Contents

0 Introduction and Review

0.1 The Scientific Method . . . . . .

0.2 What Is Physics? . . . . . . . .

Isolated systems and reductionism,

0.3 How to Learn Physics . . . . . .

0.4 Self-Evaluation . . . . . . . . .

0.5 Basics of the Metric System. . .

The metric system, 28.—The second,

The meter, 30.—The kilogram,

Combinations of metric units,

0.6 The Newton, the Metric Unit of Force

0.7 Less Common Metric Prefixes. . .

0.8 Scientific Notation . . . . . . . .

0.9 Conversions . . . . . . . . . .

Should that exponent be positive or

negative?, 35.

0.10 Significant Figures . . . . . . .

1 Scaling and Order-of-

Magnitude Estimates

1.1 Introduction . . . . . . . . . .

Area and volume,

1.2 Scaling of Area and Volume. . . .

Galileo on the behavior of nature on large

and small scales, 46.—Scaling of area and

volume for irregularly shaped objects,

1.3 ? Scaling Applied to Biology. . . .

Organisms of different sizes with the same

shape,.—Changes in shape to accommodate

changes in size,

1.4 Order-of-Magnitude Estimates. . .

I Motion in One Dimension

2 Velocity and Relative Motion

2.1 Types of Motion . . . . . . . . .

Rigid-body motion distinguished from motion

that changes an object’s shape,

—Center-of-mass motion as opposed to

rotation, —Center-of-mass motion in

one dimension,

2.2 Describing Distance and Time. . .

A point in time as opposed to duration,

.—Position as opposed to change in

position, .—Frames of reference,

2.3 Graphs of Motion; Velocity . . . .

Motion with constant velocity,

Motion with changing velocity,

Conventions about graphing, .

2.4 The Principle of Inertia .

Physical effects relate only to a change in

velocity, 80.—Motion is relative, 81.

2.5 Addition of Velocities. . . . . . . 83

Addition of velocities to describe relative

motion, 83.—Negative velocities in relative

motion, 83.

2.6 Graphs of Velocity Versus Time . . 85

2.7

Applications of Calculus . . . . 86

3 Acceleration and Free Fall

3.1 The Motion of Falling Objects . . . 91

How the speed of a falling object increases

with time, 93.—A contradiction in Aristotle’s

reasoning, 94.—What is gravity?, 94.

3.2 Acceleration . . . . . . . . . . 95

Definition of acceleration for linear v − t

graphs, 95.—The acceleration of gravity is

different in different locations., 96.

3.3 Positive and Negative Acceleration . 98

3.4 Varying Acceleration . . . . . . . 101

3.5 The Area Under the Velocity-Time

Graph. . . . . . . . . . . . . . . 104

3.6 Algebraic Results for Constant

Acceleration . . . . . . . . . . . . 107

3.7 ? Biological Effects of Weightlessness109

Space sickness, 109.—Effects of long space

missions, 110.—Reproduction in space,

110.—Simulated gravity, 111.

3.8

R

Applications of Calculus . . . . 111

4 Force and Motion

4.1 Force . . . . . . . . . . . . . 122

We need only explain changes in motion,

not motion itself., 122.—Motion changes

due to an interaction between two objects.,

123.—Forces can all be measured on the

same numerical scale., 123.—More than

one force on an object, 124.—Objects can

exert forces on each other at a distance.,

124.—Weight, 124.—Positive and negative

signs of force, 125.

4.2 Newton’s First Law . . . . . . . 125

More general combinations of forces, 127.

4.3 Newton’s Second Law . . . . . . 129

A generalization, 130.—The relationship

between mass and weight, 130.

4.4 What Force Is Not . . . . . . . . 132

Force is not a property of one object.,

132.—Force is not a measure of an object’s

motion., 132.—Force is not energy., 133.—

Force is not stored or used up., 133.—

Forces need not be exerted by living things

or machines., 133.—A force is the direct

cause of a change in motion., 133.

4.5 Inertial and Noninertial Frames of

Reference . . . . . . . . . . . . . 134

5 Analysis of Forces

5.1 Newton’s Third Law . . . . . . . 141

A mnemonic for using Newton’s third law

correctly, 143.

11

5.2 Classification and Behavior of Forces146

Normal forces, 149.—Gravitational forces,

149.—Static and kinetic friction, 149.—

Fluid friction, 152.

5.3 Analysis of Forces. . . . . . . . 153

5.4 Transmission of Forces by Low-Mass

Objects . . . . . . . . . . . . . . 156

5.5 Objects Under Strain . . . . . . 158

5.6 Simple Machines: The Pulley . . . 159

II Motion in Three Dimensions

6 Newton’s Laws in Three

Dimensions

6.1 Forces Have No Perpendicular

Effects . . . . . . . . . . . . . . 171

Relationship to relative motion, 173.

6.2 Coordinates and Components. . . 175

Projectiles move along parabolas., 176.

6.3 Newton’s Laws in Three Dimensions 177

7 Vectors

7.1 Vector Notation . . . . . . . . . 183

Drawing vectors as arrows, 185.

7.2 Calculations with Magnitude and

Direction . . . . . . . . . . . . . 186

7.3 Techniques for Adding Vectors . . 188

Addition of vectors given their

components, 188.—Addition of vectors

given their magnitudes and directions,

188.—Graphical addition of vectors, 188.

7.4 ? Unit Vector Notation . . . . . . 189

7.5 ? Rotational Invariance . . . . . . 189

8 Vectors and Motion

8.1 The Velocity Vector . . . . . . . 194

8.2 The Acceleration Vector . . . . . 195

8.3 The Force Vector and Simple

Machines . . . . . . . . . . . . . 198

8.4

R

Calculus With Vectors . . . . . 199

12

9 Circular Motion

9.1 Conceptual Framework for Circular

Motion . . . . . . . . . . . . . . 207

Circular motion does not produce an outward

force, 207.—Circular motion does not

persist without a force, 208.—Uniform and

nonuniform circular motion, 209.—Only an

inward force is required for uniform circular

motion., 209.—In uniform circular motion,

the acceleration vector is inward, 210.

9.2 Uniform Circular Motion . . . . . 212

9.3 Nonuniform Circular Motion . . . . 215

10 Gravity

10.1 Kepler’s Laws . . . . . . . . . 222

10.2 Newton’s Law of Gravity . . . . . 224

The sun’s force on the planets obeys an

inverse square law., 224.—The forces between

heavenly bodies are the same type of

force as terrestrial gravity., 225.—Newton’s

law of gravity, 226.

10.3 Apparent Weightlessness . . . . 229

10.4 Vector Addition of Gravitational

Forces . . . . . . . . . . . . . . 230

10.5 Weighing the Earth . . . . . . . 232

10.6 ? Evidence for Repulsive Gravity . 235

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