### Video Transcript

In this video, we’re going to learn
about inertia and Newton’s first law of motion. We’ll see what inertia is, how it
relates to the first law, and we’ll learn how to solve problems involving this law
of motion.

To start out, imagine that you are
the captain of a huge oil tanker, the S.S. Really Gigantic. After filling up with oil from the
gulf, you’re headed back to your home port. As the boat enters the port, you
arrive at the point where you want to stop and pull up an anchor. The one issue is that the S.S. Really Gigantic when full of oil is
also really, really massive. It’s going to take quite a lot of
rear thrusting of the engines to slow the boat down so it doesn’t run into
shore. The question of how to slow the
boat down successfully so it comes to a stop relates to the topic of inertia. And that connects to Newton’s first
law of motion.

If we start off talking of inertia,
we can understand this term as the tendency of an object’s motion not to change
unless a net force acts on that object. Let’s say we’re at an ice skating
rink and a hockey puck sits at rest on the ice. If we were to watch the hockey puck
for some time, we would notice that it continues not to move. It just sits there still. As uninteresting as that may seem,
it’s actually an expression of inertia. The puck which isn’t in motion
continues not to have any motion. Let’s imagine that a second puck
which is in motion at a constant speed slides across the ice in front of us. If we were to watch this puck, we
would notice that it continues moving in that same straight line over time. This also is this hockey puck’s
expression of inertia that because no net force acts on it, it continues to move as
it was.

Inertia is all about things staying
the same — staying as they are. This connects to the first law of
motion as Newton stated it. Newton’s first law says that an
object at rest will stay at rest and an object in motion will stay in motion unless
the object is acted on by an unbalanced force. This law by the way is also called
the law of inertia. It has to do with how objects move
when they are subjected to balanced forces. Let’s talk a bit more about what
happens when an object experiences a balanced force.

Imagine we have our hockey puck
again and we’re looking down on it from above. The puck is subjected to three
different forces: 𝐹 one, 𝐹 two, and 𝐹 three. If we add all three of these forces
together, we get zero. That means that the forces on the
puck are balanced. A balanced force on an object means
a few different things. For one thing, it means the net
force on that object is zero. Second, it means that the object is
either at rest. That is, its velocity is zero. Or it means its velocity is
constant as in the case of the sliding hockey puck. In that case, its acceleration is
zero. That is the puck’s speed and
direction are both staying the same. Let’s get some practice using
Newton’s first law of motion in a couple of examples.

A force is applied to accelerate an
object on a smooth icy surface. When the force stops, which of the
following will be true? Assume that friction is zero. The object’s acceleration becomes
zero. The object’s speed becomes
zero. The object’s acceleration continues
to increase at a constant rate. The object accelerates, but in the
opposite direction.

Of these four statements, we want
to find which one is true, considering the given information that a force is applied
to accelerate an object on a smooth surface, but the force then stops. When the force on the object stops,
that means the object will be under a balanced force. With no net force acting on it, its
acceleration will go to zero. This tells us that the first
statement given is correct. Let’s consider the three statements
that remain to understand why they’re not true.

The second statement says that
after the force on it stops, the object’s speed becomes zero. When an object experiences a
balanced force, that means the net force on it is zero, but the object to be moving
at a constant speed and remain that way even when it’s subjected to a balanced
force. So it’s not always true that an
object speed becomes zero. The third statement says that the
object’s acceleration continues to increase at a constant rate. But we’ve seen that when an object
is under a balanced force, its acceleration is zero. So this statement can’t be
true. For the same reason, the fourth
statement is incorrect as well. The object’s acceleration is
zero. Now, let’s look at an example
involving balancing forces so that the net force acting on an object is zero.

Two forces 𝐅 one equals 82.6 over
root three 𝑖 minus 𝑗 newtons and 𝐅 two equals 177.2 over root three 𝑖 minus 𝑗
newtons act on an object. What force must be added to 𝐅 one
and 𝐅 two to produce a net force of zero?

We can name the force that we want
to solve for to make all the forces add up to zero together 𝐅 three. When we consider 𝐅 three, 𝐅 one,
and 𝐅 two, we’re specifically designing 𝐅 three so that their sum is equal to
zero. That is, that the object is
subjected to a balanced force. This means that 𝐅 three is equal
to negative the sum of 𝐅 one and 𝐅 two, both of which are given in our problem
statement. If we write out 𝐅 one and 𝐅 two
as they’re given to us and then add these two forces together, their sum is 259.8
over root three 𝑖 minus 𝑗 newtons. Since 𝐅 three must equal the
negative of that, 𝐅 three is negative 259.8 over root three 𝑖 minus 𝑗
newtons. That’s the force which added to 𝐅
one and 𝐅 two will produce a net force of zero.

Let’s summarize what we’ve learnt
so far about inertia and Newton’s first law of motion.

We’ve seen that Newton’s first law
of motion — also called the law of inertia — says that an object at rest will stay
that way and an object in motion will stay that way unless acted on by an unbalanced
force. We’ve also seen that when a
balanced force acts on an object, the object either stays still — that is remains at
rest — or it moves with a constant velocity. Its acceleration is zero and so is
the net force that acts on it. Newton’s first law of motion where
objects experience a balanced force leads us into the second law, where objects
experience an unbalanced force.