Force, Inertia, & Newton’s First Law of Motion (RP4)

Force, Inertia, & Newton’s First Law of Motion (RP4)

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Welcome back to Radical Physics. It’s time
to learn our first official law of physics. This is exciting: the first law of physics!
We might call it the first — and most basic — law of nature. No one knows why this law is true. And it
took people a LONG time to realize that it *is* true. In fact, we now think that it’s
true everywhere, for all time, and applies to all things. We might call it “the law of stubbornness.”
Its more formal name is “the law of inertia.” And even more formally, it’s called Newton’s
first law of motion. For that reason, I’m going to call it N1. N1 is Newton’s first
law of motion, the law of inertia, the law of stubbornness. Here it comes… N1: “If no net force acts on an object, then
that object’s motion does not change.” Said more simply, this law states that “objects
are stubborn”: they tend to keep doing what they were doing before — unless a net force
intervenes to change that situation. Uh-oh. N1 involves an expression that is slightly
new to us, and sounds a little technical: “net force.” All the other expressions in
this law seem familiar. But we need to be clear about the meaning of “net force” before
we can fully appreciate N1. Let’s dissect this term “net force.” The meanings
of both words, “net” and “force,” are important and subtle. “Force” is a hard thing to define,
but we tend to know it when we see it. A force is a push or a pull. Here’s a simple device that measures force.
Its called a spring scale, a force scale, or a force meter. I’m going to call it a FORCE
METER because it measures (i.e., it “meters”) force. Notice the UNITS of force inscribed on this
scale: newtons. The internationally agreed upon unit of force is the newton. (There are
plenty of people who live happy and productive lives without ever hearing of the newton.
However, I think I will convince you that your life will be happier and certainly MORE
productive if you will learn what a newton is!) Let’s get used to the newton as the unit of
force. Notice that it’s not much force. One newton is about the force of a fierce breath
of air. When you blow hard on your hand, you’re exerting about one newton of force on your
hand. When you tap your head, you’re exerting about one newton of force on your head. Of
course, you can tap hard or soft. But we’re just trying to get a “feel” for this unit
of force. That’s good enough for now. (I’m sorry that’s so vague, but a force is
a mysterious thing. And measuring it is a little mysterious, too. Here’s a newton of
pull. … And here’s a newton of push. Notice that the only difference between a pull and
a push seems to be my vantage point. I tried to define a force as a “push or a pull.” But
I can’t even quite say how these two things differ, far less what they are!) So one newton of force is about the force
of a fierce breath on your hand. Remember that. Notice something else about forces: they act
ON objects. We just talked about the force ON my hand, and the force ON my head, and
here’s the force ON this force meter. Forces act ON things. But notice, also, that my hand,
and my head, and this force meter don’t HAVE force. Forces cannot be HAD. Nothing HAS force.
My breath doesn’t HAVE force. Rather, it APPLIES a force to my hand. And, even then, my hand
does not HAVE the force. Language is very important here. We’ve got
to use words carefully in describing something so ephemeral — and yet so important — as
force. Objects don’t HAVE force; although they can APPLY a force to another object.
When talking about force, get used to the verb “to APPLY,” and forget the verb “to have.”
Nothing HAS force, not even a stick of dynamite. Here’s something else mysterious about forces:
They come into and out of existence … from nowhere. A force can act for a short time
or for a long time. But when the force stops, it’s gone. It came from nowhere and it went
nowhere. Force is not a thing. I’m not sure what it is, but it is not a thing! In this
sense, force is more a verb than a noun. The verb APPLY goes well with force; so does the
verb EXERT. But the vert “to have” does not. I started this soliloquy on force in order
to explain Newton’s First Law of Motion. Remember N1? … “If no net force acts on an object,
then that object’s motion does not change.” We were trying to understand what “net force”
is. Well, perhaps you’re getting a feeling for “force,” but what about “NET force”? The
word “net” means what you might guess: TOTAL. “Net force” means simply “total force.” Phew!
At least THAT seems easy. But it’s not, because forces add up in an
unusual way. One newton plus two newtons is not necessarily three newtons. When you’re
dealing with force, two plus two does not always equal four. Look: two newtons to the
left plus two newtons to the right gives a net force, a total force, of zero newtons.
Direction matters whenever we talk about force. So we represent forces with arrows. The fancy
way of saying this is that force is a VECTOR quantity. And to learn how to add forces requires
that you learn how to add vectors — how to add arrows. For a taproot understanding here in Radical
Physics, your intuition about adding arrows will be enough. If you understand how 2+2
can be zero, then you’re fine. But if you want more than a taproot understanding of
what “net force” means, then learn about “vector addition” in RP3b, Radical Physics episode
3b. N1 says, “If no net force acts on an object,
then that object’s motion does not change.” Let’s see if I can make this easier to write.
Let’s symbolize force with the letter capital F. And I’ll put an arrow over the F to remind
me that direction matters; force is a vector quantity. And we can denote “net” force by
writing that word as a subscript. F-sub-net. Remember: “net” just means total force — the
sum of all the force vectors that act on an object at any given time. So the start of N1 says “If F-vector-sub-net
equals zero.” “If no net force acts on an object…” Now I just want to translate “motion
does not change” into symbols. The symbol for motion, here, is v-vector; this is velocity.
Velocity is just SPEED with direction. Direction matters for velocity just as it does for force.
Like force, velocity is a vector quantity. So the word “motion” is denoted by v-vector
(velocity). But what about “change”? How do I symbolize that? If you know just a little
bit of math, you have probably seen the Greek letter capital delta represent change. In
particular, the delta, that triangle, means “difference in.” So “change in motion” is
symbolized by “delta v-vector.” And NO change in motion means “delta-v-vector equals zero.” Finally, we can symbolize Newton’s first law
of motion: If no net force acts on an object, then that object’s motion does not change.
If F-vector-net equals zero, then delta v-vector equals zero. Does the symbolic expression of N1 really
help? Yes, it really does. First, it get’s us used to symbols in physics. Each of us
spends years in school learning how to use symbols in math class; here in physics is
where that work really pays off! The symbols — the mathematics — will give physics much
of its power to solve problems. But it will also afford a kind of understanding and insight
all by itself. Look… N1 says: If F-vector-net equals zero, then
delta v-vector equals zero. But nature shows us that every logical rearrangement of this
sentence is also true! If delta v-vector equals zero, then F-vector-net
equals zero. If delta v-vector does NOT equal zero, then
F-vector-net does NOT equal zero. … But best of all:
If F-vector-net does not equal zero, then delta-v-vector does not equal zero.
I.e., if a net force acts on an object, then that object’s velocity will change!
That’s a very cool insight into the universe. It’s describing THE SOURCE OF ALL CHANGE!
Net force is the source of all change! Of course, we’ll explore this version of N1 in
much more depth in later Radical Physics episodes. But, congratulations, you’ve just learned
the first laws of nature: N1!

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