velocity with instantaneous velocity. Average velocity over a trip can be zero (if you return to your starting point) even though your instantaneous velocity was nonzero at every moment along the way.

Important Questions:

• What is the difference between distance traveled and displacement? Distance traveled is the total length of the path covered, always positive and always adding up. Displacement is the straight-line change in position from start to end, which can be zero (if you return to your starting point) even after traveling a large distance.
• Under what condition can you use the constant-acceleration kinematic equations? Only when acceleration is genuinely constant over the time interval in question. If acceleration changes with time, the constant-acceleration equations give wrong answers and you need calculus-based methods (Section 3.6) instead.

Chapter 4: Motion in Two and Three Dimensions

Difficulty: Medium · University Physics I · Key topics: displacement/velocity/acceleration vectors, projectile motion, circular motion, relative motion

Real motion is rarely a straight line, and this chapter extends Chapter 3’s one-dimensional kinematics into two and three dimensions using the vector tools from Chapter 2. It rebuilds position, velocity, and acceleration as vectors, then applies that machinery to three classic cases: projectile motion (an object launched into the air under gravity alone, its horizontal and vertical motions independent of each other), uniform and nonuniform circular motion (constant versus changing speed along a circular path), and relative motion (how velocity looks different to observers moving relative to each other).

Key Points:

• In 2D/3D motion, position, velocity, and acceleration are all vectors — each has both a magnitude and a direction that can change independently
• Projectile motion separates cleanly into independent horizontal (constant velocity) and vertical (constant acceleration) components — this is the single most useful simplification in the chapter
• Uniform circular motion has constant speed but constantly changing velocity direction, which means it IS accelerating (centripetal acceleration), even though its speed never changes
• Nonuniform circular motion adds a tangential acceleration component (changing speed) on top of the centripetal component (changing direction)
• Relative motion combines velocities using vector addition: your velocity relative to the ground equals your velocity relative to a moving platform plus that platform’s velocity relative to the ground

Practice Tip: For any projectile motion problem, immediately split it into two separate 1D problems — horizontal (constant velocity, Chapter 3 tools) and vertical (constant acceleration g, Chapter 3 tools) — solved independently and combined only at the end.

Common Mistake: Assuming uniform circular motion has zero acceleration because speed is constant. Speed being constant does NOT mean acceleration is zero — the direction of velocity is constantly changing, and that change IS an acceleration (centripetal acceleration), pointing toward the circle’s center.

Important Questions:

• Why can projectile motion be analyzed as two independent one-dimensional problems? Because gravity only affects the vertical direction — there’s no horizontal force (ignoring air resistance), so horizontal velocity stays constant throughout the flight, while vertical motion follows the same constant-acceleration equations as free fall. The two directions never interact.
• Does an object in uniform circular motion have acceleration? Explain. Yes. Even though its speed is constant, its velocity’s DIRECTION is constantly changing, and any change in velocity (magnitude or direction) is an acceleration. This is centripetal acceleration, and it always points toward the center of the circle.

Chapter 5: Newton’s Laws of Motion

Difficulty: Medium · University Physics I · Key topics: forces, Newton’s three laws, mass vs. weight, common forces, free-body diagrams

This chapter moves from describing motion (kinematics) to explaining it (dynamics) — the conceptual turning point of the whole course. It starts by defining force itself, then presents Newton’s three laws in sequence: the First Law (an object’s motion doesn’t change unless a net force acts on it — inertia), the Second Law (net force equals mass times acceleration, the quantitative engine behind almost every later chapter), and the Third Law (forces come in equal-and-opposite pairs acting on different objects). It clarifies the frequently confused distinction between mass and weight, surveys common everyday forces, and closes by teaching free-body diagrams — the single most important problem-solving tool in mechanics.

Key Points:

• Newton’s First Law: an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force
• Newton’s Second Law: net force equals mass times acceleration (F = ma) — this is the quantitative relationship used to solve nearly every mechanics problem from here forward
• Newton’s Third Law: forces always come in pairs — if object A pushes on object B, object B pushes back on A with equal magnitude and opposite direction
• Mass measures how much matter (and inertia) an object has and never changes with location; weight is the gravitational force on that mass and DOES change with location (your weight on the Moon is about 1/6 your weight on Earth, but your mass is identical)
• A free-body diagram isolates ONE object and draws every force acting ON it (never forces it exerts on other things) — getting this diagram right is usually the hardest and most important step in a mechanics problem

Practice Tip: Draw the free-body diagram FIRST, before writing any equations. Every force on the diagram becomes one term in your F = ma equation — skipping this step is the single most common source of wrong answers in mechanics.

Common Mistake: Confusing mass and weight, or treating Newton’s Third Law pairs as acting on the SAME object. Action-reaction pairs always act on two DIFFERENT objects (you push the wall, the wall pushes you) — they never cancel each other out in a free-body diagram of just one of those objects.

Important Questions:

• State Newton’s Second Law and explain what each symbol represents. F = ma, where F is the net force acting on an object (a vector, in newtons), m is the object’s mass (in kilograms), and a is the resulting acceleration (a vector, in m/s²). The net force is the vector sum of every force acting on the object.
• Why don’t the two forces in a Newton’s Third Law pair cancel each other out? Because they act on two different objects, not the same one. When you push a wall, your force acts ON the wall, and the wall’s reaction force acts ON you — to analyze your own motion, only the force acting on YOU (the wall pushing back) matters; the force you exert on the wall is irrelevant to your own free-body diagram.

Chapter 6: Applications of Newton’s Laws

Difficulty: Hard · University Physics I · Key topics: problem-solving strategy, friction, centripetal force, drag force and terminal speed

Where Chapter 5 introduced Newton’s laws in the abstract, this chapter applies them to genuinely harder, more realistic situations. It opens with a systematic strategy for multi-force problems — the kind with several objects, several forces, and several unknowns — before tackling friction (static friction resists the start of motion; kinetic friction resists motion already in progress, and the two have different coefficients). It then covers centripetal force, the actual force (tension, friction, gravity, or normal force, depending on the situation) that causes circular motion’s centripetal acceleration from Chapter 4, and closes with drag force and terminal speed, where resistance grows with velocity until it exactly balances gravity.

Key Points:

• Static friction resists the START of relative motion and can take any value up to a maximum (μs times the normal force); kinetic friction resists motion already happening, at a roughly constant value (μk times the normal force)
• The coefficient of kinetic friction is almost always smaller than the coefficient of static friction for the same surfaces — it’s harder to start something sliding than to keep it sliding
• Centripetal force is not a new, separate type of force — it’s whatever real force (tension, friction, gravity, normal force) happens to point toward the circle’s center and causes the centripetal acceleration
• A banked turn lets a component of the normal force itself provide centripetal force, reducing (or eliminating) the need for friction to keep a car from sliding off a curve
• Terminal speed is reached when drag force (which increases with speed) grows large enough to exactly cancel gravity, so net force and acceleration both become zero

Practice Tip: For any circular-motion force problem, ask explicitly: WHICH real force (or combination) is providing the centripetal force here? Naming it before writing equations prevents inventing a nonexistent “centripetal force” as a separate item on the free-body diagram.

Common Mistake: Drawing a separate arrow labeled “centripetal force” on a free-body diagram alongside the real forces. Centripetal force is not its own force — it’s the net effect (or component) of the real forces already on the diagram (tension, friction, gravity, normal force) that happens to point toward the center.

Important Questions:

• What’s the difference between static and kinetic friction? Static friction acts on objects that are not yet sliding relative to each other and can take any value up to a maximum threshold (μs N) needed to prevent motion from starting. Kinetic friction acts on objects already sliding and has a roughly constant value (μk N), which is usually smaller than the maximum static friction for the same surfaces.
• What happens to an object’s velocity when it reaches terminal speed while falling through air? At terminal speed, drag force has grown large enough to exactly equal gravitational force, so net force is zero and acceleration is zero — the object continues falling but at a constant velocity that no longer increases.

Chapter 7: Work and Kinetic Energy

Difficulty: Medium · University Physics I · Key topics: work, kinetic energy, the work-energy theorem, power

This chapter opens an entirely different toolkit for solving motion problems — energy methods, an alternative to Newton’s laws that is often far simpler for complex trajectories. It defines work (force acting through a distance, accounting for the angle between them) and kinetic energy (the energy an object has because it’s moving), then connects the two through the work-energy theorem: the net work done on an object equals its change in kinetic energy. This single relationship sidesteps needing to know the exact forces at every instant — only the total work matters. The chapter closes with power, the rate at which work is done or energy is transferred.

Key Points:

• Work is done by a force only when there’s displacement in the direction of (a component of) that force — a force with no resulting displacement, or one perpendicular to the displacement, does zero work
• Kinetic energy is the energy of motion: KE = ½mv² — it depends on speed squared, so doubling speed quadruples kinetic energy
• The work-energy theorem states that the NET work done on an object equals its change in kinetic energy — this bypasses needing to solve Newton’s second law directly for complicated force histories
• Energy methods are often much easier than force methods for problems involving varying forces over a path, because you only need the total work, not the force at every point
• Power is the rate of doing work (or transferring energy) — measured in watts (joules per second)

Practice Tip: When a problem asks for a final speed or the work needed to reach one, and the forces involved are complicated or vary along the path, try the work-energy theorem before attempting a force-by-force Newton’s-law solution — it’s frequently much faster.

Common Mistake: Forgetting to account for the angle between force and displacement when calculating work. A force applied perpendicular to an object’s motion (like the normal force on a horizontally sliding block) does ZERO work, no matter how large that force is.

Important Questions:

• State the work-energy theorem in words. The net work done on an object by all forces acting on it equals the change in that object’s kinetic energy. If the net work is positive, kinetic energy increases (the object speeds up); if negative, kinetic energy decreases (it slows down).
• Why does a force perpendicular to an object’s displacement do zero work, even if the force is large? Work depends on the component of force ALONG the direction of displacement (W = Fd cosθ). When force is perpendicular to displacement, θ = 90° and cos(90°) = 0, so the work done is exactly zero regardless of how strong the force is — this is why the normal force on a horizontally moving object never does any work.

Chapter 8: Potential Energy and Conservation of Energy

Difficulty: Medium · University Physics I · Key topics: potential energy, conservative vs. non-conservative forces, conservation of energy, energy diagrams

This chapter completes the energy toolkit begun in Chapter 7 by introducing potential energy — stored energy associated with an object’s position or configuration — and the crucial distinction between conservative forces (like gravity and spring forces, where energy put in can always be fully recovered, regardless of path) and non-conservative forces (like friction, which dissipates energy as heat and can never be recovered). This distinction leads directly to the conservation of mechanical energy for systems with only conservative forces — one of the most powerful problem-solving shortcuts in the entire course — and to potential energy diagrams, a graphical way to read off a system’s equilibrium points and stability at a glance.

Key Points:

• Potential energy is energy stored due to position or configuration — gravitational potential energy depends on height; spring potential energy depends on how far the spring is stretched or compressed
• A force is conservative if the work it does depends only on starting and ending position, never on the path taken — gravity and spring forces are conservative; friction is not
• Non-conservative forces (friction, air resistance) dissipate mechanical energy, usually as heat, and that energy cannot be recovered as useful mechanical energy again
• When only conservative forces act, total mechanical energy (kinetic + potential) is conserved — it can convert between forms but the total stays constant, a powerful shortcut for solving otherwise-hard problems
• A potential energy diagram (potential energy plotted against position) shows equilibrium points as flat spots — a local minimum is stable equilibrium, a local maximum is unstable equilibrium

Practice Tip: Before applying conservation of mechanical energy, check explicitly whether friction or another non-conservative force is present in the problem — if it is, you must either account for the energy it removes or fall back to work-energy methods instead of pure conservation.

Common Mistake: Applying conservation of mechanical energy to a system that includes friction without accounting for the energy friction removes. Mechanical energy is only conserved when ALL forces doing work are conservative — with friction present, total energy is still conserved, but mechanical energy alone is not, since some becomes heat.

Important Questions:

• What distinguishes a conservative force from a non-conservative force? A conservative force’s work depends only on the starting and ending positions, never on the path taken between them — gravity is a classic example. A non-conservative force’s work DOES depend on the path (friction does more work, dissipated as heat, over a longer path between the same two points).
• On a potential energy diagram, how can you tell whether an equilibrium point is stable or unstable? A local MINIMUM of the potential energy curve is a stable equilibrium — small displacements push the system back toward it. A local MAXIMUM is an unstable equilibrium — small displacements push the system further away from it.

Chapter 9: Linear Momentum and Collisions

Difficulty: Hard · University Physics I · Key topics: linear momentum, impulse, conservation of momentum, elastic/inelastic collisions, center of mass, rocket propulsion

This chapter introduces momentum as a second conserved quantity, alongside energy, giving another powerful constraint on how systems can evolve. It defines linear momentum (mass times velocity) and impulse (force acting over time, which equals the change in momentum), then establishes conservation of linear momentum for isolated systems — the tool of choice for collision problems, where forces are large but brief and hard to measure directly. It distinguishes elastic collisions (kinetic energy conserved) from inelastic collisions (kinetic energy lost, often to heat or deformation), extends the analysis to two dimensions, introduces center of mass, and closes with rocket propulsion — a real system where mass itself changes over time.

Key Points:

• Linear momentum is mass times velocity (p = mv); like velocity, it’s a vector
• Impulse (force multiplied by the time it acts) equals the change in momentum — useful when force varies rapidly and is hard to measure directly, as in a collision
• In an isolated system (no external net force), total momentum is conserved — this holds true regardless of what happens INSIDE the system, even during a violent collision
• In an elastic collision, kinetic energy is conserved along with momentum; in an inelastic collision, momentum is still conserved but kinetic energy is not (some converts to heat, sound, or deformation)
• Center of mass is the single point where a system’s total mass can be treated as concentrated for the purpose of describing its overall translational motion
• Rocket propulsion is explained by conservation of momentum applied to a system of changing mass — the rocket gains forward momentum as it ejects mass (fuel) backward at high speed

Practice Tip: For collision problems, always check first whether momentum, kinetic energy, or both are conserved — momentum is conserved in EVERY collision within an isolated system, but kinetic energy is only conserved if the collision is elastic. Confusing the two leads to wrong equations.

Common Mistake: Assuming kinetic energy is conserved in every collision. Momentum is ALWAYS conserved in an isolated system’s collision, but kinetic energy is only conserved in elastic collisions — most real-world collisions (a car crash, a lump of clay hitting a wall) are inelastic, and kinetic energy is lost.

Important Questions:

• Is momentum conserved in an inelastic collision? Is kinetic energy? Momentum IS conserved in an inelastic collision (as it is in every collision within an isolated system). Kinetic energy is NOT conserved in an inelastic collision — some of it converts to heat, sound, or permanent deformation of the colliding objects.
• How does rocket propulsion work, in terms of conservation of momentum? The rocket-plus-fuel system starts with some total momentum. As the rocket ejects burned fuel backward at high speed, that ejected mass carries momentum in the backward direction — for total momentum to stay conserved, the rocket itself must gain an equal and opposite (forward) momentum, propelling it forward.

Chapter 10: Fixed-Axis Rotation

Difficulty: Hard · University Physics I · Key topics: rotational variables, constant angular acceleration, moment of inertia, torque, Newton’s Second Law for rotation, rotational work and power

This chapter rebuilds the entire mechanics toolkit — kinematics, energy, and Newton’s second law — for rotating rigid bodies, since a real object (unlike the point masses used in earlier chapters) can spin as well as translate. It defines rotational analogs of position, velocity, and acceleration (angle, angular velocity, angular acceleration), and shows the constant-angular-acceleration equations are structurally identical to Chapter 3’s constant-acceleration equations, just with rotational variables substituted in. It introduces moment of inertia (rotational mass — how hard an object is to spin up, depending on how its mass is distributed relative to the axis) and torque (rotational force), culminating in a rotational version of Newton’s Second Law and rotational work-energy relationships.

Key Points:

• Every translational concept from earlier chapters has a direct rotational analog: position → angle, velocity → angular velocity, acceleration → angular acceleration, mass → moment of inertia, force → torque
• Moment of inertia depends not just on an object’s total mass but on HOW that mass is distributed relative to the rotation axis — mass farther from the axis contributes much more to moment of inertia than mass near the axis
• Torque is the rotational equivalent of force: it depends on both the force applied and the distance from the axis at which it’s applied (and the angle of application)
• Newton’s Second Law for rotation states that net torque equals moment of inertia times angular acceleration (τ = Iα), the direct rotational parallel to F = ma
• Rotational kinetic energy and rotational work follow the same pattern as their translational counterparts, with moment of inertia and angular velocity replacing mass and linear velocity

Memory Tip: Every equation in this chapter is a direct rotational “translation” of an equation from earlier chapters — F becomes τ, m becomes I, v becomes ω, a becomes α. If you know the translational version, you already know the rotational one’s structure.

Common Mistake: Treating moment of inertia as if it only depended on total mass, ignoring how that mass is distributed. Two objects with identical total mass can have very different moments of inertia — a mass concentrated far from the rotation axis is much harder to spin up than the same mass concentrated near the axis.

Important Questions:

• What two factors does an object’s moment of inertia depend on? An object’s total mass, and how that mass is distributed relative to the rotation axis. Mass located farther from the axis contributes disproportionately more to moment of inertia than the same amount of mass located close to the axis.
• State the rotational version of Newton’s Second Law. Net torque equals moment of inertia times angular acceleration: τ = Iα. This is the direct rotational parallel to F = ma, with torque replacing force, moment of inertia replacing mass, and angular acceleration replacing linear acceleration.

Chapter 11: Angular Momentum

Difficulty: Hard · University Physics I · Key topics: rolling motion, angular momentum, conservation of angular momentum, gyroscopic precession

This chapter introduces angular momentum as the rotational parallel to Chapter 9’s linear momentum, and it is genuinely one of the more conceptually demanding chapters in the book. It opens with rolling motion (an object simultaneously translating and rotating, like a wheel), then defines angular momentum for both rigid bodies and point particles orbiting an axis. The chapter’s central result is conservation of angular momentum for isolated systems — used to explain everything from a figure skater speeding up by pulling in their arms to a helicopter’s tail rotor countering the main rotor’s spin. It closes with gyroscopic precession, the counterintuitive wobbling motion of a spinning object under an applied torque.

Key Points:

• Angular momentum is the rotational parallel to linear momentum — for a rigid body, it equals moment of inertia times angular velocity (L = Iω)
• Rolling without slipping links an object’s translational velocity to its angular velocity through its radius, combining Chapters 10 and 11’s tools in one motion
• In an isolated system (no external net torque), total angular momentum is conserved — a system can redistribute mass to change its moment of inertia, but its angular velocity must adjust to keep L constant
• A figure skater spins faster when pulling their arms in because reducing their moment of inertia (mass closer to the rotation axis) forces angular velocity to increase to keep angular momentum constant
• Gyroscopic precession is the wobbling motion of a spinning object’s rotation axis under an applied torque — a genuinely non-intuitive result of how torque and angular momentum interact for spinning bodies

Practice Tip: When a problem describes a spinning system changing shape (arms pulled in, a platform’s mass redistributed) with no external torque mentioned, reach for conservation of angular momentum (L = Iω stays constant) rather than trying to track forces directly.

Common Mistake: Assuming angular velocity is conserved instead of angular momentum. When a spinning system’s moment of inertia changes (like a skater pulling in their arms), angular velocity CHANGES to compensate — it is angular momentum (L = Iω), not angular velocity alone, that stays constant.

Important Questions:

• Why does a figure skater spin faster when they pull their arms in? Pulling their arms in reduces their moment of inertia (mass is now distributed closer to the rotation axis). Since angular momentum L = Iω is conserved (no external torque acts), a smaller I requires a larger ω to keep L constant — so their angular velocity increases.
• What physical quantity is conserved in an isolated rotating system, and what stays constant as a result? Angular momentum (L = Iω) is conserved in an isolated system with no external net torque. As a result, if moment of inertia I changes (mass redistributes), angular velocity ω must change inversely to keep their product L constant.

Chapter 12: Static Equilibrium and Elasticity

Difficulty: Medium · University Physics I · Key topics: conditions for static equilibrium, examples, stress/strain/elastic modulus, elasticity and plasticity

This chapter bridges translational and rotational mechanics by studying objects that experience no net force AND no net torque — true static equilibrium, meaning genuinely no motion at all, not just constant velocity. It establishes the two independent conditions equilibrium requires (forces summing to zero, and torques summing to zero) and works through practical examples like ladders, beams, and bridges where both conditions must be satisfied simultaneously. The chapter’s second half shifts to material science: stress, strain, and elastic modulus describe how real materials deform under load, and the chapter closes by distinguishing elastic deformation (the material returns to its original shape) from plastic deformation (the shape change becomes permanent).

Key Points:

• Static equilibrium requires BOTH conditions simultaneously: the net force on the object is zero, AND the net torque about any point is zero
• An object can have zero net force but nonzero net torque (it would spin without accelerating linearly) — both conditions are independently necessary
• For torque calculations, you can choose ANY pivot point — a smart choice (often where an unknown force acts) can eliminate that unknown from the torque equation entirely
• Stress is force per unit area within a material; strain is the resulting fractional deformation; elastic modulus is the ratio between them, describing a material’s stiffness
• Elastic deformation is temporary — the material returns to its original shape once the load is removed. Plastic deformation is permanent, occurring once stress exceeds the material’s elastic limit

Practice Tip: When solving a static-equilibrium problem, choose your pivot point at the location of an unknown force you don’t want to solve for — that force then contributes zero torque (since its distance from the pivot is zero), simplifying the torque equation immediately.

Common Mistake: Checking only that net force equals zero and forgetting the torque condition. An object can be perfectly balanced in terms of force (net force zero) while still experiencing a net torque that would cause it to rotate — static equilibrium requires checking BOTH conditions, not just one.

Important Questions:

• What are the two independent conditions required for an object to be in static equilibrium? The net force acting on the object must be zero, AND the net torque about any point must also be zero. Both conditions are required independently — satisfying only one does not guarantee equilibrium.
• What is the difference between elastic and plastic deformation? Elastic deformation is temporary — the material returns fully to its original shape once the applied load is removed. Plastic deformation is permanent — it occurs once stress on the material exceeds its elastic limit, and the shape change persists even after the load is removed.

Chapter 13: Gravitation

Difficulty: Medium · University Physics I · Key topics: Newton’s law of universal gravitation, gravity near Earth, gravitational potential energy, satellite orbits, Kepler’s laws, tidal forces, Einstein’s theory of gravity

This chapter examines gravity across every scale physics studies, from objects on Earth’s surface to planetary orbits. It starts with Newton’s law of universal gravitation (every mass attracts every other mass, with a force depending on both masses and the square of the distance between them), then specializes it to gravity near Earth’s surface (the familiar g ≈ 9.8 m/s²), gravitational potential energy, and the energy requirements for satellite orbits. It covers Kepler’s three laws of planetary motion — the empirical patterns Newton’s law of gravitation later explained — and closes with tidal forces (gravity’s differential pull across an extended object) and a brief, conceptual introduction to Einstein’s geometric theory of gravity.

Key Points:

• Newton’s law of universal gravitation: every pair of masses attracts with a force proportional to both masses and inversely proportional to the square of the distance between their centers
• Gravitational force follows an inverse-square law — doubling the distance between two masses reduces the gravitational force between them to one-quarter, not one-half
• Gravitational potential energy is negative by the usual convention (zero defined at infinite separation), reflecting that gravity is always attractive and work must be done to separate two masses further
• Kepler’s three laws (elliptical orbits, equal areas in equal times, and the period-radius relationship) describe planetary motion empirically; Newton’s law of gravitation later explained WHY they hold
• Tidal forces arise because gravity’s strength varies with distance — the near side of an extended object (like Earth, relative to the Moon) is pulled more strongly than the far side, stretching the object slightly

Practice Tip: Remember gravity is an inverse-SQUARE law, not inverse-linear — when a distance in a gravitation problem doubles, triples, or halves, square that factor before applying it to the force, not just the distance itself.

Common Mistake: Forgetting that gravitational force follows an inverse-SQUARE law and applying a simple inverse relationship instead. Doubling the distance between two masses reduces the gravitational force to 1/4 of its original value (1/2²), not 1/2.

Important Questions:

• According to Newton’s law of universal gravitation, what happens to the gravitational force between two objects if the distance between them triples? The force decreases to 1/9 of its original value, because gravitational force is inversely proportional to the SQUARE of the distance — tripling distance means dividing force by 3² = 9.
• What causes tidal forces, in one sentence? Tidal forces arise because gravitational attraction weakens with distance, so the side of an extended object nearer to the attracting body (like Earth’s near side relative to the Moon) is pulled more strongly than the far side, stretching the object slightly along the line connecting the two bodies.

Chapter 14: Fluid Mechanics

Difficulty: Medium · University Physics I · Key topics: density and pressure, measuring pressure, Pascal’s principle, Archimedes’ principle, fluid dynamics, Bernoulli’s equation, viscosity

This chapter shifts from rigid-body mechanics to fluids — liquids and gases that continuously deform under stress — covering both fluids at rest (fluid statics) and fluids in motion (fluid dynamics). It starts with density and pressure, then covers pressure measurement and Pascal’s principle (a pressure change applied anywhere in an enclosed fluid transmits undiminished throughout, the basis of hydraulic systems). Archimedes’ principle explains buoyancy — why objects float or sink based on displaced fluid weight. The chapter’s second half covers moving fluids: Bernoulli’s equation relates a fluid’s pressure, speed, and height along a flow, and the closing sections cover viscosity and turbulence, the real-world complications that make actual fluid flow messier than the idealized equations suggest.

Key Points:

• Pressure in a fluid at rest increases with depth — this is why ears pop during a flight’s descent and why deep-sea divers must decompress slowly
• Pascal’s principle: a pressure change applied anywhere to an enclosed, incompressible fluid is transmitted undiminished to every point in the fluid and to the walls of its container — the working principle behind hydraulic lifts and brakes
• Archimedes’ principle: the buoyant force on a submerged (or floating) object equals the weight of the fluid it displaces — an object floats if this buoyant force can equal its own weight before it’s fully submerged
• Bernoulli’s equation relates pressure, fluid speed, and height along a streamline — where a fluid speeds up, its pressure drops, all else being equal
• Real fluids have viscosity (internal friction that resists flow) and can become turbulent (chaotic, unpredictable flow) at high enough speeds, complicating the idealized predictions of Bernoulli’s equation

Practice Tip: For buoyancy problems, always calculate the weight of the DISPLACED fluid, not the weight of the object itself — whether an object floats or sinks depends entirely on comparing its own weight to the maximum possible buoyant force (the weight of fluid it could displace if fully submerged).

Common Mistake: Confusing an object’s own density with whether it floats, without considering the displaced fluid’s weight explicitly. An irregularly shaped or hollow object (like a steel ship) can float even though the material it’s made of (steel) is denser than water, because it displaces enough water to generate sufficient buoyant force.

Important Questions:

• State Archimedes’ principle. The buoyant force on an object submerged (fully or partially) in a fluid equals the weight of the fluid that object displaces. If this buoyant force equals the object’s own weight before it’s fully submerged, the object floats; otherwise, it sinks.
• According to Bernoulli’s equation, what happens to a fluid’s pressure when its speed increases (at the same height)? Its pressure decreases. Bernoulli’s equation shows that pressure and speed trade off along a streamline at constant height — a fluid moving faster through a constriction has lower pressure than the same fluid moving slower in a wider section.

Chapter 15: Oscillations

Difficulty: Medium · University Physics I · Key topics: simple harmonic motion, energy in SHM, SHM and circular motion, pendulums, damped oscillations, forced oscillations

This chapter studies periodic motion — systems that repeat the same pattern of movement over and over, from a mass on a spring to a swinging pendulum to a skyscraper swaying in wind. It centers on simple harmonic motion (SHM), the specific case where the restoring force is directly proportional to displacement from equilibrium, and develops its kinematics, energy behavior, and surprising mathematical connection to uniform circular motion viewed edge-on. It covers both the simple pendulum (small-angle approximation) and physical pendulums, then introduces two real-world complications: damped oscillations (where friction or resistance gradually reduces amplitude over time) and forced oscillations (an external periodic push, which can produce resonance when it matches the system’s natural frequency).

Key Points:

• Simple harmonic motion occurs whenever the restoring force is directly proportional to displacement from equilibrium and points back toward it (Hooke’s law is the classic example, for a spring)
• SHM’s position, velocity, and acceleration as functions of time are sinusoidal — and remarkably, SHM is mathematically identical to the horizontal projection (shadow) of uniform circular motion
• In SHM, total mechanical energy (kinetic + potential) stays constant, continuously trading between the two forms as the object oscillates through its equilibrium position
• A simple pendulum’s period depends only on its length and gravitational acceleration (not on mass or amplitude, for small angles) — this is why pendulum clocks are so reliable
• Damping removes energy from an oscillating system over time, shrinking its amplitude; forced oscillations at a frequency matching the system’s natural frequency produce resonance, a dramatic amplitude increase

Memory Tip: Picture SHM as the shadow cast by an object moving in a circle at constant speed, viewed edge-on — the shadow’s back-and-forth motion IS simple harmonic motion, which is why SHM’s equations look so similar to circular motion’s equations.

Common Mistake: Assuming a pendulum’s period depends on its mass. For a simple pendulum, period depends ONLY on length and gravitational acceleration (for small swing angles) — mass cancels out of the equation entirely, which is why a heavier and lighter pendulum bob of the same length swing with identical periods.

Important Questions:

• What condition defines simple harmonic motion? Simple harmonic motion occurs when the restoring force on an object is directly proportional to its displacement from equilibrium and always points back toward that equilibrium position (F = −kx, as in Hooke’s law for a spring).
• What two factors does the period of a simple pendulum depend on (for small swing angles), and what does it NOT depend on? It depends only on the pendulum’s length and the local gravitational acceleration. It does NOT depend on the mass of the bob or (for small angles) on the amplitude of the swing.

Chapter 16: Waves

Difficulty: Medium · University Physics I · Key topics: traveling waves, mathematics of waves, wave speed on a string, energy and power of a wave, interference, standing waves and resonance

This chapter introduces mechanical waves — disturbances that propagate through a medium (like a stretched string or the surface of water) without the medium itself traveling along with the disturbance. It develops the mathematical description of a traveling wave (position as a function of both space and time), derives how wave speed depends on a string’s tension and mass density, and shows that a wave’s energy and power scale with the square of its amplitude — the same amplitude-squared relationship seen in Chapter 15’s oscillations. The chapter’s second half covers what happens when waves meet: interference (waves adding constructively or destructively) and standing waves, which arise from interference between a wave and its own reflection and are central to how musical instruments and other resonant systems work.

Key Points:

• A mechanical wave transports energy through a medium without the medium itself undergoing net displacement — individual particles oscillate in place as the wave pattern passes through them
• A wave’s energy (and the power it carries) is proportional to the square of its amplitude — doubling amplitude quadruples the energy carried
• Wave speed on a stretched string depends on the string’s tension (higher tension, faster wave) and its mass per unit length (denser string, slower wave) — not on the wave’s frequency or amplitude
• Constructive interference occurs when two waves’ displacements add in the same direction (larger resultant); destructive interference occurs when they add in opposite directions (partially or fully canceling)
• A standing wave forms from the interference of a wave and its own reflection, creating fixed points of zero displacement (nodes) and maximum displacement (antinodes) that don’t travel — this is how a guitar string produces a specific musical pitch

Practice Tip: When comparing two waves’ energy or power, work directly with the ratio of their amplitudes SQUARED — a wave with twice the amplitude carries four times the energy, not twice, a relationship that trips up quick mental estimates.

Common Mistake: Assuming wave speed on a string depends on the wave’s frequency or amplitude. Wave speed on a string is determined entirely by the string’s physical properties — tension and mass per unit length — NOT by properties of the wave itself like frequency or amplitude, which is a common point of confusion.

Important Questions:

• What two physical properties of a stretched string determine the speed of a wave traveling along it? The string’s tension (higher tension produces a faster wave) and its mass per unit length, or linear mass density (a denser, heavier string produces a slower wave). Wave speed does NOT depend on the wave’s own frequency or amplitude.
• What is the relationship between a wave’s amplitude and the energy it carries? A wave’s energy (and power) is proportional to the SQUARE of its amplitude. Doubling the amplitude of a wave quadruples the energy it carries, not merely doubles it.

Chapter 17: Sound

Difficulty: Easy · University Physics I · Key topics: sound waves, speed of sound, sound intensity, standing sound waves, musical sound, beats, Doppler effect, shock waves

This closing chapter applies Chapter 16’s wave concepts to sound specifically — a mechanical pressure wave traveling through air (or another medium) as regions of compressed and rarefied molecules. It covers the speed of sound (which depends on the medium’s properties, not on the source), sound intensity (and why the decibel scale is logarithmic, matching how human hearing perceives loudness), and standing sound waves, applied directly to how musical instruments produce specific pitches. The chapter’s most practically important sections cover beats (the periodic loudness variation heard when two close-but-different frequencies overlap, used to tune instruments) and the Doppler effect (the frequency shift heard when a sound source and listener move relative to each other), closing with shock waves for sources moving faster than sound itself.

Key Points:

• Sound is a mechanical pressure wave — a series of compressions and rarefactions traveling through a medium (commonly air) as molecules push against their neighbors
• The speed of sound depends on the properties of the medium it travels through (temperature, density, elasticity), not on the loudness or frequency of the sound itself
• Human hearing spans roughly 20 Hz to 20 kHz; sounds below this range are infrasound, and above it are ultrasound (used in medical imaging and some animal communication)
• Beats occur when two sounds of slightly different frequencies overlap, producing a periodic rise and fall in loudness at a beat frequency equal to the difference between the two original frequencies — this is the standard technique for tuning instruments by ear
• The Doppler effect shifts the frequency a listener hears when the source and listener are moving relative to each other — frequency increases as they approach and decreases as they separate

Memory Tip: Remember the Doppler effect direction with a simple rule: approaching means higher pitch (compressed waves arrive more often), receding means lower pitch (stretched waves arrive less often) — like an ambulance siren rising in pitch as it approaches and dropping as it passes.

Common Mistake: Assuming the speed of sound depends on how loud or high-pitched the sound is. The speed of sound is a property of the MEDIUM it’s traveling through (air temperature and density, for instance), not a property of the sound wave itself — a loud sound and a quiet sound of the same frequency travel through the same air at exactly the same speed.

Important Questions:

• What causes the beat phenomenon when two sounds of slightly different frequencies play together? The two sound waves periodically move in and out of phase with each other as they overlap, alternately reinforcing (louder) and partially canceling (quieter) — this produces a periodic rise and fall in loudness at a beat frequency equal to the difference between the two original frequencies.
• According to the Doppler effect, what happens to the frequency a listener hears as a sound source approaches them, compared to when it moves away? The listener hears a HIGHER frequency (higher pitch) as the source approaches, because sound waves arrive more frequently (compressed together by the source’s motion toward the listener). As the source moves away, the listener hears a LOWER frequency, because the waves are stretched apart.

Download University Physics Volume 1 PDF (Free)

This book is free from its official source, OpenStax. Click below to download the complete PDF — a free web-based reader edition (with per-section, linkable pages) is also available on the OpenStax site if you’d rather read online.

How to Study This Book

Chapters 1–4 (Units, Vectors, 1D Motion, 2D/3D Motion) are foundational tools, not optional review — every later chapter uses vectors and kinematics without re-explaining them. Do not skip ahead until these feel routine.

Chapters 5–9 (Newton’s Laws through Momentum) are the conceptual core of the course — free-body diagrams (Chapter 5) and the work-energy theorem (Chapter 7) are the two single most-used tools for the rest of the book.

Chapters 10–11 (rotational motion, angular momentum) are usually the hardest material in University Physics I for most students — they rebuild every earlier mechanics concept for rotating bodies. Expect to need more practice time here than the chapter lengths suggest.

Chapters 12–14 (Equilibrium, Gravitation, Fluids) can largely be read in the order your syllabus assigns — they build on Chapters 1–11 but don’t depend heavily on each other.

Chapters 15–17 (Oscillations, Waves, Sound) form the book’s second Unit and are more self-contained — some University Physics I courses cover only Mechanics (Chapters 1–14) in a single semester and defer waves/sound to Volume 2’s course, so check your syllabus before assuming you need all 17 chapters.

This is the first volume of OpenStax’s three-volume University Physics series — Volume 2 continues with Thermodynamics and Electricity & Magnetism, and Volume 3 covers Optics and Modern Physics.

Used In These Programs

This book is used for the University Physics I course in: BS Physics and Engineering programs. Browse all Physics books or all Physics category books.

Who Should Read This

University Physics Volume 1 is written for a student in their first semester of calculus-based physics — typically a BS Physics or Engineering student who has completed, or is concurrently taking, Calculus I. Unlike algebra-based introductory physics texts, this book uses derivatives and integrals throughout, so calculus fluency (not just familiarity) genuinely matters. Its traditional, example-and-exercise-driven style, with large end-of-section problem sets and a full Chapter Review for every chapter, suits a student who learns best by working through many worked examples before attempting problems independently.

Applicable Universities

This book is useful for students at Pakistani universities offering BS Physics or Engineering programs, including Punjab University, Virtual University, COMSATS, FAST, UET, NUST, GIKI, and other HEC-recognized institutions, where a calculus-based University Physics I course is a standard first-semester requirement.

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Related Books

• Calculus Volume 1 – Strang & Herman (OpenStax)
• Active Calculus – Matthew Boelkins (2nd Edition)

University Physics Volume 1 is this project’s first Physics-category book, covering Mechanics, Oscillations, Waves, and Sound for BS Physics and Engineering students. Browse more Physics books or Mathematics books for the rest of your semester.

University Physics Volume 1, by Samuel J. Ling, Jeff Sanny, William Moebs, and contributors. OpenStax, Rice University. Free under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 licence. Access for free at https://openstax.org/details/books/university-physics-volume-1