### 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.