Program 15 - "Newton and The Laws of Motion"

Music"If I have seen further than others it is because I havestood on the shoulders of giants."MusicWe're back with Science 122, "The Nature of Physical Science,"the telecourse that gives you action and reaction.This program is Number 15, which is Lesson 2.7 in the Study Guide.In this program we will focus on the lifeand influences of Sir Isaac Newton.We will look at the 17th century as a period of blossomingcreativity, but examining the contributions of other majorscientists of this rich period in history.We will take a quick trip through the life of Isaac Newton througha resume, stopping to look more closely at events which ledto the publication of his life's work.After a short focus on vectors, we will view Newton's lawsof motion from a perspective which is intendedto complement the materials in the textbook and the Study Guide.Finally we will examine the background, premisesand assumptions of the Newtonian paradigm and its wide ranging influences.

Here are the objectives for today's lesson.These objectives are also in the Study Guide at the beginning of the lesson.Before you begin to study the lesson, take a few minutesto read the Objectives and the Study Questions for this lesson.Look for key words and ideas as you read.Use the Study Guide and follow it as you watch the program.Be sure to read these objectivesin the Study Guide and refer to them as you study the lesson.Focussing on the learning objectives will help youto study and understand the important concepts.

Compare the objectives with the study questions for the lessonto be sure you have the concepts under control.Silico: "Why didn't you let me read "We are back" part?"Oh, no reason at all.We just like to do things differently from time to time, that's all.Oh, hey, the camera's on.We have to start the class, come on.We are now ready for the final piece of the revolutionary puzzle.With Newton we see the organization of the newscience into a paradigm that has not persisted for more than 300 years.This is not long as history goes, but the Newtonian paradigm haswithstood the rigorous tests of time to a more severedegree than any of its predecessors.Although it breaks down in extreme cases, such asin the very small, or in very large, or very fast moving, the physicsof Newton is little changed today from the way hepresented in 1686 in the "Principia."That was the title of the book he published.The place of Sir Isaac Newton in history is well justified,both for his scientific contributions and alsofor the effect that his viewpoints have had on subsequent thought.No one since Aristotle has had such an influenceon the global world view as Newton.

Unlike Aristotle, whose work was speculative although brilliant,Newton developed precise mathematical tools.He developed specific definitions of mass, space and time,and he also employed a variety of inductive and deductivetechniques to answer the questions of the agesregarding the motion of the planets.In doing so, he removed the last trace of Aristotle's authorityon matters of motion and cosmology.He set a new way of thinking about the universe, established theCopernican system with planets moving according to Kepler'slaws, and described, according to Galileo's kinematics.Newton's synthesis of gravity ranks as one of the greatest,if not the greatest achievements of the human mind,both for its conceptual simplicity, but also for its logicaland mathematical elegance, and its potentialto describe complexity in simple terms.Added to that is the paradigm shift which had culminated.Newton's writings on gravity and motion showed an extraordinaryintelligence and talent for logical discourse and alsofor rationalizing intuition about the physical world.We'll come back and deal with this ideaof rationalizing intuition a little bit later.

Newton's laws, which are simply and concisely statedin three sentences, are, in fact, the basis for all of physics.And these, along with an equally concise law of gravitation,form the most complete formal system everfor describing forces and motion.Everything from the stresses on a bridge to the orbitalcharacteristics of satellites comes from Newton's laws.We are able to calculate the masses of the sun,and the planets, and even the masses of distant stars usingNewton's law of gravitation exactly as he formulated it 300 years ago.The mind of such a thinker is hard to envision.So great, in fact, were Newton's powers of concentrationand problem solving that he was revered as a Demigodin his native England and considered somewhat superhuman worldwide.His name brought images of raw intellect the wayEinstein's name does to us today.

It's impossible to detail all of Newton's contributions in a single program.In fact, it may be impossible in any form at all.He's had literally an immeasurable influence on our world view,and along with Descartes is responsible for muchof our current attitudes about man versus nature, as well as themechanistic view of the universe.His amazing synthesis of ideas combined the works of Galileo,Kepler, Euclid and others of his own time and prior generationswith his own new methods of analysis and creative insights.His incredible mathematical analyses and inventions not onlysolved the problems of planetary motions, but also, became thestandard for a whole new way of using mathematicswhich launched our modern scientific era.Newton had an unusual ability to rationalize his intuitions.By that, I means he could clearly and concisely state principleswhich are so intuitively obvious that they're really hard to recognize.It's sort of like that fish in water thing again.Newton was also a creative and thorough scholar, and he wentto great lengths to locate the best information about the distanceand sizes of the planets and other relevant works, such as thewritings of Galileo and Kepler, among others.

Newton's three laws of motion, which we'll study later in thisprogram, formed the basis for all physics.Mechanics is the science which deals with theactions of forces on bodies and with motion.Subcategories of mechanics are kinetics, kinematics, and statics.You may wish to spend 10 minutes or so looking up these wordsin the dictionary, and it will give you a betterunderstanding of what mechanics really is.Newton's description of the relationship between forces,motion, and equilibrium, that he stated in his three laws,was found to apply not only to motion in the earthly realm,such as that described by Galileo for projectiles, but he foundthat the planets also move according to these sameprinciples and relationships.The precision and elegance of Newton's explanationof the principles of planetary motion ended foreverthe problem of prediction of the location of a particular planet.Using his gravitational equations, the motions could be calculatedas accurately as desired for anytime in the past, future orin the present, after only three observations.In fact, Newton's analysis confirmed the Copernicanuniverse with Kepler's modifications and his lawof gravitation framed the development of modern science.

Newton's method of analysis became the model from whichall new methods of science were derived.And, in fact, he formalized the physics of Galileo by providinga set of rules and a system of operation which could beapplied to all physical phenomena,not only mechanics and engineering, but also, to a whole new way of seeing.For example, through the conservation laws,but also, through the study of electricity and magnetism.And even the study of light, the behavior of gases,and the chemical behavior of matter, all of these things cameunder closer scrutiny once it was realized that all matter, largeor small, near or far, is subject to the same universal laws.To compare the revolution to the freezing of water, using theterm crystalize, may seem far fetched, but by this time you'vebeen watching the program, you should be accustomedto these weird metaphors and abstractions.This analogy that brings to mind is this.Imagine a liquid such as water which is put into a freezer.Now eventually the water will freeze, but what if it's continually stirred.Have you ever seen an Icee machine?Inside is a slush composed of crystals and liquid which willbe kept well below freezing temperature, but preventedfrom freezing by continual stirring.Now imagine that suddenly the stirring is stopped.This is the method by which we make ice cream, gelato, or sorbet.What will happen?Well, the mixture will freeze or crystallize, almost immediately.

Now do you see this metaphor?If you don't, we hope you'll see it before you finish the lesson today.So, from Copernicus to Newton is a little over one century,a very short time for such a radical shift in world view for an entire culture.Newton's work provided a well documented and convincingproof that opposition to heliocentrism, which wasadmittedly weakened during the heyday of the Scholastics,amongst intellectuals and laypersons alikevirtually vanished overnight with the publication of Newton's book, literally overnight.The book was called "The Mathematical Principles of Natural Philosophy."It was published in 1686.Newton's work had the effect of nullifying the last of Aristotle'smisconceptions, and, in fact, establishing the validityof scientific reasoning and showing the efficacy of mathematical models.In Program 10 we described the 16th century and the changesthat were taking place in thought patterns and the new discoveries.You may want to review this to put yourself in perspectivefor the 17th century, which was one of the most creativeand prolific periods in all of history, and was also thebeginning of the modern era of the dominance of science and technology.

Galileo and Newton were not the only naturalphilosophers of the 17th century.Changes of the magnitude of the paradigm shift whichaccompanied the scientific revolution did not take placebecause of the ideas of one individual, no matter howinfluential that individual may be.An individual is always born of his or her culture and the society.The beliefs and practices of a culture and its associatedsociety represent in some way the collectiveinfluences of all the individuals.In the 17th century the authority of the Church was eroding,largely to the growth of Protestantism all over Europe.The Protestant movement was weakest in Italy.Obviously, traditionally this was the seat of the power of the Church.In northern Europe and the British Isles the movement was verystrong, and in England, the movement was already in its second century.In Galileo, in Italy I should say, Galileo was a criminal.He was tried and convicted by the Churchfor his politics, not for his science.It was that refusal to acknowledge the authorityof the Church that got him in trouble.Galileo, remember, had attacked the geocentric systemof the Scholastics indirectly through his studies of motion.He used the results of his motion studies to discredit Aristotle,and then used that to discredit Aristotle's cosmology.This was a clever tactic, and well executed, but Galileopresented no replacement model.He didn't say what else would work.He had no explanation for Kepler's laws, which he was aware of,but ignored in his writings, and he had no connection between hisdescriptions of earthly motion and the celestial motions,other than the fact that Aristotle was wrongabout sublunar motion, then he was probably wrong about celestial motion as well.

Galileo also worked on other things.For example, the concepts of time and air pressureand temperature and things like that, and, in fact, he wroteabout these things, and some of his students went on to do other work.For example, Toricelli invented the barometerand used it to measure air pressure.Toricelli did that.Pascal did the same thing.In England, Robert Boyle, who instigated a radical paradigmshift in chemistry, and we'll meet later on in the chemistrysection, was working with the nature of gases.Boyle's law describes the relationship betweenthe pressure of a gas and its volume.We've already noted that Descartes' contributionsto deductive logic, and analytic geometry and dualism.He also contributed to the growth of the field of optics,which was of growing interest in the middle to late 1600s.Another Dutchman, Christian Huygens, was anotherof those geniuses of the century.He was actually the son of a multilingual Dutch poet,very intelligent family, and he published the wave theoryof light which was at odds with Newton's corpuscularor particle theory of light.

The wave theory of Huygens, by the way, was shown to be thecorrect one in the early 19th century.Huygens also contributed the idea of centrifugal force, althoughNewton wasn't aware of it and came to the same conclusions independently.Also Huygen suggested that the freezing and boiling pointof water be used as standardsfor the construction of a thermometer.This is an idea that was used by Fahrenheit and Celsius to makeaccurate thermometers, and it was also Huygens whoinvented the pendulum clock.So, Huygens was a fairly influential guy and we'll comeback and see his role in Newton's things a little bit later on.Also in England was Robert Hooke.He was a charter member of the Royal Society of London,and he was one of the first ones to theorize that the motionsof the planets was a mechanical problem,not a moral problem, but a mechanical problem.He also invented the spiral watch spring, and constructed the firstmachine that did arithmetic, the first number machine.He also described cells in plant tissues.He's most famous, at least in our context here, for his ridiculeof Newton's theory of color which opposed his own.It turns out that Newton was correct, and also for Hooke'slaw which states the proportionalitybetween the force and stretch of a spring.

Now all of these things will play direct roles in Newton'stheories and we'll encounter the name of Hooke againin this lesson as well as in the future.In the same century, Olaus Roemer was a Danishastronomer who measured the speed of light.He did this actually after Newton's publication of the lawof gravity and he used Newton's theory to do this by calculatingthe travel time of the eclipse of one of Jupiter's moons.

In this program we could really only look at the principalreasons for this sudden blossoming in the 17th century.We will no doubt leave out something that someonesomewhere thinks should be included,but in the interest of brevity, we offer this defense.Hopefully, the student who's watching the telecourse will beable to see the complexity and connections which wereemerging as the printed words spread ideas far beyond their source.As improvements in the printing press and book binding madethese things accessible to a much higher percentageof the population than ever before, and in more languages.And, by the way, at that time it was not uncommon in Europefor the well educated citizen to be fluent in four, five or even six languages.It's not really surprising that all these things boomed,the creativity, curiosity, and scientific inquiry during thisperiod when you take into account the wholepolitical, social, economic and religious climate.Remember, this was a time of rapid change and any attemptto really put this in its proper perspective is beyond the scope of this course.

I would encourage you to take a history course where you studythe European history during this time.What was happening here is like the pyramiding effectof the accumulation of knowledge.It's sort of like a river downstream whereseveral large rivers suddenly join it.This effect, by the way, continues today at accelerating pace,leading to terms such as future shock where things change sorapidly that you can't even keep up with them let...what happened yesterday, let alone what's going to happen tomorrow.The 17th century is the point where these things begin to fall into place.Sort of like a football game when the team finally begins to playas a team after struggling in the early season.Another reason here was that increasing commercebetween nations and the distribution of wealthof the new world was attracting men of ability,interest, and means to science.Craftsmen were interested in the improvement of methodsand products as the negative value placed on manual laborby the ancient Greeks began to give way to the pride of accomplishment in work.Men of wealth were also attracted to the sciences as a trendyand somewhat exciting hobby of diversion from the aristocraticexcesses and bureaucratic minutiae.Not only that, there was money to be made in newinventions and new products.Several other things are here too.

In England, especially, but to a lesser degree everywherein Europe, the skills of the artisans and craftsmencombined with the money of the wealthy was producingprecision instruments of all kinds.These could be used to making increasingly accurateinstruments, but also, could be used to make money.Most notable were improvements in things like telescopesand clocks, but also in barometers and thermometers.The vacuum pump was invented in the later part of the centuryand provided new opportunities to study airpressure and also motion in the vacuum.And, of course, we can't forget here Galileo's influence.Galileo's method of formulating problems and simply Galileo's,extreme influence had much impact all over Europe.I hinted earlier at the role of communications.And, of course, from the beginning of the course, we've talkedabout physical science as a shared reality.And, of course, to share reality requires communication.

As we noted earlier in Lesson 5 when we discussed the roleof language in the beginning of science, the growthof knowledge depends upon the exchange and criticism of ideas and methods.But also keep in mind in this period that the printingpress was now becoming widespread.

The printing press was actually invented in China but the firstGutenberg bible was published in the middle of the 15th century,so a couple of hundred years before.So printing was still a fairly young art, but it was growingvery rapidly and there was simply many more books availablethan there ever had been in the past.One major innovation in the spread of communicationsbetween scientists was the formation of scientific societies.The first of these was the Royal Society of London.Actually it was called the Royal Society of Londonfor Improving Natural Knowledge.And this was started by Hooke and Boyle whose names we justheard, along with architect Christopher Wren and the astronomer Edmund Halley.We'll encounter these names later on, too.

Today this is simply known as the Royal Society.It is a government subsidized organization which fundsresearch and stimulates research and also advises the Britishgovernment on science and technology.There are several things that make these important.One of these is the fact that the numbers of people in society,the scientific society makes it easier to find moneyto do research, and also, of course, provides a sort of a cushion against criticism.If a whole bunch of people believe one idea, then it's much lesslikely that they're going to be criticized.By the sixth decade of the century Aristotle had simply fallen outof favor as the authority on motion, both earthlyand celestial, and his theories on matter weresoon to suffer the same fate.At the same time, the circular perfection of Plato regardingthe heavens had been shattered by Kepler's laws.So what actually remained of the old theories that was worth keeping?Not much.Plato's question no longer held much interest.Instead the questions of the times were directed towardmechanical things like the forces which act on the planets,and what kinds of things cause the planets to take the paths thatthey do, and how do we explain the observed effects of gravity here on earth.What was missing was the connectionbetween the two things, that is, the motion of the planets and gravity here on earth.

On one hand was earthly motion, uniformlyaccelerated as Galileo had described it.On the other hand was the elliptical motions of the planetsas described by Kepler and driven by some mysterious force,perhaps emanating from the sun, acting like one of Gilbert's magnets.And this is where Newton really come in here, to make thisconnection in what turns out to be the greatest synthesis probably of all times.You may remember that Plato's question established the circular paradigm.And this was actually replaced by a new type of questions basedupon mechanical principles largely led by the new physics of Galileo.That these questions seem obviously connected to us,was not so obvious to them.In fact, it took Newton's genius to see that these two questionsof the times really had the same answer, which is universal gravitation.So, the two questions are: What forces act on the planetsto account of their observed paths? And,How were the observed effects of terrestrialgravitation to be explained?As we did with Galileo, we'll present a chronologyof Newton's life in sort of an annotated outline form.

We'll give some attention to the significant events,because it really does effect what happened to Newtonand the way history proceeded.But as before, it's not our intention that you shouldnecessarily "know" everything, or that youshould know all of the particular details.But as you watch the program and look over the resume,try to build a picture of Newton the man, as well as Newton the scientist.He is one of the most interesting, intelligent, and influential menin all of history, scientific or otherwise.It's interesting, but also important, in understandingthe nature of science to see how the man who has such a greatimpact on our lives was influenced and shaped by his environment.

Newton was a loner, whose low self esteem, even in adulthood was very low.He preferred to keep his work secret or within at leasta circle of a few not particularly close friends.He didn't have many friends to begin with.His work was very personal and someone once said of him thathe seemed depressed, as if he was indulging in a private vice,the way one might if they were obsessed with the dark arts,or some other socially unacceptable behavior.And also his powers of concentration werelegendary, even in his own lifetime.He was known on several occasions to disappearinto his own room where he'd remain for days without eatingand refusing food and growling at people who came to the door.Most of us are not so fortunate to be ableto isolate ourselves from distraction in that manner.

So Newton was born in 1642 in Woolsthrope which is the family estate in England.His father died two months before he was born on Christmas eve,in the same year that Galileo died.Just to keep things in perspective here, Benjamin Franklin was 21years old when Newton died and George Washingtonwas born five years after Newton's death.So you kind of get a picture of where we are here.Newton, as a child, was not very healthy.In fact he was a very frail child, and also a difficult child.He had tantrums and misbehaved and for allwe know might have even been abused.He was not particularly a protege, but he did have a knackfor building windmills and clocks and things like that.

In 1661, he was admitted to Cambridge Universitythrough the intervention of an uncle.He didn't meet the qualifications, but he wasadmitted, and there he began to blossom.In fact, he graduated with a Bachelor of Arts in 1665,in four years, right into the heart of the beginning of the third wave of the plague.Now try to imagine graduating from college, youngand ambitious, and walking out with a diploma in hand,and all of a sudden there you are and it's the middle of the plague.The whole city closes down, the University closes down.So Newton goes back to Woolsthrope where he spenttwo years being incredibly productive.During this time he did things like improved the binomial theoremand developed methods of differential and integral calculus.He invented vector algebra, invented the laws of motion,began the science of mechanics and physics, explained gravityand gravitation, studied optics, practiced alchemy and alsostudied the prophecies and the Scriptures.And for what it's worth, he thought at the time that hiswork on alchemy was the most important.

In 1667, he returned to Cambridge where he pursued a graduatedegree and at the time his former mathematics professor,Isaac Barrow, resigned to give Newton his job.Imagine that!You go back to school to be a graduate student and yourteacher says, "Oh, you're so good, here, take my job."So this is where the interesting part begins.In 1672, this is five years now.This is after he'd finished his graduate work.Newton finally organized his thoughts and he decides to givea paper to, to present a paper, that is, to the Royal Society.The problem was that the paper he presented was about the historyof optics which happened to go counter to Robert Hooke's idea.And Hooke was, remember, one of the founders of the Royal Society.Well, Hooke, basically rejected the ideaand ridiculed Newton and turned the entire Royal Society against him.And Newton, because of his low self esteem, decided at thatpoint, "I'm never going to do science again."And basically walked out in a huff.It was several years later when Newton was having a talkwith Halley, and Halley had said that Hooke had made this assertion.The assertion was: (this was from Hooke.)That if gravity is an inverse square force, then the planetswill move according to Kepler's laws.Now, we haven't studied the inverse square force yet,but we'll get back to that a little bit later on.

The idea here was that Newton said to Halley,"Hey, I proved this years ago, it's no problem."And Halley said, "Really?Can you do it again?And Newton, to spite Hooke, went back, worked on it for threeor four days and presented a report to Halley.This is interesting, you see, because it's his antagonismagainst Hooke that really drove this.Halley then, Halley then, later on was in a dispute with Hookeabout this very thing, and Halley went back to Newtonand Newton said, "Gee, I've forgotten how to do it already."So he went back and did it again, and brought it back to Halley.And this time, Halley looks at it and says, "You've got to do something about this.You've got to publish it."Newton said, "No way, Jose."Well, he probably really didn't say that, but something to that effect.And at Halley's insistence, basically, Halley said, "I'll payfor this, I'll do your job, I'll do anything I have to do to get you to do this."So Newton went back to Woolsthrope where he workedfor 18 months and eventually produced his Magnum Opuswhich is entitled " The Principia," or in English "Principles,""Mathematical Principles of Natural Philosophy."This book was a masterpiece of organization and clear thought.In fact, it was written in the scholarly Latin of the time.And Newton did this deliberately so he could made it obscure.He wanted to make sure that only those people who werequalified, and who had a background, could understand the book.This is very different from Galileo.

Galileo, remember, had published his book in the native vernacularItalian, specifically so that the laymen could read it.Newton didn't want people to read it unless theyknew what they were talking about.So, the book, this is interesting, too.The book is 250,000 words, a quarter million words.The day the book was published it sold out.No one could understand it except people who were very wellschooled, but it sold out and Newton became a hero overnight.Now try to imagine becoming a hero overnight as a result of publication of one book.The problem with this was that Newton was not very wellatuned to the publicity and in 1690, he suffered what we might call a nervous breakdown.He basically became nonfunctional,and after that did almost no scientific work.He was appointed the Warden and Master of the Mint in 1699,where he made a few major changes in the Britishcurrency, but nothing worthy of science.He was a member of Parliament in 1689 to 1701.There's an interesting story here that:Here's the great Issac Newton, a member of Parliament.He sits in Parliament all this time and never says a word, just sits there.Finally one day the great Isaac Newton stands to speak.Everyone in Parliament turns around the looks at himto see what the great Isaac Newton is going to contribute.You know what he said?He said, "Will someone please close the window,it's a little drafty in here."He was knighted in 1705 and was president of the Royal Societyuntil he died in 1727 and he was buried in Westminster Abbey.Being the basis for all of physics, Newton's laws are very welldocumented in many sources, including the textbooksfor this course and we aren't really going to tryattempt to duplicate that coverage here.

In the Library you'll also find numerous bookswhich describe the laws and their use at all levelsfrom basic elementaryschoolthrough the multi-years of graduate school.We recommend that you consult some of these outside sourcesif you need more understanding of the laws.The video program that we're going to do here will elaborateon the laws using some demonstrations and stuff,but we won't go into the same kind of details the textbook does.We'll present the outline of the material only, basically.It's designed to focus on those aspects of the laws which wethink are important for the course.It will help you to study if you try to relate the laws to the outlinein the textbooks and also to talk about,think about them in terms of your own lives.This is a good time to communicate with yourclassmates, electronically or otherwise, and alsowith the instructor to discuss the laws and the utility of things.Try to picture the laws in your everyday life,like when you're riding on the bus or in the car.This is really the way to assimilate them.

The laws of nature as we often refer to them, as if they werecapitalized, are not only the basis for all of physics,and for that matter, all of physical science.They're also, perhaps, the best example of what welike to call "rationalized intuition."One of the reasons for the success of Newton's physics is that thelaws are particularly self evident once you've them.Once you allow your mind to understand them, in fact,they become immediately obvious and not contrary to common sense at all.Part of Newton's genius was his ability to state these simplebut abstract principles in a way that someone 300 years latercan read them and "Yeah, I knew that."So one of the most useful tools that Newton invented is the concept of vectors.Once this concept was conceived, it became usefulin applications far beyond its original intention.It's an essential feature of all physical analysis, in fact.The concept, although formalized by Newton, is actually littlemore like Galileo's separation of horizontaland vertical motion in the study of projectiles.It's...you may want to review Galileo's synthesis and analysisof the projectile motion to see how this double thing works.

In the" Principia" Newton states this as the first corollaryto the laws for which he offers both an elegant Euclidianargument and also sets the stage for the type of geometricanalysis which will follow in his book.I want to read for you one of his corollaries.He says, "A body acted on by two forces simultaneously,will describe the diagonal of the parallelogram in the same timeas it would describe the sides by those forces separately."Now, his argument, although Euclidian, is not comprehensibleto the typical freshman in physical science student,so we want to spend some time looking at that.If you want to look at it, by the way, there are many copiesof the "Principia" available, and this is also in the Study Guide, this quote.So, we want to offer a slightly less Euclidian example,but one which was probably easier to understand.I call this the bug on the board.So, let's go to the ELMO.

OK.So, here's one way to look at this.Imagine a board, like a long flat board, like this.Imagine a bug crawling on the board.So, here's the bug.I know you can laugh at my art work but I'm not an artist, but there's a bug.Now, suppose that this bug crawls at a fixed speedand crawls across the board like this.I think that you would agree that it will take the bug a certainamount of time to crawl that distance depending upon how fast the bug crawls.

OK, now, suppose that we start dragging the board.Suppose I move the board so that the board now moves along like this.How long is it going to take the bug to crawl acrossthe board while the board's moving?Well, obviously, it's going to take the same amount of time, right?So, let's look at what happens if the bug crawls across the board.So, if the board, for example, were to move this much distance,in other words, move from here to here, while the bug's crawlingacross the board from here to here, what's the actual path of the bug look like?Well, let's see.Let's put the board back here where it was in the first place.And let's put the bug over here to start with.So, what path would the bug actually take to get there?Well, the bug would describe the diagonal path like this.Right?In other words, the bug is moving as if he first walked across theboard this way, and then the board was dragged this way.And I think you can see now what the corollary says.Let's, in fact, go back and look at the corollary one more time.A body acted on by two forces simultaneously would describethe diagonal of a parallelogram in the same time as it woulddescribe the sides by those forces separately.

So, now you can restate this, this way.An ant moving in two directions simultaneously would describethe diagonal of a parallelogram in the same time as it woulddescribe the sides by those motions separately.So, the ant moving along on two different directions woulddescribe the diagonal of this parallelogram in the same timehe would describe the two sides independently.So, here's the parallelogram.The ant crawls from here to here in the same time as if he wereto crawl here and then the board moves this way.You see the parallelogram is actually a double triangle.In other words, the triangle is half of a parallelogram.So, what's important to note here is that it doesn't matterwhether the two motions are combined or whether they'reundertaken separately as far as the final result of the bug.This is what we mean by the vector.So, here, for example, I can write this.And suppose this represents the ant's motion, and suppose thisrepresents the board's motion, the result of the two motionstogether is this diagonal of the parallelogram.

OK, the result is here.So, I can write this as a sum.I can say that the action "A," that is, the ant crawling, plus,combined with the action "B" which is the boardmoving, results in the result "R."So, notice I'm using the "plus" sign here the same way we'duse it in arithmetic, but I'm taking into account that this is notjust a plus sign, but it's the result of having done two things simultaneously.One of those is to move the direction "A."The other is to move the direction "B."Actually there are two main reasons why this particular technique is useful.It's not just because we want to trace the motion of a bug on a board.First it allows us to find the results of many forces or manydifferent motions that are going on all at the same time,and secondly, it allows us to take an existing force or motionand break it into components, thus, simplifying the situation.This is basically what Galileo didwith the motion of the projectiles in two dimensions.So let's go to the ELMO and I'll draw a couple of pictures here.

OK.If, in the case where, try to imagine for example, a ringand imagine someone pulling on the ring in this direction.Now I can represent the direction that the person is pullingby the length, by the direction the arrow is pointing,and I can represent how hard the person is pulling by the length of the arrow.So, someone pulling twice as hard or with twice asmuch force, the arrow will be twice as long.So, imagine that two people are pulling in opposite directions.What's the result of this with the forces as it is, or you can seethat the person "A" is pulling harder than person "B,"so the result is that the person, well, here's the way to do this.If I take this arrow "A" and draw it like this, and take the samearrow "B" and line it up here, you can see thedifference between the two arrows.In other words, this length represents the forceby which person "A" is pulling stronger than person "B."This is fairly straightforward.This is like a tug of war, right?If you had two extra people on one side as opposed to the other.The other way we can do this is to lookat two forces in two different directions.

Suppose, for example, that we look down on the top of a box and oneperson's pulling on the box in this direction and another person'spulling on the box in this direction.So here's person "A" and person "B."Which direction is the box going to move as a result of this?I think it's fairly clear, isn't it, that the box is going to moveoff in some direction along the diagonal like this.In fact, we can represent this in exactly the same way that werepresented the motion of the bug on the board.This is what Newton was saying.So, we can look at this and say, "Here's the force exertedby the person "A" and here's the force exerted by the "B."The resultant force is exactly the same as if,here's the parallelogram, the box.If I were to draw this arrow across the diagonal of the box,I can say that the resultant force "R" is exactly the same as thecombination of the forces "A" and "B."So that in understanding the motion of the box, I can replacethe two forces "A" and "B" simply with the force "R."Works the same way backwards, right?By backwards I mean this.If I had a force "R" one person is pulling with a certain forcein this direction, I can easily break this into componentsin two perpendicular directions, "A" and "B,"because we know how the two forces work.

Now, see the utility of this technique is that it doesn't onlywork for two forces, it works for any number of forces.In fact, suppose, let me turn this over, suppose there were threepeople working on or pulling on the same ring.One person is pulling this way, other person's pullingthis way, other person's pulling this way.How can we represent that?Well, very simply.We can note here that all three of these forces comefrom the same point and we can simply add them upin the same way we did before.We can move this arrow over here and say that the resultantof those two is an arrow that goes along the diagonal of that box, and once we've done that, we can replace these two forceswith a single force, and now we see that we've reduced theproblem down to two different forces pulling at opposite directions.We can do this for any number of forces,no matter how complicated the situation is.Once we know what the rules are for combining the forces in this way.So, it's not necessarily always easy to do this, but visuallywe can see how it works, and mathematically there are waysto combine the vectors knowing their directions and their lengths.So we can do it very precisely, much the wayGalileo did with the projectiles.Before we get into the laws of motion themselves,I want to first take a look at Newton's definitions.

Newton was very precise in his definitions as well asin the statement of the laws, and we'll find that the definitionsactually overlap the laws somewhat.Keep in mind that Newton was trying to be very, very sure thathe could not be criticized for any weaknesses hemight have presented with this theory.The definitions are good definitions and they, he openshis book, in fact, with these definitions.This is the first thing after the preface, as opposed to Kepler,remember, who buried these things very deeply in the writings.So let's look at these definitions.The first definition says, the quantity of matter is themeasure of the same, arising from its density and bulk cojointly.Huh?What does that mean?Well, it's actually written in English, but this is a translationfrom the Scholarly Latin, remember, so."The quantity of matter."He's defining something called the quantity of matter.This is what we would today call mass.But we'll come back and see how Newton defined it a little bit later on."is the measure of the same."In other words, the quantity of matter is the measureof the amount of matter that arises from its density and bulk cojointly."

Now in Newton's time people didn't talk about the weightof something as much as they talked about the density,because this is what Archimedes had figured out how to save theking a fortune by measuring the density of gold back in the time of Alexandria.So, basically what he's saying here is that we're goingto define matter as the product of the density and the volume.The bulk here refers here to the volume.And so we're going to define matter as the product of the density and the volume.Definition II: The quantity of motion is the same as themeasure of the same, arising from the velocityand quantity of matter cojointly.Notice this definition sounds very much like Definition I, but herehe's saying we're going to define something called the quantity of motion.

Later on we'll refer to this particular thing as momentum.But for now, we want to stick with Newton's definition.So, the quantity of motion is the measure of the same,that is, the measure of the motion, arising from the velocityand the quantity of matter cojointly.So now he's using the quantity of matter which he definedin Definition I, combining that with the concept of velocity.So he's saying that the quantity of motionis the product of the mass and the velocity.And again, we'll come back to this when we studymomentum in a little later lesson.Definition III: The vis insita, or innate force of matter,is the power of resisting by which every body, as much as in itlies, continue in its present state, whether it be of rest,or of moving uniformly forwards in a right line.Oh, how English sounding.It's the power of resisting.Notice he's talking about innate force of matter, its powerof resisting by which every body as much as in it lies,continues in its present state.What he's defining here is what we would call today, inertia.It's an object's resistance to a change in motion.

Every body continues in its present state whether it beof rest or moving uniformly forwards in a straight line.Here he's picking up Galileo's principleof inertia and defining it as this innate force.It's the ability of an object has to exert a force, and we'll see howthis relates when we get to the third law.Definition IV: An impressed force is an action exerted upon a body,in order to change its state, either of rest, or of uniform motion in a right line.In other words, he's saying here that in Definition IIIan object resists the change of motion.Here in Definition IV he's saying what it takesto change that state of motion.What it takes is this thing we're defining as a force.Right?A force is an action exerted upon a body to change its stateof motion either of rest or uniform motion in a right line.Oh, by the way, when he says a right line in here, he meanswhat we would call today a straight line.So, basically he's saying that if a body is at rest, you haveto force it, act on it to move it, and if it's moving,you also have to act on it to change its motion.Definition V is a little bit more obscure and we'll get to this later on.But here he's defining a centripetal force.Centripetal means toward the center, like the petalof a flower points towards the center.

A centripetal force is that by which bodies are drawnor impelled, or any way tend, toward a point as to a center.In other words, he's defining here what it takes to keep somethingmoving in other than a straight line.Oh, let's see.Could he be getting ready to explain Kepler's laws here,where the planets are moving around in curved paths?Here he's getting ready to define for us what it is that keepsthe planets in these Keplerian orbits, which,of course, will turn out to be gravity.So now it's time to finally focus on the three laws.The three laws very simply stated are generally referred to asfirst of all the law of inertia, secondly the law of forceand motion, and third, the law of action and reactions.So let's take each of these in turn and see if we can firstof all read Newton's statement of themand then see if we can figure out what they mean.

The first law is the law of inertia.It says, "An object at rest will remain at rest and an objectin motion will continue to move in a straight line at constant speedunless acted upon by a non zero net force."We need to think about what these mean.First of all, this is a restatement of Galileo's inertia.What he's saying here basically is simply that an object willcontinue at rest or continue in motion in a straight line.There's a word here we need to consider and that's the net force.A net force is simply when you add up the vectors, remembervectors, and if they all add up to zero, in other words, if they allcome back to the same starting point, then you have a zero net force.Notice it's the concept of net force here.This is not the same thing as saying that if no forces are acting at all.It's an important distinction again.Because, for example, when you're driving a car down the highway,you may be moving at a constant speed, but there'recertainly forces acting on the car.There's forces of friction tending to slow the car down,and the engine has to work against those forcesof friction to keep the car moving.

So, we could say that the forward force exerted by the engine isequal to the backward force exerted by the frictionof the wheels and everything else and as long as the car is movingat a constant speed, we know from the first lawthat those two things are the same.If we can go back to the slide for a minute.At the top of the slide is some symbolism.It says "A" equals zero and there's this little double arrow.And then this sort of thing that says "F" equals zero.Well, this simply a shorthand way of saying what the law says.What this is saying is that acceleration is zero, if,and only if, the sum of the forces is equal to zero.Notice the double arrow.Means if, and only if.This is a very powerful, logical symbol.And what it's saying is that if the thing on the left is true,in other words, if acceleration equals zero, then we can implyfrom that, that the sum of the forces is equal to zero.The double arrow means that it also means that it works backwards.That if the sum of the forces is equal to zero, then wecan also say that the acceleration is zero.So, in other words, knowing either one of these two statementsmeans that the other one is also true.

Now keep in mind that the arrow doesn't always have to work backwards.I mean you have a logical statement that says"Garfield is orange, therefore, all cats are....Garfield is orange, Garfield is a cat, therefore, all cats are orange."That statement doesn't work, right?So there are certain statements that work one way but not the other.So, having a double arrow, an if then statement, is a very powerful statement.OK, let's go to the second law.

The second law defines what happens if the force is notzero or if the net force is not zero.In this case, "an object acted upon by a non zero net force willaccelerate in direct proportion to the forceand inversely proportional to its mass."Once again at the top of the screen you see the symbolism.This says that acceleration equals the net force divided by the mass.Now this is an important concept.Because notice what's happening here.Is on a one hand you have mass which according to Newton'sdefinition the quantity of mass has to do with resistanceof an object to its change in motion.So the more mass something has the more it resists changing motion.In fact, we can even say here that the mass is a measure of inertia.On the other hand, force is what causes the change of motion.So, what he's saying here is that acceleration is a balancebetween something which causes a force on one hand, causes,I should say, acceleration on the other hand, and the mass whichis a resistance to a change in motion.So, the actual acceleration is a balance between a cause and a resistance.You all heard the expression, I think, that what happens whenan irresistible force meets and immovable object.Well, of course, this is a way of looking at Newton's law, sayingthat something's got to give is the line here.

OK.So, this is basically telling you what happens if the net force is non zero.I should point out here that since any change in velocityrepresents an acceleration, the change in direction alsoindicates an acceleration is taking place because velocity,after all, is a vector which means that if you change either thedirection or the magnitude of it, then, it constitutes a change in the velocity.OK.Let's go to the third law.The third law is one which is actually more difficultto explain, because it's probably the deepest of all of them.The third law basically says that forces occur onlyin pairs which are equal and opposite.Equal and opposite forces have to do with the laws,well, I think we have to do a demo for this.So, let's see, how can I do this?Oh, you know, I'm going to have to unplug you because I need to use the table.So, I'm sorry, but I have to do this.Silico: "Do not do that, please, I want to watch.This is the fun part."I'm sorry, I have to.OK, let's do this.We'll be back later, don't worry about it.OK.

I have some toys here.This is the fun part because we get to play with toys.I've got these high tech physics carts.They're high tech becausethey're made out of steeland wood, and we can demonstrate all of the laws here, actually.You will notice, by the way, that the first law says thatthe object will continue to move unless a force acts on it.So, I'll give this a very small push and sureenough it will roll across the table.But, oh, look, it does come to rest.That's because although the wheels are relativelylubricated, they are still, they still have a little bit of friction.So, it's not possible for us to show inertia exactly because wealways have friction, but we certainly can demonstrate itlike in outer space when we send a satellite and so forth.

OK.So, let's look at the third law first, and I'll come backand do some stuff with the second law.What the third law is saying, basically, is that wheneverforces are exerted, they exert, there has to be an object thatdoes the exerting and also an object on which the force is exerted.I'll call your attention to the old Buddhist question,the Zen question about what is the sound of one hand clapping?And I would ask you to consider the same question in respectof what is the result of one force acting?You'll notice that in order for me to move the cart,I have to push on it to exert a force on it.But at the same time, the cart exerts a force back on me.I can demonstrate this with the two carts.Actually this cart has a spring loaded thingon it here, so, notice what happens here.If I push the two carts together like this with the spring,you'll notice that if I hold this cart steady, that one cart will be driven away.But, I have to exert a force on this cart because this cartis exerting the force which accelerates the second cartat the same time the second cart pushes back on the first cart.What do you think would happen if I didn't hold down the first cart?Well, let's see.If they exert forces on each other, you would expect that both the carts move.

Let's see if that's actually the case.See what happens.If I hold down this cart and exert a force, then I have to pushagainst the force that cart "A" exerts on cart "B."If I hold down cart "A," then I have to push back, to hold backthe force that cart "B" exerts on cart "A," at the same time cart"A" is exerting a force on cart "B."And so, the two carts exert equal and opposite forces on each other.This is true even if we weight down the cart.I'm going to put this box of heavy weights on the cart,and you'll see here, we can demonstrate both thethird law and the second law at the same time.Because, I'm claiming here that the two carts are going to exertequal, but opposite forces on each other, but because this cartcontains much more mass, the result of that force will bemuch less than it would be on this one.So, let's see what happens.What would you expect to happen here?The carts going to push away at the same rate of accelerationor is one of the carts going to accelerate fasteror slower than the other one?What do you think?Let's see what happens.See what happens here?

Now, the cart that has the most mass is accelerated lessby the force, even though the force is equal.The second law says that the acceleration isproportional both to the force and the mass.So, here we see a case where the forces are equal and opposite,but the affect of the force is much greater on the cart with the lesser mass.Of course, if I switched the mass to this side of the cartor to this other cart, we should see the effect reversed.So, that now, again, the less massive cart,will accelerate at a much faster rate than the other.There's lots of other things to think about here with the third law.One is the balance of forces.I want to go to the ELMO for a minute for this.Let's try this with the balls.If I let the two balls collide, you can see that they obviouslyexert forces on each other because the motion of both of the balls is changed.So, I'll take the balls away, and draw this out.Suppose we try to imagine that we can control our own Newtonian universe.And let's put into this universe a single balland let's give it a certain amount of velocity.In other words, we have this Newtonian universe whereNewton's laws apply and we're going to give this ball a speed.

Now if there's nothing else in the universe besides this ball,then there's nothing that can change the motion of this ball.Right?Because there has to be a force exerted on it in order to change its motion.So, that means that a universe which containsonly one object can exert no forces.There can be no forces exerted.There have to be at least two objects.Now that object might be a planet with gravitation, or it might be another ball.So, let's put into our Newtonian universe a second ball.And just to make things the same, make things symmetrical,let's give both the balls the same mass.And let's give them exactly the same velocity and since we'recontrolling our universe, let's throw the ballsin such a way that they will collide with each otherperfectly head-on.And let's consider what happens during and after the collision.

OK.So, when the balls collide, they will exchange forces with each other.We saw that with the two balls, right?They both changed their motion.After the motion, the balls are moving nowin opposite directions, away from each other.So, what about the forces?Well, its pretty obvious, isn't it, that...Let me label the balls ball "A" and ball "B."It's pretty obvious that isn't it the forces on the balls had to be equal and opposite.Well, let's see if it makes sense.Let's look first of all at ball "A."Notice what I'm doing here.I'm isolating this particular object and we're goingto consider the forces acting on that ball.So, let's say that the force acting on this ball issimply some amount which we can call "F."OK?Where's the direction of the force on that ball?Well, let's see.First the ball was moving in this direction.So what do you have to do to it to turn it around?You have to push on it in this direction.Right.So, there was a force acting on the ball that was in this direction.Let me draw a little arrow here.Where did that force come from?Well, the force must had been exerted on ball "A" by ball "B."I know it's hard to read this when all it says is "F"with a little "A" and a little "B."In fact I can zoom in a little bit on this, I think, to make this a little easier to see.It doesn't say "FAB."I know it looks like that.But it says "the force acting on ball "A" exerted by ball "B."Now, let's look at the force.Isolate object "B" and see about the force acting on it.So, here's ball "B."We'll isolate this.And I can talk about the force exerted on ball "B" by ball "A."

Now, can you see from this that it's impossible that the twoforces are anything other than equal and opposite.Because notice that concerning the motionof this ball, it's the force acting on it.The motion of ball "B," it's the force acting on that ball.Where do these forces come from?Well, the force acting on ball "A" must have come from ball "B,"and the force acting on ball "B" must have come from force "A,"so, there's no other choice except that the two balls had to exertequal but opposite forces on each other.In other words, one ball can't push any harder on the otherthan the other pushes on the first one.So, what we see here is that the forces must be equalin magnitude, but they also must be opposite in direction.Because in order to change ball, the motion of ball "B,"the force on it must be exerted in this direction.So we can wind up writing this now, the third law, simply this way.That the force acting on ball "A" exerted by ball "B" is equaland opposite to the force acting on ball "B" exerted by ball "A."So, what we have here is an expression which simply saysthat the forces are equal and opposite.And I have to note here that the forces are not only equaland opposite, but they act on two different objects.And that you cannot have a single force acting on a single object,because there always has to be something that exerts the forceand something on which the force is exerted.So, forces must always occur in pairs.

Now, of all the laws, this one is the most profound and the deepest.It's also the one that requires the most, I think,the most analysis to really make sense of.So, you might want to look at some of the examplesin the textbook and see exactly how these laws and workand get in touch with the instructor if you have questions about this.This will be a great thing for a dialogue and I hope someof you will write your responses about this particular third law.Well, we have covered a lot of ground in this lesson,and you won't be able to remember it all, nor are you expected to,anymore than you're expected to memorize ascript of a movie that you've just seen.When you see a movie you're generally more interestedin understanding the plot and the interaction between thecharacters, than in memorizing the script.It's the same here.So in this program we've seen how the scientific inquiryand creativity, in general, blossomed in the 17th centuryas scientific revolution came into full swing.Bruno was executed for heresy in 1600.

In 1632 Galileo was placed under house arrest, and by 1700,scientific inquiries were the fad, and people were doingscience religiously, literally.So, we took a look at Newton's laws whileencouraging you to study the text and lookat the material that's present along with the program.Hopefully, all these different perspectives from the textand the program will allow you comprehend both themeaning and the significance of the laws.We left an outline of Newton and the relevant featuresof the Newtonian paradigm at the end of the Study Guide.If you skim this outline, it should stimulate someideas that you might want to follow up on.Well, you know, I guess that's it.We're done with Program 15, Lesson 2.7.My friend is still sleeping so I guess it's up to me.So we hope you understand Newton's laws and appreciatethe extent of his contributions and his influence on our livesfrom science all the way to our democratic system.Well, that's it, I guess.So, remember, when it comes to science, get physical!Bye.Music