## January 10, 2013

### Newtonian Physics by Benjamin Crowell

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,
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.
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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
given their magnitudes and directions,
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

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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