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.
Table of Contents
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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