How does a skater start, stop, or turn? The answer is that a force acts on the skater and causes the skater to accelerate. Once again, it's an answer that involves a new physical quantity. This time, acceleration. And it's time for me to introduce that term. As I said earlier, a skater's velocity consists of the speed in which the skater is traveling and the direction in which he's heading. If he's inertial, that is if he's experiencing no overall force, then his velocity is constant. He has a constant speed and a constant direction of travel. But if he's not inertial, if he's experiencing an overall force, then his velocity changes with time. He's accelerating. Acceleration measures the rate at which an object's velocity is changing with time. It's a subtle quantity. It's not so easy to observe. You have to look carefully. Moreover, it's another vector quantity. It has an amount and a direction. Let me show you. I'm going to, I'll be the object, and I'm going to accelerate. But first, let me get myself some room. I'll head over here to start with. And I'm about to accelerate toward your right. Now initially, I'm not going to accelerate. Here I am at velocity zero. I'm still at velocity zero, still at velocity zero. So, my velocity is not changed with time, I'm not accelerating. But I'm about to accelerate to the right at a slow rate and my velocity will develop. Here we go, toward the right. And it will become faster and faster and faster and faster until I disappear from view. Alright. So, what you should be looking for is not mine, my movement, per se, that I simply have a velocity. You should look for my velocity changing. It goes from slowly to the right, to faster and faster and faster and faster to the right. Now, let me show you acceleration towards your left. And I'm going to do a rather fast acceleration to the left. Ready, get set. Whoa, off I go. Alright. In those cases, I was accelerating in the direction of my velocity. And my velocity was increasing as a result. I was going faster and faster. My speed was steadily increasing and that's how a skater starts. The skater starts from rest with a velocity of zero, chooses a direction to accelerate, and begins to pick up speed in that direction. And continues to accelerate in that direction, thereby, going faster and faster and faster. The SI unit of acceleration is the meter per second per second or meter per second squared. Now, acceleration isn't all that familiar to anyone. So, the familiar unit for acceleration in the United States is not so familiar. But it is the foot per second squared. Well, we now have velocity and acceleration. My velocity is the speed of my motion in the direction which I'm heading. My acceleration is how that velocity is changing with time. And that acceleration has both an amount and a direction. Well, let me show you a couple of examples of this. If I accelerate in the direction of my velocity as we've seen, I speed up. On the other hand, if I accelerate opposite the direction of my velocity, I am going to slow down. Let me show you. Don't watch yet. Let me get started because I, I, I can't do everything at once. So, I'm going to get started. Now, I'm moving to the right but I'm accelerating to the left, and watch what happens to my velocity. I come momentarily to a stop and if I keep accelerating backwards here towards your left, I pick up speed and disappear off out of view on the, on the left. Well, accelerating forward, that is in the direction of my velocity, I pick up speed we, we're comfortable calling that acceleration. if I however, I accelerate opposite my velocity, so let me do this again. So, I'm going to, let me get started. So, here we go, ready, start. And now, I'm going to accelerate opposite my velocity, I come to a stop, and then I pick up speed in the opposite direction. During the stopping part of that story, so as I was heading to the right but accelerated to the left and slowing down, we have a special name that we often apply to that type of acceleration, acceleration opposite your velocity. We call it deceleration. It's, it's not necessarily a completely separate concept. It's a, just a special case of acceleration. Acceleration opposite your velocity causes you to decelerate. But there's at least one other interesting example of acceleration. What happens if instead of accelerating in the direction of my velocity or opposite the direction of velocity, I accelerate to the side. So, suppose I get started, I'll get started heading to your right, my velocity will be at the right. Here it is. Okay, I'm now moving right. And I'm going to accelerate away from you. Oh, I turned and now I'm going to keep accelerating to my left, look at what happens to me. I go in a circle. The point of this is, that if you accelerate not in the direction of your velocity, and not opposite but rather to the side, you turn. So, we now can really answer the question of how a skater, starts, stops and turns. To start, the skater, say, the skater is at rest, the skater has to pick a direction and begin to accelerating that direction. So, so here, I'll, I'll be the skater and I will start from rest and I want us, I want to hit to the right. We'll talk about what causes this acceleration surely but I am going to develop a velocity that gets larger and larger toward the right. Here we go. Okay. So, to start, I pick a direction and then I continue to accelerate in that same direction, thereby picking up speed in the direction that I had chosen. Alright. To stop, what does the skater do? Well, the skater then starts the situation already moving and accelerates opposite the skater's velocity. So, I'll do it again. Here we go. So, let me get started. Okay, I'm a skater moving along and I want to stop. I accelerate backwards opposite my velocity and I slow down. Come to a stop. And if the skater wants to turn and the skater accelerates in a direction neither forward or backward but rather, to the side. So, the skater might have been heading, let me do it differently. Might have been heading again to the right. And now, decides to, to, to turn more and more towards you all. And so, the skater is heading to the right and accelerates towards you. And the skater's velocity changes and the skater begins to turn. So, let's see whether you got all of this. I'm going to move. And then, I'm going to ask you about my velocity and my acceleration. In which direction are my velocity and acceleration, not yet, but now. My velocity was up the stairs because that's the direction that I'm moving, but my acceleration was down the stairs because I was slowing down. I was accelerating opposite my velocity and therefore, I was losing my upward speed. So, I started up at great speed and then, because I'm accelerating down the stairs, I slow down. And had I accelerated down the stairs enough? I would actually have stopped. And if I continued to slide down the stairs, I would have picked up speed in the downward, down the stairs direction. One of the reasons it's so difficult to see acceleration is that it takes at least three glances to measure it. In contrast, it takes only one glance to measure position and two glances to measure velocity. I'll show you. First, my position. There, in a single glance, you know my position. Now, my velocity. [SOUND] There, in two glances, you can see my position at one moment in time and one second later. And by comparing the two, you can see how my, my position is changing with time so you know my velocity. But to see my acceleration, you need three glances. [SOUND] If you look at those three glances, the first pair tell you my velocity early on. By comparing those two positions, you know how fast I was moving and in what direction. The second pair tell you my velocity one second later. And by comparing those two, you, those two positions, you can tell my velocity, direction, and speed. And by comparing those two velocities, the first velocity and my velocity one second later, you can see how my velocity was changing with time. You can see my acceleration. When a skater is starting, stopping, or turning, that skater is accelerating. And the skater's acceleration is caused by an external force exerted on the skater by something in her environment. When the skater is on level ground or ice, the something that usually pushes on her is the ground itself. For example, I can accelerate toward the right by pushing the ground toward the left. When I push the ground toward the left, it will react by pushing me toward the right. That will be an external force on me toward the right and I'll accelerate toward the right. Here we go. Well, I'm not much of a skateboarder. But, you could see that the act of pushing the ground toward the left caused the ground to push me toward the right and I accelerated toward the right. We'll talk about the interaction between my foot and the ground another day. What does matter is that I obtained a force toward the right and I accelerated toward the right in response. Now, in most cases, the skater is experiencing more than a single force. There are many forces. For example, when I was on the skateboard just standing there, gravity was pulling me downward and the skateboard is pushing me upward. There are already two extra forces in the mix plus the one got from the ground up. It's complicated. Well, you can't have many accelerations. You don't respond to each individual force by accelerating. Instead, you respond to the sum of all the forces acting on you, where both the amount and the direction of each of those individual forces is taken into, into account. That sum of all forces acting on you is called the net force. The net force is acting on you and you accelerate in response to that net force. When I was accelerating toward the right by pushing the ground towards the left, like this again. [LAUGH] Woah. Danger, danger. I briefly had a net force toward the right acting on me and I accelerated in response to that. Your acceleration in response to net force is proportional to that net force. The larger the net force, the greater your acceleration. And the two are in the same direction. That is, your acceleration is in the direction of the net force acting on you. Now, suppose I decide to go skateboarding with a lead brick. Physicists like lead bricks. So, I have this brick. I go and get my skateboard and so now, I'm not going to do this, I'm bad enough at skateboarding without the lead brick in my hand. But if I go and stand on the skateboard and push the ground toward the left, the ground pushes me the same just as hard as before toward the right and I begin to accelerate toward the right but not as rapidly. Somehow, having this extra object with me greatly decreases my acceleration. Why is that? Well, I have more inertia. And actually, I have more of the measure of inertia which is known as mass. So, mass is the measure of an object's inertia. And my mass without the brick is a certain amount and I accelerate relatively rapidly. My mass with the lead brick is greater and I accelerate less rapidly. So, what we see is, the more mass an object has, that is, the larger its inertia, the less it accelerates in response to a given force. In fact, an object's acceleration is inversely proportional to its mass, everything else left the same. If you push the same hardness on several different objects, each one will accelerate in proportion to one over its mass. So, we see overall, I'm going to put this down. We see overall that an object accelerates in proportion to the net force acting on it and in inverse proportion to its mass. We can bring those together into a single equation, which is known as Newton's Second Law of Motion, that an object accelerates and its acceleration is equal to the net force acting on it divided by its mass. The two physical quantities on the right side of that equation, the net force acting on the skater, and the skater's mass are the cause of this effect and the result is the skater's acceleration. So, we have cause and effect clearly distinguished in this form of Newton's Second Law of Motion. Nonetheless, it's become traditional to rearrange that equation algebraically to get rid of the division. And so, the equation is traditionally written as the net force acting on the skater is equal to the mass of the skater times the skater's acceleration. That traditional way of writing Newton's Second Law of Motion confuses, mixes up cause and effect, and so I'm not particularly fond of it. Nonetheless, it appears in an awful lot of textbooks.
