Video: Newton’s First Law of Motion

In this video, we will learn how to use Newton’s first law of motion and how to apply it to objects that are stationary, as well as objects moving at a constant velocity.

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Video Transcript

In this video, we will be discussing Newton’s first law of motion. This is one of Isaac Newton’s three famous laws that form a cornerstone of classical physics. But before we look at a statement of the first law, let’s imagine the following scenario.

Let’s say we’ve got a ball and this ball has a mass, which we will call 𝑚, of one kilogram. For now, the ball is just sitting here. It’s stationary; it’s not moving. But then let’s just say that someone comes along and pushes the ball from left to right. In other words, this person’s hand exerts a force on the ball. We can represent the force that the person exerts on the ball with an arrow acting on the ball to the right. Now, the magnitude or size of a force is most commonly measured in a unit called the newton. So let’s say that the person exerts a force of one newton on the ball.

In this scenario, what happens to our ball now? Well, intuitively, we might think that the ball will begin to move. After all, somebody’s pushed it from left to right. So we think the ball will move to the right, and this would be correct. Exactly how the ball moves — that is, how quickly and how rapidly it accelerates — we will see in a moment. But a general statement we can make here is that the ball starts moving to the right when initially it was stationary. And that is all because of the force exerted by this person on the ball.

Okay, now, let’s imagine the same ball once again, the ball with a mass of one kilogram, and it’s initially stationary, just like before. Now, instead of having just one person exerting a force on our ball, let’s see what happens when two people exert a force on our ball, specifically when one person exerts a force on the ball to the right and the other person exerts a force on the ball to the left. Importantly, in this scenario, we will assume that the force being exerted to the right is one newton, and the force being exerted to the left is also one newton.

In other words then, both people pushing the ball are pushing with the same magnitude or size of force. They’re just pushing in opposite directions because it looks like this person was going to push the ball once again to the right, as we saw here. But then this person drawn in blue decided to prevent this by exerting a force in the opposite direction of the same magnitude. In this situation, the force being exerted to the right is being exactly canceled out by the force being exerted to the left. They both have the same magnitude of one newton.

Is this therefore effective in keeping the ball stationary exactly where it is? Well, this is when Newton’s first law of motion can come into the picture. Newton’s first law of motion tells us that an object at rest will remain at rest. And an object moving with a constant velocity will continue to travel at that velocity unless acted on by an unbalanced force. Now that’s a lot to take in. So let’s break this sentence down bit by bit. The first part of the sentence talks about an object at rest. This means it’s talking about an object initially stationary, just like the ball that we were discussing here. And this law is saying that the object at rest will remain at rest. And we’ll ignore the bit about constant velocity for now. So our object will remain at rest unless it’s acted on by an unbalanced force.

Now what do we mean by an unbalanced force? Well, an unbalanced force is simply one that is not balanced by other forces. That is when forces acting on an object do not completely cancel each other out. In the first scenario that we considered, we had one hand exerting a one-newton force to the right on our ball. And that one-newton force was not counteracted by any other forces. Therefore, this one-newton force is indeed an unbalanced force. It is worth noting, though, that an unbalanced force does not have to simply be one force acting on an object. We could, for example, have lots of forces acting on our object.

In this case, we’ve shown three forces all acting to the right. And the net or overall effect of these three forces acting together, we can call this the net force on the ball, is in this case equal to a very large force acting to the right which has a magnitude equal to the magnitudes of the three pink forces added together. And even this net force counts as an unbalanced force because there’s no other force acting in the opposite direction to completely balance it out or to counteract it. So if our object has an unbalanced force acting on it, then the object will no longer remain at rest. This is what Newton’s first law of motion is telling us.

And remember, the object in this particular scenario, our ball, was initially at rest. So it started out stationary and then we exerted a net force on it, in which case the ball now starts to move. It stops being at rest. Specifically, it accelerates or changes velocity in the direction of the net force. And as we saw with this ball over here, when we pushed it to the right, the ball started moving toward the right.

However, if we now consider our ball that was initially stationary and we exert another force on it that exactly counteracts the first force to the right — so let’s say the force to the right has a magnitude of one newton and the force to the left also has a magnitude of one newton, kind of like this scenario here — then the net or overall effect of these two forces combined, the one-newton force to the right and the one-newton force to the left, is equivalent to if the ball had no forces acting on it at all.

We describe this by saying that the net or resultant force on our object is equal to zero. And this is when the forces on the ball are balanced. The one-newton force to the right is balanced completely by the one-newton forced to the left or, in other words, canceled out completely because both these forces have the same magnitude, but they act in opposite directions. So because the forces on our ball are balanced, Newton’s first law of motion tells us that the ball which was initially at rest continues to remain at rest. In other words, it’s not going to start moving in any particular direction.

So for this scenario here, where we had a ball that was initially stationary — and we had two people exerting force is on our ball, one to the right and one to the left, and those forces were exactly the same magnitude but obviously were acting in opposite directions — we can say that our ball did not have any unbalanced forces acting on it. All of the forces on the ball were balanced. And therefore, the ball initially at rest continue to remain at rest. So we’ve seen that an initially stationary object continues to remain stationary if the forces acting on it are balanced. And if an unbalanced force acts on this initially stationary object, the object accelerates. It stops being stationary.

Exactly how an unbalanced force affects the acceleration of an object is actually given by Newton’s second law of motion, which tells us that the net unbalanced force on an object is equal to the mass of the object multiplied by the acceleration it experiences in the direction of the unbalanced force. However, our focus here is on Newton’s first law of motion. And there is still one scenario we haven’t considered yet. Specifically, Newton’s first law of motion talks about an object initially moving with a constant velocity.

So let’s imagine our two pink balls once again, except that this time the top ball is initially moving with a velocity to the right, which we will call 𝑣. And let’s say that this velocity 𝑣 is equal to one meter per second. So this ball is just minding its own business, moving toward the right at a constant velocity, and then we come in and exert a force to the right on this ball of a magnitude one newton. Now, as we’ve already seen, this is an unbalanced force. And Newton’s first law of motion states that an object initially moving with a constant velocity continues to travel at a constant velocity unless acted on by an unbalanced force.

Now, in this scenario, we do have an unbalanced force acting on our object. Therefore, a ball will no longer continue to travel with that constant velocity of one meter per second. In fact, the ball will accelerate in the direction of the unbalanced force, as defined by Newton’s second law of motion, which we saw a little bit earlier. So we can say that exerting a one-newton force to the right on our ball, which was initially traveling at one meter per second to the right, results in the ball accelerating or gaining velocity in the direction of the unbalanced force.

So in this particular case, our ball at some later time will have a velocity toward the right that is greater than one meter per second because of the force we’ve exerted on it. However, if we were to instead exert the force of one newton in the opposite direction to the ball’s initial velocity, then the ball would accelerate in the direction of the unbalanced force, meaning some time later the ball would have a velocity of less than one meter per second to the right. And eventually, the ball would actually stop and then start moving toward the left. Because the one-newton force is acting in the opposite direction to the ball’s initial velocity, so in this particular case, it will slow the ball down first and then start it moving toward the left.

Now, let’s consider our second ball. Once again, it’s moving toward the right with a velocity of one meter per second. And this time, we exert one force to the right on this ball with a magnitude of one newton and another force to the left with a magnitude of one newton. Once again, as we’ve seen previously, these forces are balanced. Therefore, the net force or overall force or resultant force on our ball is equal to zero. Now, for this scenario, Newton’s first law tells us something that might be rather surprising. It tells us that an object that was initially moving with a constant velocity continues to move with that same constant velocity if there’s no net force acting on the object.

So in this particular scenario, our ball continues to move to the right with a velocity of one meter per second. Now this fact, as we’ve mentioned already, might seem a little bit surprising to us because we might imagine, for example, rolling a ball along the ground with an initial velocity toward the right of one meter per second. Why does this ball not just continue to roll at one meter per second forever? Why does it eventually slow down and stop as it’s running along the ground?

Well, the reason for this is that there is actually an unbalanced force acting on the ball, specifically, the friction between the ball and the ground. This frictional force acts in the opposite direction to the balls initial velocity. And therefore, this scenario is more like the first scenario that we considered where there is an unbalanced force acting on the object. And that is why, as the ball moves from left to right, it eventually slows down and stops.

Lastly, there is one other consideration to be made about Newton’s first law of motion. Specifically when talking about an object initially moving at a constant velocity, we’ve been told that an unbalanced force acting on this ball will cause the velocity of the ball to change. We’ve already considered what happens to a ball if we exert an unbalanced force in the same direction as the object’s velocity and if we exert an unbalanced force in the opposite direction as the object’s velocity. However, both velocities and forces are vector quantities. And the definition of a vector quantity is one which has magnitude or size and direction.

We’ve already seen how a force acting in the same direction as the object’s initial velocity causes it to speed up and a force acting in the opposite direction as the objects initial velocity causes it to slow down. But what if we exert an unbalanced force on the object that acts in a direction perpendicular to its initial velocity? Well, in this situation, the magnitude of the object’s velocity will not change. It won’t speed up or slow down. However, the direction of motion of the object will indeed change. In fact, this set-up here, where the force is constantly perpendicular to the velocity, is a prerequisite for circular motion. In other words, the object will move along a circular path if at every point along the path, the velocity is perpendicular to the direction of the force exerted.

And note here that this is not breaking Newton’s first law of motion. An object which had an initial velocity of 𝑣 to the right will at some point later have a different velocity, specifically a velocity with the magnitude 𝑣 still, but say at this point pointing downwards. And this is all because of the unbalanced force we’ve exerted on the object. In other words then, an unbalanced force doesn’t necessarily have to cause an object to speed up or slow down. It could also cause it to change direction. And at this point, we’ve covered the basics of Newton’s first law of motion.

So now that we’ve stated this law in a fair amount of detail, let’s summarize what we’ve talked about in this lesson. We firstly saw that Newton’s first law of motion states that an object initially at rest will remain at rest and an object initially moving with a constant velocity will continue to travel at that velocity unless an unbalanced force acts on the object. We also saw that an object has an unbalanced force acting on it if all the forces acting on the object do not combine together to give a net force of zero. So that is a summary of Newton’s first law of motion.

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