 I'd like to begin this introduction on the lecture on Newton's Laws with a bit of a historical perspective. And I'd like to go back to the year 1638. Now 1638 was the year in which Galileo Galilei was 74 years of age. Galileo is one of the first modern scientists combining mathematical prowess with experimental rigor. He was an engineer. He was an experimental scientist. He was a theoretical scientist. He was all of these things in one. And for better or for worse, he was completely focused in his use of the scientific method to understand the world. Now he wouldn't have called it the scientific method. That's a more modern understanding of the practice of inquiry in the natural world using both prediction and the outcome of experiment to determine the reasons why things are actually happening. But nonetheless Galileo was definitely an adherent to what we think of as modern science. And it got him into a lot of trouble for a variety of very complicated reasons. He was found guilty, deeply suspected of heresy by the Inquisition in Italy. And in 1638 he was in about the fifth year of his house arrest. He would die in 1642 just a few years later, but in 1638 something incredible happened. And that was the publication of one of his most famous scientific works which we would translate roughly as Two New Sciences. So what were the two new sciences that Galileo was talking about in this volume? Well, one in our modern way of discussing these topics would be known as kinematics. So kinematics is the study of motion. We've been engaging in kinematics in this course. We've been looking at position. We've been looking at time. We've been looking at how position changes with time, velocity. We've been looking at how velocity changes with time, acceleration. We have seen objects in motion at a constant velocity and we have considered changes in the state of motion of objects, acceleration. Galileo did what for his time would have been considered extremely careful in detailed experiments to understand motion in the natural world. To understand what for instance might be the natural state of motion of an object. Do objects want to come to rest or do they want to remain in motion as if we're ascribing them some personality? Now we might consider many of those experiments kind of silly, but experiments as simple as this. Carefully timing the motion of objects rolling or sliding down an inclined plane like the one shown here, they can be used to slow the pull of gravity on an object to only sample part of the gravitational force that tends to want to pull objects like this down toward the center of the earth. And using extremely carefully designed instrumentation of his own conception and devising, he was able to make precision measurements the likes of which the world had really never seen before. And in doing so he built a body of data and brought to that data a keen mathematical mind that revealed deep insights into motion, the motion of material bodies in the universe around us. Now the other science that is embodied in two new sciences is the science of materials. Why are materials strong? Why are materials brittle? What do those things mean? Why is aluminum silvery and white? Why is wood darker and more muted, more of a matte, less shiny finish to it? These are deep questions. These are not silly questions. These are questions that actually ultimately bear on the atomic structure of matter, something that Galileo could not even with his keenly developed instrumentation have glimpsed at his time in history. It simply wasn't within his grasp to be able to glimpse the atom as we now understand it. But nonetheless this work was a triumph coming just four years before his death in our understanding of nature. Published outside of Italy to avoid the censors in Italy who otherwise would have prevented people from seeing this work. Now what's sort of fascinating about this period is that Galileo who invented much of his own instrumentation and then used it to do things nobody before him could have done, really embodied the modern scientist. When you invent something you can be the first person to use that something to do a task that nobody's ever done before and that makes discovery possible and people continue to do that today. When you invent a tool you are the first person to use the tool and that's something that for instance engineers in the audience should be keenly aware of. If you make something you own it for at least a little while and you get to make all the discoveries with it. Galileo was one of those kinds of minds. Now in the year of his death which was in January of 1642 another incredible event occurred about half a continent away in England on December 25th much later that year in 1642. A person was born who became in many ways even more famous and in many ways although he stood on the shoulders of the giants that came before him he surpassed those giants in ways that nobody could have imagined with so humble a beginning as being born. This person was Isaac Newton and it is Isaac Newton whose name is affixed to Newton's laws the really foundational laws of mechanics motion and so forth. So let's talk a little bit about Isaac Newton and what he did over the course of his life as a scientist. What is the natural state of motion for an object? If we could ascribe a personality to material objects for a second personify them the way that humans often do to things that they don't understand. What does an object really want to do? This was a question that had consumed many people who thought about the natural world. Let's take a look at a natural object like this very massive weight that I have here. I will set it on the table. If I leave it there, if I don't touch it any further it seems to me that its natural state of motion is to be at rest. What if I begin by moving this object? What if I do this experiment? Give it a gentle nudge. A moment later it comes back to rest and as it settles into that state you might be tempted to draw the following conclusion that objects want to be at rest. Now we do have a problem with that already having looked at relative motion, relativity. We have some sense already that what it means to be at rest is a bit of a subjective notion. After all this metal object is certainly at rest with respect to the table. The table is affixed to the ground and appears to be at rest with respect to that. But the ground is affixed to the earth and the earth that we live on spins. It makes one revolution about every 24 hours. And so certainly this object here much like the table and the surface of the earth is not at rest with respect to the stars which because their motions are so slight to the human eye they might appear to form some kind of fixed background, some absolute stationary frame of reference against which we could measure all motions in the cosmos. But of course we also know that the stars though distant are moving and some of those things we call stars are themselves actually made from hundreds of billions of stars or trillions of stars, their galaxies. So they have their own complicated motions as the stars inside of them move around. The whole universe is in motion. So what does it mean to be at rest? That's a difficult question. The scientists roughly of Galileo's era and before that the natural philosophers what we would now think of as perhaps physicists, they wrestled with that question. And many of them drew the conclusion nonetheless that rest is the natural state of all objects in the universe. I mean after all if I nudge this thing, again I gave it some ability to move but then it settles down and then it comes back to a state of rest again relative to the table. It was Isaac Newton that finally codified what was really going on here. Galileo had some insights. Galileo doing experiments had suggested that the natural state of motion for an object is whatever state it's in absent any external influences. So if an object is moving it will remain moving at constant velocity. If an object is at rest it will remain at rest assuming no influence comes along and moves it. Galileo didn't quite put that on firm mathematical footing. He had some notions. He wrote them down and certainly they were the foundations of thought for what came next. There was Isaac Newton working over the course of his life culminating in 1687 with the publishing of perhaps his greatest scientific work that really figured out that in a sense whether he realized it or not at the time and he certainly did because he denoted them as laws in his writing he uncovered really what are the foundational laws of motion, of mechanics, the science of matter and forces. Let's get into those laws in a bit. But I think it's interesting to note a few historical things. First of all Isaac Newton born in 1642. In 1666 is when most scholars would argue he first made public his development of the calculus. Calculus is something you've learned some of and you've been using in this course. You've learned it in other courses, other venues, you're applying it here. We've looked at calculus from a physics perspective to motivate the need for it and indeed this is what Isaac Newton essentially did as a natural philosopher as what we would now call a physicist. He recognized that there was a need to understand infinitesimal change in something and the influence of that infinitesimal change on other things. And so he developed what we now think of as differential calculus. He wasn't the only one. Gottfried Leibniz also around that same decadal period developed calculus somewhat independently of Newton. And so together Leibniz and Newton are credited with the creation of calculus as a new branch of mathematics. That was in 1666 at least when Newton published or made public his first works on the subject but it was 1687 when Newton published this work which is shortened in English translations to the Principia but in its full English translation would be the mathematical principles of natural philosophy. You can see why it's shortened to the Principia, the principles. This was a work that really brought together mathematics and experimentation culminating in the three laws of motion that we are going to look at now. This is an incredible work and what I think is particularly ironic about how incredible it is is how little of what we would think of as calculus actually appears in this book. This book is an extremely deep dive into geometry which was an extremely highly developed mathematics at the time of Newton. And you can see it on nearly every page as you look through this book. You have diagrams, angles, all kinds of associations between sides and angles and so forth. It's really quite incredible. There is of course calculus in here but not in the form that we would recognize it. So there are discussions of small variations and infinitesimal changes and things like that but really this is a tour de force of geometry and the power of what it can reveal about the natural world. But that is also what makes this a bit of an unapproachable work to a modern audience. It's a slog to work through this book although it's all in there. The foundations of mechanics as a science are all in here. They're not so accessible to a modern audience which gets geometry and calculus given on roughly equal footing and so it's very difficult to look at this when you take introductory physics and you see calculus as such an important thread. In fact many of the things that are laid out in here are ironically much easier in the calculus that Gottfried Leibniz or Isaac Newton had developed. But that's neither here nor there. It stands on its own as an incredible work of science. This really gave voice, codified mathematical voice with rigorous scientific experimentation to back it up, real data to the first laws of nature as we would now understand them, the laws of motion. They still stand today as valid laws of nature in so far as we understand their limitations. Of course we've discovered other laws since then, some far more comprehensive than the ones that Newton laid out in this book which include those laws. Nonetheless this is the foundation of mechanical engineering and in many ways because of some of the other things laid out in this book it's the foundation of other kinds of engineering like electrical engineering. Electrical engineering in part deals with the electric and magnetic forces and their influence on modern electronics, their uses, their challenges in modern electronics. How do you move charge from one place to another and thus carry information from one place to another? This is at the core of what electrical engineers are doing. Mechanical engineers, it's very obvious how they're using mechanics. I'll come back in a little bit at the end of this video to talk just as a teaser about why there are other things in this work that are foundational to other kinds of engineering and certainly all of this is foundational to physics as one of the core sciences that we as humans have developed. With this little introduction in mind, let's take a bit of a dive into each of Newton's laws. We'll begin with some foundational concepts before we move forward into the laws themselves. We'll take a look at the laws and what they say and what they imply. I'll come back at the end and talk a little bit more about the Principia and especially about the way that Isaac Newton closed out this work, not with a statement of absolute certainty about the cosmos based on everything that he had discovered, but rather with a kind of wonderment about what was still yet unknown about the cosmos and how in many ways, despite having gone so far, he failed to achieve many of the things that I think he had ultimately set out to achieve in doing this. But he commented on the implications for future work and future generations and it's those things that I'll come back to at the end as we come to this pivotal lecture in this part of your physics course on Isaac Newton's laws of motion. Let us begin to lay the foundations for a study of what will come to see our Newton's laws of motion, the foundational laws to understand motion in the natural world. The key ideas that we're going to explore in this section of the course are the following. We're going to come to understand that it is forces that are the cause of changes in states of motion and by a state of motion I mean the velocity of an object. We will understand that force is also described as a vector of vector quantity and it obeys as a result of that all the properties of all vectors. And finally we will then dive into an exploration of Sir Isaac Newton's three laws of motion. These are the very first laws of nature that we're going to encounter in this class and everything that we have studied so far has been leading up to this moment. But to begin we need to lay down some foundational concepts that will allow us to dig a little deeper into the laws themselves as we encounter them. And the first concept we're going to look at right now is the concept of inertia. What exactly is inertia? You're going to see that it arises quite a bit in this discussion. And quite simply it is merely the tendency for objects to oppose changes in motion. This is not an unfamiliar experience for all of us. Maybe you've never actually played with a bird feather before but if you think about a very light object something that doesn't feel very heavy in your hand and a feather is a good example of that you can imagine blowing very gently on the feather. And even a light breath will cause it to move in the direction of the breath. It will catch on the wind that you generate in the air around you and it will flutter from your hand. It does not take much force, much of an impulse to move a light object like a feather or a piece of paper or something like that. But if you then compare that to your experience with something that feels far heavier in your hand than for instance a piece of paper or a bird's feather, for instance a bowling ball or a large rock, some kind of big chunk of metal or a very large piece of wood, this is something which if you were to blow on it even as hard as you could and certainly far more than you would need in order to move a feather or a piece of paper it will be very unlikely that you are able to make that same object move for the same or even much more force than was required to move the object that felt lighter in your hand. And so we can simply say that there's some property of objects, we can call it inertia, and it's a property that both the feather and the bowling ball have. The feather has very little of this property, very little inertia, while the bowling ball has very much more inertia. Again this is simply some kind of inherent resistance to changes in the state of motion. So for instance if a feather or a bowling ball begin with zero velocity and you wish to give them the same velocity, say one meter per second, it requires a lot more force to make that change in the heavy object than it does in the light. We can say that the light object is more susceptible to significant changes, even given small forces or actions that we take upon it. As we'll see, there is a law of motion in the three laws which includes a quantity that takes the place, it represents the inertia of an object. This is something that's very well represented in the laws of motion and that's why this concept is introduced right now. Now there's one more thing that we need to take a look at. Before we can embark on an appropriate discussion of forces, we have to understand that when we discuss forces and changes in the state of motion or even just states of motion themselves, we have to understand that there are two major kinds of frames of reference that we can be working in. One of these is an inertial reference frame and there's that word again, inertia, something about a tendency to be resistant to changes in state of motion. An inertial reference frame is simply a frame of reference in which there are no unaccounted for net unbalanced forces and thus no net accelerations. These are frames of reference that can be established to be either at rest or moving with a constant velocity. You're going to see a demonstration of an alternative to this in a moment once we define it. But basically if you are able to say with confidence by doing some kind of modest experiment that there don't seem to be any forces present when there shouldn't be any, then you probably have established that you're working in an inertial frame of reference. Now contrast that with non-inertial reference frames. It's a very nice categorization. These are reference frames in which there are in fact some net unbalanced forces and thus there are accelerations that occur even when you don't think that there should be any. Even when you think I should be able to move an object at a velocity and I have looked around and I don't see any obvious sources of additional force around me in this frame of reference, what does the velocity of the object do versus what do I expect? Well if this is truly an inertial reference frame the velocity of the object should remain constant. There are no forces, thus there are no changes in the state of motion. But in a non-inertial reference frame even when you think you've accounted for all forces and that they should all have canceled each other out, you may still observe that your object nonetheless experiences some kind of change in the state of motion, some kind of acceleration, and that would indicate to you that you're in a non-inertial reference frame. Again, we're going to see an example of this in a moment. It's really quite stunning. The following video is from the Physical Science Study Committee in 1960. And while it may seem a bit dated to you, it captures all of the essential ingredients we've just been talking about. This video had a particular effect on me when I first saw it in college because it really helped me to rethink my understanding of motion. Here we see the two individuals sitting at a table passing a puck on a relatively low resistant surface back and forth between each other. They don't appear to be in motion relative to anything else. Nothing in this picture seems to be moving. And so of course when they push the puck once they let go, it moves at a constant velocity between them until the other one stops it. Now what they're going to do is they're going to change the state of motion of the frame of reference. They're sitting on a cart, the cart can be moved, and the two individuals, the table, and the puck will all begin to move at a constant velocity, and they'll repeat the game of pass-back. And we see that yet again from our perspective in this frame, the puck appears to move at a constant velocity between them. We could say therefore that they must be in an inertial reference frame. Even though they're at motion, they are moving at a constant velocity, and so there appear to be no net accelerations on the puck. Once it's in free motion between the two of them, it maintains its state of motion. It maintains a constant velocity. We're going to see this experiment one more time, but viewed from a vantage point outside of the whole frame so you can see the whole thing in action. And so you can see the cart is moving, and they're passing the puck between them. Now, for this is great for relative motion because we can see that the puck appears to almost stand still from our perspective, but nonetheless, everything's moving with constant velocity once accelerations from their hands stop. Now, let's contrast that with what we're about to see. Here again, we have the table in the puck, and one of the gentlemen pushes on the puck, but instead of moving straight between them, the puck now goes in a circle. Watch. It will execute circular motion, and when something executes circular motion, there's an implied centripetal acceleration. What's going on? Nothing appears to be in motion, and yet the puck is now executing a very strange motion compared to before, whereas before it moved at a constant velocity once the hand let go of it, now it seems to move at a constant speed, but it does so in a circle. I could possibly explain this strange motion. What's going on is that these two individuals are now in a non-inertial reference frame. They're in a frame where there are, in fact, net accelerations, and we can see this from a camera mounted above them. The table on the platform is now spinning. These two individuals are spinning, and the puck is standing relatively still in space when he lets go of it, but it appears from the perspective at the table who's in the non-inertial reference frame that, in fact, the puck is executing circular motion. It's a perspective from this non-inertial reference frame that there is an acceleration and thus an implied net unbalanced force. I certainly wouldn't want to be sitting in this frame. This would be a very uncomfortable and unpleasant experience, but nonetheless it illustrates beautifully this effect of what appears to be an acceleration when you're in a frame that itself is experiencing an acceleration. The object is, in fact, moving at a constant velocity along a straight line from the perspective of someone outside of this frame, but inside of this frame it appeared to be moving in a circle, as if there was some unbalanced and tripital acceleration, something holding it in circular motion. It's really quite a stunning thing, and when you begin to understand frames of reference and what can happen to them, what kinds of motion they can execute, you can begin to see these effects in the world around you, even on Earth. For now, we're going to work with inertial reference frames, and as we'll see, defining a frame as inertial or non-inertial will be really best served by applying one of Newton's laws of motion, but this concept is introduced now ahead of that law of motion so that we might feel more comfortable with this concept once we actually encounter the laws of motion themselves. Another important concept regarding force, that is, actions that can change the state of motion, the velocity of an object is that it is a vector quantity. So I've stated that, but I haven't really demonstrated that, and it's important to demonstrate things in the world so that you can build some confidence that in fact this is a reliable observation of the natural world. So how do we describe those influences that cause the state of motion, that is the velocity of an object, to change? Well, these things we call forces. So we can name them, but how do we describe them? How do we assign a mathematical vocabulary to these things, these forces, so that we might on paper describe them, use them, and most importantly make predictions with them? After all, we are scientists and it's not enough to be able to write down a self-consistent mathematical explanation of something. You have to use it to make predictions and you have to do experiments to test those predictions to see if they are accurate or inaccurate descriptions of the natural world. I think it's useful for us to actually look at forces in action in the wild so that we can see their underlying mathematical character reveal directly to the eye. Let's do a simple experiment with a heavy brick made out of iron. I place it on the table, rest the knuckles of my right hand against it and I exert a push, a force. I'm pushing it along a horizontal axis to the right. So you can write this as a vector. What if I take the knuckles of my left hand and I now push down in the camera view? We see that the brick moves down in the same direction I'm pushing. So this can also be described as a vector in the negative Y direction for instance. I'll reset the brick and I will put the knuckles of both my right hand and my left hand on the brick and I will push in those perpendicular directions. Watch what happens. The brick moves not only in the horizontal or only in the vertical direction but in a combination of both. It's exactly like adding two vectors with components along X and Y. Now from this simple experiment we can see that a force that is directed along say one coordinate axis, one specific direction and a force in a direction perpendicular to that along another coordinate axis, they add up and they add up in exactly the way that you would expect vector quantities to add. The direction of one component and the other component together combine to define the total direction of the final resultant motion. They add up to a force in exactly the same sense that the vectors that we've been playing with in class would in fact add. Thus although this is a simple experiment and by no means a definitive way of establishing this character of forces nonetheless I think you can see that we have revealed that forces themselves much like velocity and acceleration have a vector nature and we shall henceforth describe forces in this way. Now what happens when there's more than one force? Your experience at this point with vector quantities should provide you with something resembling a kind of intuition to the answer. We can describe what we saw in the video a moment ago in that experiment with the large metal brick. In the video we saw the following situation. I first applied a force along one axis. We could call this the x axis and this is how mathematically I might describe this force. I might write down a vector f1 with the vector hat over it and I might set that equal to the strength of that force. This could hide a minus sign here. Maybe I want to put the direction in this number f with the subscript x as well but somehow I have a number describing the magnitude, possibly the sign of this force and I put here the unit vector i hat to indicate that whatever it's sign it's directed along the x axis in some way. And then I separately showed you what it would look like to apply another force in a perpendicular direction to that. We saw what happened to the brick as a result and we might describe that force with a separate symbol f subscript 2 with a vector hat over it and here again I might describe possibly including the sign of this force with a number f subscript y, f y and it's in the j hat direction. It's entirely along the y axis. Well then in the video I showed you what would happen if I pushed simultaneously with f1 vector and f2 vector and we saw that we didn't only get motion along the x axis we didn't only get motion along the y axis we got motion in both directions with different degrees simultaneously and that's exactly how vectors add you would add f1 to f2 and the resulting final vector which cannot really be any further simplified is a total vector with an x component and a y component and thus we get the resulting sum of the two actions acting along a diagonal kind of direction in that coordinate system. And then of course you can immediately generalize this to any two or even more vectors, forces just like adding any other vector so we might have a new f1 and a new f2 vector. They might each have their own x and y components and when we add these together we add the components together with their signs and keep only the ones grouped together that are in the x direction and we do the same exercise grouping only the components in the y direction and if we can actually put in numbers for this then we might get numbers in the i hat plus numbers in the j hat direction and we have our vector describing the total sum of these two forces. It's really nothing new here it's just that we are establishing a definition a mathematical description for something we already felt we already had experience with and that is that if I apply some action on an object I can change its state of motion we call that action a force and we can describe forces as vectors because we can reveal quickly that they have a vector character to them and so finally we arrive now having established a basis on which to digest Newton's laws of motion we arrive finally at the first law and the first law is the mathematical expression of something that Galileo articulated and that Newton codified mathematically establishing this really as a reliable description of nature regardless of what part of nature you are considering and it can be stated in multiple ways it can be stated mathematically it can be stated verbally so let's try verbal first Newton's first law says the following an object at rest will remain at rest and similarly an object that's already in motion will remain at constant velocity unless in either case that object is acted upon by some external force and by an outside force I mean for instance it could be three or four forces whose net effect is an imbalance a non-zero force left on the object so an object at rest remains at rest and an object in motion remains at constant velocity unless acted upon by an outside force now another way of saying this is objects on which the net force is zero maintain their current state of motion they're at rest no net force they stay at rest if they're in motion they will be in motion at a constant velocity no acceleration unless the net force is not zero in which case their state of motion can be changed forces change velocities they change the state of motion of an object so the first law of motion can be written in a mathematical form as shown below and in many ways this is kind of an extension of the vector example I gave you on the previous slide and that is that if we have a whole bunch of forces F1 vector and F2 vector and a bunch of others all the way up to some number N N could be 100 N could be 3 some number N I don't know how many but if I have a vector that represents sum those vectors together assuming they all act on the same object then the that sum can be represented mathematically using the capital Greek letter sigma you put underneath it the beginning of the sum and you put above it the final number in the sum so we have some index that represents each force I can be equal to 1, I can be equal to 2 I can be equal to 3, etc. all the way up to I equals N this symbol compactly represents this much longer sum that I've written out over here and the first law of motion simply states that if the sum of the forces whatever they are acting on an object is equal to 0 there is no net force on the object then you shall find that the acceleration experienced by that object the change in its state of motion the change in its velocity with time is 0 I write it over here as it was presented in Latin from Isaac Newton's mathematical principles of natural philosophy or the Principia I don't translate it here but essentially in Latin what Isaac Newton is telling us is the summary of his investigations and the investigations that came before him is what I've written up here in one English sentence or another now Newton's first law is the law that I referred to earlier as being the one that allows us to establish that we are indeed in an inertial frame of reference it gives us a way of defining inertial reference frames if we're in a frame that we believe is inertial how would we verify that? well, we could take an object and we could briefly accelerate it with a force that we know will cut off at some point we get it up to some velocity we remove the source of that acceleration we stop pushing on the object for instance and we simply do an observational test if the object continues to move now at a constant velocity its speed unchanged its direction unchanged then the sum of all forces on the object must be 0 and if the sum of the forces on an object is 0 then it must be that we are in now in an inertial frame of reference if however we take away our force which should result in the object remaining then in a state of constant velocity and yet we still observe it to accelerate in some way either changing its speed or changing its direction of motion then there must be some net unbalanced acceleration and Newton's first law would tell us that if there's a net unbalanced acceleration we could say that there must be some force causing this but in a non-inertial reference frame what's actually happening is that the frame itself is experiencing an acceleration for observers in the frame who may be unaware of that they see objects moving along strange paths that imply that there's some net unbalanced force and this leads to the concept known as fictitious forces that is if you are in a non-inertial frame you will observe unbalanced accelerations non-zero accelerations and from that you would conclude from Newton's first law that there must be some kind of force that's acting this concept of fictitious forces can seem a little confusing what's really going on is it's the motion of the frame that's causing the acceleration to appear to the observers in the frame but this manifests as if a force were acting in the object as we can see in this clip that I keep showing you and so it is that we can really use Newton's first law not only to define these frames of reference as inertial or non-inertial but to understand the consequences of what it would be like to be in a non-inertial reference frame making observations that would appear to us that there are some forces acting in nature and we would have to account for them in some way to give you an example of this technically the surface of the earth which we look around and we believe to be at rest is in fact a non-inertial reference frame why? well the surface of the earth is a fixed to planet earth which rotates about once every 24 hours and the fact that you are standing on the surface of the earth and that the earth is rotating once every 24 hours means that you have a centripetal acceleration now you can't perceive this easily but for instance if you launch an object up into the sky and it stays up in the air in projectile motion for sufficiently long periods of time you will observe that it doesn't quite follow projectile motion even taking account of air resistance from these kinds of observations you can actually learn that motion with respect to the surface of the earth is actually motion that's occurring in a non-inertial reference frame but on short distances and small time scales the earth's surface is a nearly inertial reference frame it's almost good enough in reality if you have to go to high altitudes or long flight times you will observe these effects these net unbalanced forces that result from accelerations that we can't really perceive over short times and distances and so often we'll approximate experiments done on the surface of the earth as being in an inertial reference frame but buyer beware if you have to go long distances or long flight times over the surface of the earth in fact you do have to compensate for these effects of the earth rotating and as we saw earlier in this video from the 1960s these nice demonstrations of what it would look like for an object to be in a non-inertial reference frame and experience a net unbalanced force or at least be subject to an acceleration that causes an object to look like it's experiencing a net unbalanced force then of course things get more complicated very very careful but for our purposes it's good enough and as long as we consider short distances and short flight times these effects are quite small and we don't have to worry about them too much but if you're tasked for instance with launching an object over a vast distance you do have to be careful with these effects from the fact that the earth is not an inertial reference frame not perfectly so now Newton's second law is a relationship between a vector sum of forces and the change in the state of motion and this will come back to the concept that was introduced earlier and that is inertia we've seen from our little thought experiment with the feather and the bowling ball that even though these two objects can have their states of motion changed one of them requires very little force to change the state of motion and the other one requires a great deal of force to change the state of motion the bowling ball the property that these bodies have one has more than the other is inertia they're both resistant to changes in motion but one of them is less so and Newton's second law codifies this in a mathematical form and it gives us a quantity that we can go out and measure using studies of motion relating accelerations to the forces that cause them and by doing that determining the physical content of inertia so Newton's second law in sort of verbal form can be stated as follows the acceleration of a body acted upon by a net unbalanced force is proportional to the force and the proportionality is given by the mass of the body its inherent tendency to resist changes in its state of motion mass or at least one kind of mass plays the role of inertia and in fact this mass that shows up in Newton's second law of motion has a very special name it's inertial mass it's not an accident of course it is this quantity that we call mass that represents the tendency of a body to resist changes in its state of motion and it's written here mathematically forces labeled one through N and we sum them together as vectors the resulting sum will be equal to the inertial mass whatever that is of the body times its acceleration if we know the acceleration and we know the amount of force that's being applied to the body we can use this equation to solve for inertial mass on the other hand if we have a way of independently measuring inertial mass we can use that and either force and acceleration to determine the other this is a much more general statement about force and acceleration and it naturally includes the consequences of the first law if this sum is zero then acceleration must also be zero and we saw that laid out in the first law of motion it adds this new concept however that is mass or at least this mass as the source of inertia as we'll see later in the course there's another kind of mass that you can define and you can then ask questions like are these the same masses it's an excellent question and we might revisit that later now of course over here I just to impress you I put in the Latin form of law number two as written by Isaac Newton in the Principia but essentially it says exactly what is being set up here although perhaps in translation a much fancier way of saying it than I've said it here nonetheless this is the very famous equation that fits on a t-shirt F equals MA and it is one of the laws of nature it is the law that we have observed over and over again reliably relating forces accelerations and the resistance to the change in state of motion that's observed in bodies in the natural world let me give you a demonstration of inertia I'm going to take this heavy lead brick and I'm going to rest it on top of my hand now my hand is sitting on a sandbag but that's just to make the palm of my hand comfortable for the rest of what's going to happen I rest the lead brick on my hand and I pick up a standard Carpenter's hammer what I'm going to do is I'm going to repeatedly smack the brick with the hammer watch what happens despite hitting this brick with all of my might this thing is made of lead lead is very massive and that means it has a tremendous resistance to changes in state of motion so while the brick feels heavy on my hand it's not comfortable hitting it with the hammer doesn't really do anything I barely feel it it's like having a lead airbag over your hand and as you can see my hand is completely fine it's intact no problems finally we encounter Newton's third law of motion it's the final law in the set of three and it's an interesting one as we'll see later for things like rocketry for instance if you wanted to send something people or perhaps a robot or some other kind of mission equipment from a place like the earth to a place like the moon or Mars or even further Newton's third law gives you the means by which you can make this happen and we'll come back to that concept later but I want to just emphasize the basics of the third law of motion now in language form we might say Newton's third law says the following the force applied by one object on another is equal in magnitude and opposite in direction to the force applied by the second on the first another way of saying this is maybe the more popular way in which this law is depicted for every action there's an equal and opposite reaction the mutual actions of two bodies upon one another are always equal but directed oppositely so for example let's think about you standing on the floor you push on the floor but what Newton's third law tells us is that the floor pushes back on you your net force the magnitude of your force independent of its direction is equal to the magnitude of the force exerted by the floor on you but it's oppositely directed how can this be well again think about what we learned from Newton's first and second laws let's take the second law you're standing on a floor you're not moving so you're not walking you're just standing there do you fall through the floor no does the floor push you up into the ceiling cracking your skull no not in a normal functioning room so you are not accelerating your state of motion is not changing nonetheless you're very much pushing on the floor your feet and you might even interpret that sensation in your feet as the floor pushing back on you but you're not accelerating well it must be then that the net acceleration is zero nonetheless there's a push you push on the floor it pushes back on you but if there's no acceleration these forces which are vectors must add up and if they add up they must add to zero the third law is that we see the third law kind of laid out in vector form here the force that you say number one exert on the floor say number two is the same as the force that the floor exerts on you two on one except in the opposite direction and so if you move f21 to the left hand side of this equation you'll see that it's a sum of forces f12 plus f21 add f21 vector to both sides of this equation the left hand side will contain the sum but the right hand side will contain zero because f21 added to negative f21 is zero and so this sum is zero because you're not accelerating you're standing on the floor it's not pushing your head up into the ceiling there is no net vertical acceleration therefore it must be that you push on the floor with the same strength of force but different direction as the floor pushes back on you in a sense is its own observation but is tied up very neatly with the other laws of motion that we've already seen before and you can see how these laws really build on each other as we go forward again just to impress you I put law number three in its Latin form from the Principia over here but essentially it says again in its original form these little translations these different ways of thinking about it say here the third law is really boring because it tells you especially if you're in a situation where nothing is moving at all that all of these forces are balanced on the other hand you have to be careful with this because as we'll see not every situation involves a lack of motion for instance you could be standing on the floor of an elevator and that elevator overall might be lifting you up you are still pushing on the floor of the elevator and the floor of the elevator is still pushing on you but obviously there's a net acceleration in this situation and we'll come back to situations like this and explore them in the consequences of the first, second and third law of motion the first of these is friction now friction is a force that arises from two surfaces that are in contact with one another and slide over each other making contact while they move past think about having some kind of brick or block maybe you've got a rope attached to it you lay the block down on a seemingly flat, smooth surface the block itself is flat and smooth you pull on the block in an attempt to accelerate it up to a constant velocity a la Newton's second law and Newton's first law but you keep being defeated the surfaces rubbing past each other induces a force and that force opposes the motion and that's because surfaces are not perfectly flat and smooth and you can consider the cartoon shown above here where we've got one surface on the top one surface on the bottom we've zoomed way in and looked at the imperfections in those surfaces even seemingly perfectly smooth surfaces nonetheless have imperfections they have what could be pictured when surfaces move over one another the mountains get tangled up in the valleys of the other and vice versa and so you wind up with this kind of slip-stick-slip-stick motion the surfaces are slipping over each other but they lock together as they slide they collide they're bouncing past one another a little bit you can even hear sound when you slide one surface over another and sound means you're wasting energy someplace to inhibit the free motion of the surfaces past one another and as a result you get a resistance in the motion it's against the direction of motion and so you attempt to change the motion up to a constant speed but because friction acts against the direction of the velocity of the object it slows it down and eventually brings it to rest now in general friction can occur anytime two materials move past each other some materials are better than others think about non-stick cookware which is coated in a material called Teflon or the Analon process for making non-stick cookware these are very smooth surfaces you can easily pry even the most badly burned material off that surface nonetheless it's not perfect and you can't get an object to remain in motion forever if it's rubbing across that surface the surface will eventually deplete it of its energy which we'll learn more about later and the motion will stop it always opposes against the direction of motion now this force is denoted many ways for instance I've written it here as a vector F with a subscript F-R-I-C could be friction in the subscript could be a little F with a vector hat over it different books use different notations but the key thing is that it always points in the direction opposite the motion or if you are changing the motion or something it attempts to oppose that change another force that we encounter in the natural world which is really quite important to all of the structures that we build especially things like bridges as depicted on the right is the force of tension this is the force that occurs when for instance you pull on a rope or a cable or a string and the rope and cable so it doesn't for instance go anywhere for instance if it's a fix to a wall on one end and you pull on the cable until it's taut it doesn't go anywhere after that it stops it resists tearing this force of tension is a resistance to tearing or stretching it's a force that's directed in principle along the length of the object that's being yanked on so rope or cable string something like that so it's always a force that is directed along the length of the object that's being pulled or pushed it's often denoted by a symbol like a capital T with a vector hat over it it may be denoted in other ways but this one is fairly common and makes it quite distinctive in calculations and as you can imagine tension is a really crucial force when maintaining a static situation for instance one where you really don't want much or any motion although you know of course it's present in dynamical situations but if we consider the bridge on the right for instance when a bridge is standing there still it's not falling over which is what you want it maintains itself even with large numbers of cars and trucks moving over it that is largely in part due especially on suspension bridges to the tension in the structure and the way that tension distributes the overall load on the bridge across the structure that's not concentrated in any one place and the whole bridge kind of internally shares the load of the weight on it we'll come back to this kind of concept later in practice but I just want to give you a feeling for this now that there's tension in those cables even if you don't see it and because of Newton's third law we have a situation where the cables may be pulling on the tower of the bridge but the tower of the bridge is pulling back on the cable and there's no net acceleration whatsoever in this structure that you want of course bridges move a little they rock, they sway, they bounce up and down if you've ever walked across a long suspension bridge you'll notice the bridge is moving and it can be a very uncomfortable sensation especially for somebody like me who has a fear of heights nonetheless the bridge is mostly not moving especially given the forces and tensions that it's under by having things drive or walk over it so tension is an extremely crucial force in engineering extremely familiar force we've talked about it in class, we've seen it before in these lecture videos but what sets it apart from the forces that I've just been talking about friction for instance or tension is that this is a non-contact force it makes it a very strange thing for instance absolutely no physical contact between two objects is required for this force to exist you don't need air to be between the two objects no material substance can lie between two objects and yet they can experience the force of gravity this makes it extremely distinctive from other kinds of forces friction is explicitly a contact force and tension is also a contact force because if we think about the block and the rope that I just showed you I'm holding the rope on one end the rope is tied to the block on the other end it's making physical contact with the block the tension exists in the rope in between this is definitely a force that owes its origins at the largest scales to contact between two objects but gravity now gravity is a strange beast and it was a beast that vexed Isaac Newton we'll come back to that in a little bit and we're going to explore gravity itself in much more detail later but what you need to know for now is that it is an attractive force between any two bodies possessing mass so if two things have mass, if they have inertia, resistance to changes in motion and we'll come back to that relationship in a bit then it's possible for those two objects to act upon one another via the force of gravity and it can happen even if they are not in physical contact with each other, the moon makes no physical contact with the earth, not even its atmosphere and yet the moon remains bound to the earth as if on a long tether a quarter of a million mile tether stretches out into nearly empty space and holds a massive object in the grip of another massive object it's really quite stunning and it was Isaac Newton ultimately that shed the first light on this mysterious force although it would take many others in the hundreds of years that would follow to really figure this out it's often denoted in mathematics by something like F vector with a subscript G or G-R-A-V these are symbols you might find both in our textbook or in other textbooks and I have to say as I've hinted here that gravity is a much much more rich and detailed phenomenon that I've given it to I can't give it enough of an appreciation at this point in the course but for now this description as an attractive force between any two objects even if they're not in contact will suffice for our needs now related to gravity is the force which we call weight you might mistake weight for mass it's a very common misconception weight is a combination of effects it's the force that you exert on the ground due to the effect that gravity's acceleration has on your mass so you have mass therefore you are acting on the earth and the earth is acting on you Newton's third law the force that you exert on the floor when you make contact with it due to the gravitational attraction of your body to the earth pushes on the ground and the ground pushes back on you and it's this force due to your mass being yanked on by the earth that results in weight now weight is denoted many ways but one common way is a lowercase w with a vector hat over it it is a vector so it is important to note the distinction not only is weight not the same as mass weight is very distinctive from mass because it has direction and magnitude mass has no direction and only magnitude and so we have to relate them to one another and how are they related? we have to take the product of our mass with the acceleration due to gravity g with the vector hat over it that's our old friend 9.81 meters per second squared pointing downward toward the center of the earth now your mass never changes that is unless you lose or gain atoms so of course it's possible to add atoms to your body or take atoms away and that would indeed change your mass but that's the only way you can change your mass your weight however can be changed merely by being exposed to less of a gravitational acceleration so let's look at an example of this on earth I have a mass of 89 kilograms which in imperial units translates to 197 pounds or thereabouts and on earth I exert a weight on the floor of 873 newtons now what the heck is a newton? a newton is the unit of force in meters, kilograms and seconds if we take a look at this equation up here or if we take newtons second law f equals m times acceleration we can immediately get the units of force they are kilograms which is the unit of mass per second squared a kilogram meter per second squared is given a much simpler name a newton one kilogram meter per second squared is one newton and I exert 873 of those on the floor because my mass, 89 kilograms needs to be multiplied by the acceleration due to gravity on my mass which is 9.81 meters per second squared now if I were to go to the moon where the acceleration due to gravity is about one-sixth that of earth owing to the fact that there's a lot less mass in the moon and gravity is a force that is attractive between masses and determined by those masses as we'll see later my weight would actually just be 142 newtons for the same mass I can contain the same number of atoms but if I step on a scale on the moon I wouldn't exert the same force on that scale and as a result the scale would read not in fact my 197 pounds which is how scales on earth would be calibrated to read off in pounds given our gravitational acceleration but something much less if I wanted to be on the moon and have a scale still read 197 pounds I would have to do something called calibrating it I would have to change the way that it relates pounds to my force on the scale taking into account the fact that on the moon the acceleration due to gravity is one-sixth that of earth okay so scales make an assumption when you step on a scale an engineering assumption has been built into it that when you exert a force on that scale it should translate that force into something like a weight into your mass using an acceleration of 9.81 meters per second squared that same scale would tell me that I'm only 33 pounds which is kind of amazing so your weight which is a force can be altered by altering your mass but also simply altering the acceleration due to gravity on that mass now the final force that I want to talk about here is known as the normal force it's not per se independent of the ones I've already talked about but it is an important concept in aspects of Newton's third law that is when you exert a force on something it exerts a force back on you now normal here is not used in a judgmental way it's a different terminology it's a mathematical or geometric meaning normal merely means perpendicular in a mathematical or physics context so the normal force is the force exerted by a surface back on an object for instance if I'm standing on the floor I'm pushing on the floor with my weight the floor pushes back on me and the force that it pushes back on me with is what we call the normal force this is a consequence of Newton's third law of motion again this force is exerted in a 90 degree angle to the surface so if the surface is flat and I'm standing on it my weight is pushing down into the floor and the normal force is exerted perpendicular to the surface of the floor into my feet it's always exerted perpendicular to the surface at the point of contact and again normal is a mathematical or geometric term meaning at a right angle perpendicular consider the cartoon shown over here on the right we have not a flat floor but an inclined block an inclined plane that is a surface that is raised at an angle now the block shown here in a lighter blue shade is resting on the plane on the surface of this of this incline and the rule is that the normal force always is directed perpendicular to the surface at the point of contact so if we consider a point of contact right here between the block and the incline then the rule is that because of Newton's third law the block pushes on the incline and the incline pushes back on the block and this force is exerted in a direction perpendicular to the incline the normal force must point up into the block and at exactly a right angle to the inclined plane's surface it's not 90 degrees to the floor on which the incline rests but rather 90 degrees to the surface that the block makes contact with on the incline it's typically denoted by one of a couple of symbols at least a big N or F with a vector hat over it and a subscript N for normal before I close out the formal part of this lecture video I would like to make a little comment on at least some of the forces that I've just described with a focus on friction tension and the normal force it is easy in first semester physics to begin to think that there are an abundance of distinct forces in the universe I certainly believe this when I was first introduced to the study of physics as a young student but the reality is is that all of the forces that we observe in nature really boil down to aspects of so far as we know simply four distinctive fundamental forces you typically do not encounter them this early in an education in physics but nonetheless it's worth peeling away the curtain a little bit and looking behind the scenes to see what's really going on in the universe now in the second semester of this course you will explore a very specific pair of forces and those are electricity and magnetism and since atoms are made from electric charges electrons and protons and atoms bind one to another through the details of electromagnetic interactions not just the kinds of electromagnetic interactions you'll learn in a course at the introductory level but the more advanced interactions and the way you describe them that you would learn in a second, third, or fourth year physics course on quantum physics or quantum mechanics and in fact most of the mechanical forces that we explore in this course with the exception of gravity are ultimately explicable purely as aspects of electromagnetism let's take a look at friction you know most surfaces are irregular and uneven you can picture them as the image that's shown over here this has actually been drawn by generating two what are called fractal images that look like mountain ranges one surface the top gray one is one fractal mountain range and the orange or yellow one on the bottom is another fractal mountain range these geometries are not regular but they are self similar at all scales you can zoom in here you will see that it really looks the same as it did when you were zoomed out this is a pretty good representation of what the irregularities of a surface would look like for instance here is a real image of the surface of glass glass we normally think of as a very smooth material but in fact if you do careful measurements at extremely small distance scales from here to here in the image is just 5 millions of a meter 5 microns you can see that in fact the surface of glass is rich in irregularities there are these very interesting sort of striations that cut through the surface and you can see here these little mountain ranges these are not these mountains as we think of them these are the results of collections of atoms in irregular groupings atoms if you wanted to see them you would have to go down another 100,000 times or so in size to see those here you are seeing large aggregates of silicon and oxygen atoms forming these irregular structures but nonetheless we can see in a simulation of the surface say of two materials or in a real image of the surface of a material like glass that there are these irregularities these irregularities arise from the details of the bonding of atoms they jut up out of a material they create these ridges in the material these lower points and so forth and when two such surfaces pass over each other the electrons and the surface atoms repel each other electrons have a charge like charges repel one another masses attract each other gravitationally if two things with the same electric charge get near each other they push themselves away from one another and this causes the surfaces to not only keep apart and not blend into one another but to bounce over one another to feel a resistance a force against one another this can induce things like sound waves in the material as we will see in an example in a moment this is just atoms compressing and stretching their bonds there's nothing exciting going on here except the details of electricity and magnetism electromagnetism in atoms it is atoms it is the behavior of atoms at their most fundamental levels that create friction when they're aggregated together in large numbers another example is tension pulling on one end of a rope why does the other end of the rope feel anything how does the force get from the contact point at one end to the contact point at the other and the answer is very similar to what we can visualize with atoms pulling on other atoms through their electromagnetic interactions you're just yanking on these bonds between atoms and fundamentally that's just electromagnetism so as long as the force the tension for instance is not sufficient to break atomic bonds if you put in a certain amount of energy you can tear atoms apart from one another and that would be a failure of the material if you can't do that then the rope will remain intact it will simply maybe stretch a little bit and it will push back against the force on each end because the atoms are bonded to one another chemically they don't want to be pulled apart they're in a sort of happy state and they don't want to get further away from each other and so they resist that change and that's what we call tension we can visualize it by zooming in on a representation of DNA the thing that encodes all of our identities in a biological and genetic level it's really just an assemblage of atoms into different molecules four regular molecules that are then assembled together into these long chains with a double helix structure it's really atomic rope it's actually two atomic ropes bonded and twisted around each other and so here we can see an atomic kind of rope and it's easy to see here that it's just atoms acting on other atoms that transmits the tension through this structure yanking gets transmitted up the chain to the atoms on the other end the normal force at this point it's probably in your mind fairly intuitive now what the normal force is you stand on the floor your feet are in the soles of your shoes they are being pulled down toward the center of the earth by gravity therefore you're exerting weight a force on the floor and the floor pushes back on you but what is doing the pushing it's atoms the electrons in the atoms in your feet are repelled by the atoms in the electrons in the floor and you don't pass through the floor which otherwise would be what would happen it's a good thing it allows structures to stand up on the surface of the earth and not get yanked to its liquid molten core the fact that electromagnetism exists allows all of the structure we see around us to be in the first place and so you're prevented from falling through the floor by just the way that atoms behave with one another through the electric and magnetic forces that are the core of their bonds and interactions with one another it's really quite a beautiful synthesis of nature under the hood behind the scenes behind stage here this manifests as different mechanical forces friction tension the normal force but really it's just atoms being atoms and that's what's amazing about this stuff is you can understand so much by understanding the smallest things that make up everything that we see this is why physicists have a real passion for finding the building blocks of nature figuring out the rules that govern their behavior if you extend that up to the largest structures like planets or stars galaxies or galaxy clusters perhaps we can understand everything as it is now as it was near or at the beginning of time and perhaps even into the future you can see why this is such an exciting study of nature let's close the formal part of this lecture by reviewing the key ideas that we have seen we've seen that it is forces that are the cause of changes and states of motion that is if something has a velocity and that velocity is constant at its velocity you must create an acceleration and it is forces that create accelerations we have observed that force is also described as a vector and obeys all the properties of vectors and that's what allows us to make mathematical relationships between forces and accelerations and we've seen those relationships fleshed out as we have begun to explore Sir Isaac Newton's three laws of motions these are the first laws of nature so simple so compact that we have encountered in this class they seem so trivial and yet I promise you you will struggle with them conceptually and you will be better for that struggle because after all if these are some of the reasons why and how everything is in the universe shouldn't it be our job to wrestle with them so that we can come to an understanding of the cosmos as it is as it was and as it will be in the future these are the challenges to the physicist and these are the challenges I extend to you as we begin to apply Newton's laws to the universe around us I promised at the beginning of the lecture video that I would return to Isaac Newton's great work the mathematical principles of natural philosophy to close out this lecture I really want you to understand how deeply pivotal in the history of science the work of Newton was not just building on the fantastic work of people like Galileo before him but setting the stage for so many things that would come come afterward and I think it's worth taking a moment to appreciate at least in this translation of the Principia the closing words of Isaac Newton at the end of his work now what I find as I said earlier particularly fascinating was not the level of certainty that he communicates at the end of this work but rather a sense of incompleteness and that's important because after all if scientists understood everything this would simply stop doing what they're doing and just become applied we would just apply everything we had already learned and the fact that we don't all apply things is a positive sign it means that humans have not yet reached the final frontier of all knowledge we're still pushing the boundaries of what we know but we do not know everything and that of course means tremendous opportunities for all of you to make discoveries going forward one of the things that this book is about in a short while in the course is gravity we've seen how gravity is one of many forces that can be described by Newton's second law for instance but what is gravity really in this book Isaac Newton lays out the mathematical description of gravity as a force he explains that it has to do with the mass content of two bodies and because they possess mass they're able to influence each other without physical contact gravity is this contactless force it's relatively strange when you think about other mechanical forces like tension or friction these are forces that require contact but gravity does not gravity can act through the vacuum of empty space in fact it does the earth pulls on the moon the moon pulls on the earth the moon goes around the earth the sun pulls on the moon these these are just the realities of everyday life whether we take the moment to appreciate them or not Isaac Newton had accomplished a lot but he knew he had not figured out everything and he expresses this beautifully at the end of his work so in this translation it's page 442 of 443 which marks the end of the mathematical principles so let me begin to read here but he threw two I have not been able to discover the cause of gravity from phenomena he says and I frame no hypotheses for whatever is not deduced from the phenomena is to be called an hypothesis and hypotheses whether metaphysical or physical whether of occult qualities or mechanical laws have no place in experimental philosophy let's pause there for a moment what's amazing about this is that Isaac Newton admits right here at the very end I can't tell you why gravity is the things that I can describe it to do I cannot tell you what the cause of gravity is not ultimately it reaches out over a distance with nothing in between to exert an influence between two bodies but he has no idea why and in investigating this phenomenon he has not revealed the reason indeed that would be left to a later generation of scientists one of them very famous Albert Einstein but even Newton recognized the limits of what he had accomplished and I think that's incredible and what's also incredible is how responsible he is here at the end he doesn't speculate wildly he doesn't make up a good story that sounds good to the reader perhaps for fear of having that good story be left in the mind of the reader as if it were truth instead he avoids framing any hypotheses to explain why gravity he can explain how gravity but he doesn't explain why gravity is not a reader with perhaps his own speculations he won't do it continuing on in this philosophy particular propositions are inferred from the phenomena and afterwards rendered by general induction thus it was that the impenetrability the mobility and the impulsive forces of body and the laws of motion and of gravitation were discovered in other words by interrogating natural phenomena by conducting experiments by observing how matter behaves under the influence of forces it is possible to discern the laws that govern those behaviors and that's a powerful thing he says so right here so much has been accomplished by doing this but implicit in this is that the final prize the why of gravity is left undiscovered he goes on and to us it is enough that gravity does really exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and of our sea these are incredible accomplishments to understand the tides to understand the motion of the moon of the planets of our own planet around the sun all explicable by the embrace of gravity and the law that governs its strength with distance and mass but none of that explains why gravity is and where it comes from and so I think that that is particularly interesting for a scientist to admit at the end of their greatest work I don't know I don't know is a powerful statement because I don't know is the beginning of real learning and being willing to admit that even at the end of a work that's considered foundational in the history of science for so many things is in and of itself quite powerful now here's the final punchline one of the things that he then goes on to talk about in the very last paragraph of the book is the potential for this action at a distance without physical contact to perhaps have explanatory power in other phenomena he gets a little bit spiritual here at the end of the book in the last paragraph but what I find interesting about this is that while he starts invoking the word spirit I think in many ways he's attempting to suggest that if one could understand gravity based on studying the phenomena further and applying the law of gravitation as Newton discovered it maybe it would give us insight into other phenomena which are equally mysterious and unilluminated at the time of Newton so for instance maybe it would help us to understand why light is emitted reflected, refracted, inflected and heats bodies and indeed a revolution in our understanding of that would come in the next century century and a half after this work but that would be left to another generation after Isaac Newton he speculates that perhaps we'll learn more about nerve impulses and the connection between the brain and the body and that's a deep insight because it does turn out that our bodies are electrical in nature and that electric currents have a significant role to play in nerve impulses and thought at the biochemical level he concludes but these are things that cannot be explained in a few words nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates now I don't think that spirit is meant to be taken completely spiritually here but it's interesting of course as a choice of words, he was a man of great faith Isaac Newton but what's fascinating about this is that he's not entirely wrong in the sense that the law of gravity describes a force which acts over a distance and indeed is would be discovered in subsequent work in the next couple of generations the electric force itself also is known to act over distances the magnetic force is also known to act over distances without physical contact and the laws that describe those phenomena would be uncovered and in uncovering those laws the great genius of another scientist named Michael Faraday would come to a new idea that there are fields of force that stretch between the source and the recipient of the force and it's the experiencing of the field of force that allows for this force at a distance to occur we have pictures in our mind mostly because we understand gravity a lot better now about gravity as a great field of force that stretches out for instance from the earth and we're caught up in that field and so we respond to that field this concept of a field of force was one that would be introduced in about the middle of the 1800s and it wouldn't be taken very seriously until it was put on firm mathematical footing in the 1860s by another scientist named James Clerk Maxwell with all of that in place it was then possible to begin to understand what gravity was it was some kind of field of force sourced by mass and felt by mass that allowed for this weird action at a distance this non-physical, non-contact force but it wouldn't be until about 1916 or so that the final piece of the puzzle would be put into place we'll come back to this a little bit when we talk about the law of gravitation and a bit more about what Newton codified in the Principia about gravity but it is absolutely true that if you want to completely understand the modern picture of gravity which is a beautiful synthesis of space and time and energy and matter, the things that physics studies you really have to go beyond the introductory level you need to go to at least third semester physics and ideally beyond that to other coursework in the field it is a deep journey it is mathematically a very dense picture but it is a beautiful cosmos that we live in and to truly understand it you have to be willing to dive somewhat deep into these things some time I hope you enjoyed this lecture on Newton's laws of motion we're going to use this for quite some time in the course and then we're going to build on this foundation into further understanding of different kinds of motion and forces as we get into the next phase of the course