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Summary Physical science study guide
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This document contains the introductory of physical science. It explains what physical science is and it also helps you to understand the subject better. It has formulae and it shows you how to solve them.

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  • January 19, 2024
  • 185
  • 2023/2024
  • Summary

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Worked Examples from Introductory Physics
Vol. I: Basic Mechanics

David Murdock
Tenn. Tech. Univ.

September 5, 2008

,2

,Contents

To the Student. i

1 Units and Vectors: Tools for Physics 1
1.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 The SI System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Changing Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.4 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.5 Vectors; Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.6 Multiplying Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Changing Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 Vectors; Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.5 Multiplying Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2 Motion in One Dimension 27
2.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Position, Time and Displacement . . . . . . . . . . . . . . . . . . . . 27
2.1.2 Average Velocity and Average Speed . . . . . . . . . . . . . . . . . . 27
2.1.3 Instantaneous Velocity and Speed . . . . . . . . . . . . . . . . . . . . 27
2.1.4 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.5 Constant Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.6 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Average Velocity and Average Speed . . . . . . . . . . . . . . . . . . 29
2.2.2 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.3 Constant Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.4 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Motion in Two and Three Dimensions 51
3.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1.1 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3

, 4 CONTENTS

3.1.2 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1.3 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.1.4 Constant Acceleration in Two Dimensions . . . . . . . . . . . . . . . 52
3.1.5 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.6 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.7 Relative Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.3 Constant Acceleration in Two Dimensions . . . . . . . . . . . . . . . 57
3.2.4 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.5 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.6 Relative Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4 Forces I 77
4.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.1 Newton’s First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.2 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.3 Examples of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.4 Newton’s Third Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.5 Applying Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.2 Examples of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.3 Applying Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Forces and Motion II 99
5.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.1.1 Friction Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.1.2 Uniform Circular Motion Revisited . . . . . . . . . . . . . . . . . . . 99
5.1.3 Newton’s Law of Gravity (Optional for Calculus–Based) . . . . . . . 100
5.2 Worked Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.1 Friction Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.2 Uniform Circular Motion Revisited . . . . . . . . . . . . . . . . . . . 116
5.2.3 Newton’s Law of Gravity (Optional for Calculus–Based) . . . . . . . 124

6 Work, Kinetic Energy and Potential Energy 127
6.1 The Important Stuff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1.1 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1.3 Spring Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.1.4 The Work–Kinetic Energy Theorem . . . . . . . . . . . . . . . . . . . 129
6.1.5 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.1.6 Conservative Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

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