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4 Newton’s First Law of Motion—Inertia
Forces cause changes
in motion.
A ball at rest in the middle of a
flat field is in equilibrium. No net
force acts on it.
If you saw it begin to move
across the ground, you’d look
for forces that don’t balance to
zero.
We don’t believe that changes in
motion occur without cause.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
According to Aristotle, what were the two
types of motion?
Aristotle, the foremost Greek scientist,
studied motion and divided it into two
types: natural motion and violent
motion.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Natural motion on Earth was thought to be either
straight up or straight down.
• Objects seek their natural resting places:
boulders on the ground and smoke high in the air
like the clouds.
• Heavy things fall and very light things rise.
• Circular motion was natural for the heavens.
• These motions were considered natural–not
caused by forces.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Violent motion, on the other hand, was
imposed motion.
• It was the result of forces that pushed or
pulled.
• The important thing about defining
violent motion was that it had an
external cause.
• Violent motion was imparted to objects.
• Objects in their natural resting places
could not move by themselves.
Boulders do not move without
cause.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
It was commonly thought for nearly 2000 years that a force
was responsible for an object moving “against its nature.”
• The state of objects was one of rest unless they were
being pushed or pulled or moving toward their natural
resting place.
• Most thinkers before the 1500s considered it obvious
that Earth must be in its natural resting place.
• A force large enough to move it was unthinkable.
• Earth did not move.
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
What did Copernicus state about
Earth’s motion?
Copernicus reasoned that the simplest way
to interpret astronomical observations was
to assume that Earth and the other planets
move around the sun.
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
The astronomer Nicolaus
Copernicus, (1473–1543) formulated
a theory of the moving Earth.
This idea was extremely controversial
at the time. People preferred to
believe that Earth was at the center
of the universe.
Copernicus worked on his ideas in
secret. The first copy of his work, De
Revolutionibus, reached him on the
day of his death, May 24, 1543.
Nicolaus Copernicus proposed that
Earth moved around the sun.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
According to Galileo, when is a force
needed to keep an object moving?
Galileo argued that only when friction is
present—as it usually is—is a force needed
to keep an object moving.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo, the foremost scientist
of late-Renaissance Italy, was
outspoken in his support of
Copernicus.
One of Galileo’s great
contributions to physics was
demolishing the notion that a
force is necessary to keep an
object moving.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Friction is the name given to the force that acts between
materials that touch as they move past each other.
• Friction is caused by the irregularities in the surfaces of
objects that are touching.
• Even very smooth surfaces have microscopic
irregularities that obstruct motion.
• If friction were absent, a moving object would need no
force whatever to remain in motion.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo tested his idea by rolling balls along plane surfaces
tilted at different angles.
• A ball rolling down an inclined plane speeds up.
• A ball rolling up an inclined plane—in a direction
opposed by gravity—slows down.
• A ball rolling on a smooth horizontal plane has almost
constant velocity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. Downward, the ball moves with Earth’s gravity.
b. Upward, the ball moves against gravity.
c. On a level plane, it does not move with or against gravity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo stated that if friction were entirely absent, a ball
moving horizontally would move forever.
No push or pull would be required to keep it moving once it
is set in motion.
Galileo’s conclusion was supported by another line of
reasoning.
• He described two inclined planes facing each other.
• A ball released to roll down one plane would roll up the
other to reach nearly the same height.
• The ball tended to attain the same height, even when
the second plane was longer and inclined at a smaller
angle than the first plane.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. The ball rolling down the incline rolls up the opposite
incline and reaches its initial height.
b. The ball rolls a greater distance to reach its initial height.
c. If there is no friction, the ball will never stop.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
If the angle of incline of the second plane were reduced to
zero so that the plane was perfectly horizontal, only friction
would keep it from rolling forever.
It was not the nature of the ball to come to rest as Aristotle
had claimed.
Galileo stated that this tendency of a moving body to keep
moving is natural and that every material object resists
changes to its state of motion.
The property of a body to resist changes to its state of
motion is called inertia.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
think!
A ball is rolled across a counter top and rolls slowly to a stop.
How would Aristotle interpret this behavior? How would
Galileo interpret it? How would you interpret it?
Answer: Aristotle would probably say that the ball stops
because it seeks its natural state of rest. Galileo would
probably say that the friction between the ball and the table
overcomes the ball’s natural tendency to continue rolling—
overcomes the ball’s inertia—and brings it to a stop. Only you
can answer the last question!
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
What is Newton’s first law of motion?
Newton’s first law states that every object continues in a
state of rest, or of uniform speed in a straight line,
unless acted on by a nonzero net force.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Objects at Rest
Newton’s first law, usually called the law of inertia, is a
restatement of Galileo’s idea that a force is not needed to keep
an object moving.
Simply put, things tend to keep on doing what they’re already
doing.
• Objects in a state of rest tend to remain at rest.
• Only a force will change that state.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Objects in Motion
Now consider an object in motion.
• In the absence of forces, a moving object tends
to move in a straight line indefinitely.
• Toss an object from a space station located in
the vacuum of outer space, and the object will
move forever due to inertia.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Blasts of air from many tiny holes provide a nearly friction-free
surface on the air table. If you slide a hockey puck along the
surface of a city street, the puck soon comes to rest. If you
slide it along an air table where friction is practically absent, it
slides with no apparent loss in speed.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
The law of inertia provides a completely
different way of viewing motion from the
ancients.
• Objects continue to move by
themselves.
• Forces are needed to overcome
any friction that may be present and
to set objects in motion initially.
• Once the object is moving in a
force-free environment, it will move
in a straight line indefinitely.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
A force of gravity between the sun and its planets holds
the planets in orbit around the sun. If that force of gravity
suddenly disappeared, in what kind of path would the
planets move?
Answer: Each planet would move in a straight line at
constant speed.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
Is it correct to say that the reason an object resists change
and persists in its state of motion is that it has inertia?
Answer: We don’t know the reason why objects persist in
their motion when nothing acts on them, but we know that
they do, and we call this property inertia.
•Watch Cosmos Episode #3 with Neil
DeGrasse Tyson on Newton.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
What is the relationship between mass
and inertia?
The more mass an object has, the greater
its inertia and the more force it takes to
change its state of motion.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The amount of inertia an object has
depends on its mass—which is roughly
the amount of material present in the
object.
Mass is a measure of the inertia of
an object.
You can tell how much matter is in a
can when you kick it. Kick an empty
can and it moves. Kick a can filled with
sand and it doesn’t move as much.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Not Volume
Do not confuse mass and volume.
• Volume is a measure of space and is measured in units
such as cubic centimeters, cubic meters, and liters.
• Mass is measured in the fundamental unit of kilograms.
Which has more mass, a feather pillow or a common automobile
battery?
Clearly an automobile battery is more difficult to set into motion.
This is evidence of the battery’s greater inertia and hence its
greater mass. The pillow has a larger size (volume) but a smaller
mass than the battery.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Not Weight
Mass is often confused with weight.
• We often determine the amount of
matter in an object by measuring its
gravitational attraction to Earth.
However, mass is more
fundamental than weight.
• Mass is a measure of the amount
of material in an object.
• Weight, on the other hand, is a
measure of the gravitational force
acting on the object.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Inertia
The amount of material in a particular stone is the same whether
the stone is located on Earth, on the moon, or in outer space.
• The mass of the stone is the same in all of these locations.
• The weight of the stone would be very different on Earth
and on the moon, and still different in outer space.
The stone’s inertia, or mass, is a property of the stone and not
its location.
The same force would be required to shake the stone with the
same rhythm whether the stone was on Earth, on the moon, or
in a force-free region of outer space.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
It’s just as difficult to
shake a stone in its
weightless state in
space as it is in its
weighted state on
Earth.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
We can define mass and weight as follows:
• Mass is the quantity of matter in an object. More
specifically, mass is a measure of the inertia, or “laziness,”
that an object exhibits in response to any effort made to
start it, stop it, or otherwise change its state of motion.
• Weight is the force of gravity on an object.
Mass and weight are proportional to each other in a given
place:
• In the same location, twice the mass weighs twice as
much.
• Mass and weight are proportional to each other, but they
are not equal to each other.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
One Kilogram Weighs 10 Newtons
It is common to describe the amount of matter in an
object by its gravitational pull to Earth, that is, by its
weight.
• In the United States, the traditional unit of
weight is the pound. In most parts of the world,
however, the measure of matter is commonly
expressed in units of mass, the kilogram (kg).
• At Earth’s surface, 1 kilogram has a weight of
2.2 pounds.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The SI unit of force is the newton. The SI symbol for the
newton is N.
One newton is equal to slightly less than a quarter
pound.
If you know the mass of something in kilograms and
want its weight in newtons at Earth’s surface, multiply
the number of kilograms by 10.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
One kilogram of nails weighs 10
newtons, which is equal to 2.2
pounds.
Away from Earth’s surface,
where the force of gravity is less,
the bag of nails weighs less.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
think!
Does a 2-kilogram bunch of bananas have twice as much
inertia as a 1-kilogram loaf of bread? Twice as much mass?
Twice as much volume? Twice as much weight, when
weighed in the same location?
Answer: Two kilograms of anything has twice the inertia and
twice the mass of one kilogram of anything else. In the same
location, where mass and weight are proportional, two
kilograms of anything will weigh twice as much as one
kilogram of anything. Except for volume, the answer to all the
questions is yes. Bananas are much more dense than bread,
so two kilograms of bananas must occupy less volume than
one kilogram of bread.
4 Newton’s First Law of Motion—Inertia
An object in mechanical
equilibrium is stable, without
changes in motion.
Things that are in balance with one another
illustrate equilibrium.
Things in mechanical equilibrium are
stable, without changes of motion.
The rocks are in mechanical equilibrium.
An unbalanced external force would be
needed to change their resting state.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
How can you change an object’s state
of motion?
A force is needed to change an object’s
state of motion.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
A force is a push or a pull.
A force of some kind is always required to change the state of
motion of an object.
The combination of all forces acting on an object is called the
net force. The net force on an object changes its motion.
The scientific unit of force is the newton, abbreviated N.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
When the girl holds the rock
with as much force upward as
gravity pulls downward, the net
force on the rock is zero.
Tension and Weight
A stretched spring is under a
“stretching force” called tension.
Pounds and newtons are units
of weight, which are units of
force.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Tension and Weight
There are two forces acting on the
bag of sugar:
• tension force acting upward
• weight acting downward
The upward tension in the string has
the same magnitude as the weight of
the bag, so the net force on the bag
is zero.
The bag of sugar is attracted to Earth
with a gravitational force of 2 pounds
or 9 newtons.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Force Vectors
A vector is an arrow that represents the magnitude and
direction of a quantity.
A vector quantity needs both magnitude and direction for a
complete description. Force is an example of a vector quantity.
A scalar quantity can be described by magnitude only and
has no direction. Time, area, and volume are scalar quantities.
This vector represents a force of 60 N to the right.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
• PhET Force and Motion Simulation
Basics lab
How can you express the equilibrium
rule mathematically?
You can express the equilibrium rule
mathematically as F = 0.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
What forces act on a book lying at rest on a table?
• One is the force due to gravity—the weight of the book.
• There must be another force acting on it to produce a net
force of zero—an upward force opposite to the force of
gravity.
The upward force that balances the weight of an object on a
surface is called the support force.
A support force is often called the normal force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The table pushes up on the book
with as much force as the
downward weight of the book.
This force is called the support
force—the upward force that
balances the weight of an object on
a surface.
A support force is also called the
normal force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
• The upward support force is often designated positive
and the downward weight is negative.
• The two forces add mathematically to zero.
• Another way to say the net force on the book is zero is
F = 0.
The book lying on the table compresses atoms in the table and
they squeeze upward on the book. The compressed atoms
produce the support force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The upward support force is as
much as the downward pull of
gravity.
think!
What is the net force on a bathroom
scale when a 110-pound person
stands on it?
Answer: Zero–the scale is at rest.
The scale reads the support force,
not the net force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
Suppose you stand on two bathroom scales with your weight
evenly distributed between the two scales. What is the reading
on each of the scales? What happens when you stand with
more of your weight on one foot than the other?
Answer: In the first case, the reading on each scale is half
your weight. In the second case, if you lean more on one
scale than the other, more than half your weight will be read
on that scale but less than half on the other. The total support
force adds up to your weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
How are static and dynamic
equilibrium different?
Objects at rest are said to be in static equilibrium;
objects moving at constant speed in a straight-line
path are said to be in dynamic equilibrium.
For an object at rest on a horizontal surface,
what is the support force equal to?
For an object at rest on a horizontal surface, the
support force must equal the object’s weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
Mechanical equilibrium is a state wherein no physical
changes occur.
Whenever the net force on an object is zero, the object is in
mechanical equilibrium—this is known as the equilibrium
rule.
• The  symbol stands for “the sum of.”
• F stands for “forces.”
For a suspended object at rest, the forces acting upward on
the object must be balanced by other forces acting downward.
The vector sum equals zero.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the
downward vectors. F = 0, and the scaffold is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
If the gymnast hangs with her weight evenly
divided between the two rings, how would scale
readings in both supporting ropes compare with
her weight? Suppose she hangs with slightly
more of her weight supported by the left ring.
How would a scale on the right read?
Answer: In the first case, the reading on each
scale will be half her weight. In the second case,
when more of her weight is supported by the left
ring, the reading on the right reduces to less
than half her weight. The sum of the scale
readings always equals her weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The state of rest is only one form of equilibrium.
An object moving at constant speed in a straight-line path is
also in a state of equilibrium. Once in motion, if there is no net
force to change the state of motion, it is in equilibrium.
An object under the influence of only one force cannot be in
equilibrium.
Only when there is no force at all, or when two or more forces
combine to zero, can an object be in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
When the push on the desk is the same as
the force of friction between the desk and
the floor, the net force is zero and the desk
slides at an unchanging speed.
If the desk moves steadily at constant
speed, without change in its motion, it is in
equilibrium.
• Friction is a contact force between
objects that slide or tend to slide
against each other.
• In this case, F = 0 means that the
force of friction is equal in magnitude
and opposite in direction to the
pushing force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
An airplane flies horizontally at constant speed in a straightline direction. Its state of motion is unchanging. In other
words, it is in equilibrium. Two horizontal forces act on the
plane. One is the thrust of the propeller that pulls it forward.
The other is the force of air resistance (air friction) that acts in
the opposite direction. Which force is greater?
Answer: Neither, for both forces have the same strength. Call
the thrust positive. Then the air resistance is negative. Since
the plane is in equilibrium, the two forces combine to equal
zero.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
How can you find the resultant of
two vectors?
To find the resultant of two vectors, construct a
parallelogram wherein the two vectors are
adjacent sides. The diagonal of the
parallelogram shows the resultant.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The sum of two or more vectors is
called their resultant.
Combining vectors is quite simple
when they are parallel:
• If they are in the same
direction, they add.
• If they are in opposite
directions, they subtract.
a. The tension in the rope is 300
N, equal to Nellie’s weight.
b. The tension in each rope is
now 150 N, half of Nellie’s
weight. In each case, F = 0.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The Parallelogram Rule
To find the resultant of nonparallel vectors, we use the
parallelogram rule.
Consider two vectors at right angles to each other, as shown
below. The constructed parallelogram in this special case is a
rectangle. The diagonal is the resultant R.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The Parallelogram Rule
In the special case of two perpendicular vectors that are equal
in magnitude, the parallelogram is a square.
The resultant is times one of the vectors.
For example, the resultant of two equal vectors of magnitude
100 acting at a right angle to each other is 141.4.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When Nellie is suspended at
rest from the two non-vertical
ropes, is the rope tension
greater or less than the
tension in two vertical ropes?
You need to use the
parallelogram rule to
determine the tension.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Notice how the tension vectors form a parallelogram in which
the resultant R is vertical.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Nellie’s weight is shown by the downward vertical vector.
An equal and opposite vector is needed for equilibrium, shown by the
dashed vector. Note that the dashed vector is the diagonal of the
parallelogram defined by the dotted lines.
Using the parallelogram rule, we find that the tension in each rope is more
than half her weight.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
As the angle between the ropes increases, tension increases so that the
resultant (dashed-line vector) remains at 300 N upward, which is required
to support 300-N Nellie.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When the ropes supporting Nellie are at different angles to the vertical, the
tensions in the two ropes are unequal.
By the parallelogram rule, we see that the right rope bears most of the load
and has the greater tension.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
You can safely hang from a clothesline hanging vertically, but
you will break the clothesline if it is strung horizontally.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Two sets of swings
are shown at right.
If the children on the
swings are of equal
weights, the ropes of
which swing are more likely to break?
Answer: The tension is greater in the ropes hanging at an
angle. The angled ropes are more likely to break than the
vertical ropes.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Consider what would happen if you suspended a 10-N object
midway along a very tight, horizontally stretched guitar string.
Is it possible for the string to remain horizontal without a slight
sag at the point of suspension?
Answer: No way! If the 10-N load is to hang in equilibrium,
there must be a supporting 10-N upward resultant. The
tension in each half of the guitar string must form a
parallelogram with a vertically upward 10-N resultant.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
How does the law of inertia apply to
objects in motion?
The law of inertia states that objects in
motion remain in motion if no unbalanced
forces act on them.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Copernicus announced the idea of a moving Earth in the
sixteenth century. One of the arguments against a moving
Earth was:
• Consider a bird sitting at rest in the top of a tall tree.
• The bird sees a worm, drops down vertically, and
catches it.
• It was argued that this would not be possible if Earth
moved as Copernicus suggested.
• The fact that birds do catch worms from high tree
branches seemed to be clear evidence that Earth must
be at rest.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Objects Move With Earth
You can refute this argument using the
idea of inertia.
Earth moves at 30 km/s, but so do the
tree, the worm below, and even the air in
between.
Objects on Earth move with Earth as
Earth moves around the sun.
Earth does not need to be at rest for the
bird to catch the worm.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Objects Move With Vehicles
If we flip a coin in a high-speed car,
bus, or plane, we can catch the
vertically moving coin as we would if
the vehicle were at rest.
We see evidence for the law of inertia
when the horizontal motion of the
coin before, during, and after the
catch is the same.
The vertical force of gravity affects
only the vertical motion of the coin.
Flip a coin in an airplane, and it
behaves as if the plane were at rest.
The coin keeps up with you—inertia
in action!
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again