# Calculus-Based Physics by Jeffrey W. Schnick - HTML preview

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## Chapter 1 Mathematical Prelude

cbPhysicsIa18.doc

Calculus-Based Physics I

by Jeffrey W. Schnick

Copyright 2005-2008, Jeffrey W. Schnick, Creative Commons Attribution Share-Alike License 3.0. You can copy, modify, and re-release this work under the same license provided you give attribution to the author. See http://creativecommons.org/

This book is dedicated to Marie, Sara, and Natalie.

1 Mathematical Prelude..............................................................................................................2

2 Conservation of Mechanical Energy I: Kinetic Energy & Gravitational Potential Energy ......10

3 Conservation of Mechanical Energy II: Springs, Rotational Kinetic Energy ..........................18

4 Conservation of Momentum..................................................................................................20

5 Conservation of Angular Momentum ....................................................................................25

6 One-Dimensional Motion (Motion Along a Line): Definitions and Mathematics ...................30

7 One-Dimensional Motion: The Constant Acceleration Equations ..........................................39

8 One-Dimensional Motion: Collision Type II .........................................................................43

9 One-Dimensional Motion Graphs..........................................................................................48

10 Constant Acceleration Problems in Two Dimensions ..........................................................52

11 Relative Velocity.................................................................................................................62

12 Gravitational Force Near the Surface of the Earth, First Brush with Newton’s 2nd Law........69

13 Freefall, a.k.a. Projectile Motion .........................................................................................74

14 Newton’s Laws #1: Using Free Body Diagrams ..................................................................79

15 Newton’s Laws #2: Kinds of Forces, Creating Free Body Diagrams....................................86

16 Newton’s Laws #3: Components, Friction, Ramps, Pulleys, and Strings..............................95

17 The Universal Law of Gravitation .....................................................................................104

18 Circular Motion: Centripetal Acceleration .........................................................................111

19 Rotational Motion Variables, Tangential Acceleration, Constant Angular Acceleration.....117

20 Torque & Circular Motion.................................................................................................124

21 Vectors: The Cross Product & Torque...............................................................................132

22 Center of Mass, Moment of Inertia ....................................................................................142

23 Statics ...............................................................................................................................155

24 Work and Energy ..............................................................................................................162

25 Potential Energy, Conservation of Energy, Power .............................................................171

26 Impulse and Momentum....................................................................................................180

27 Oscillations: Introduction, Mass on a Spring .....................................................................185

28 Oscillations: The Simple Pendulum, Energy in Simple Harmonic Motion .........................197

29 Waves: Characteristics, Types, Energy..............................................................................202

30 Wave Function, Interference, Standing Waves ..................................................................218

31 Strings, Air Columns.........................................................................................................225

32 Beats, The Doppler Effect .................................................................................................233

33 Fluids: Pressure, Density, Archimedes’ Principle ..............................................................239

34 Pascal’s Principle, the Continuity Equation, and Bernoulli’s Principle...............................247

35 Temperature, Internal Energy, Heat, and Specific Heat Capacity.......................................257

36 Heat: Phase Changes .........................................................................................................262

37 The First Law of Thermodynamics....................................................................................266

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