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Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_18_audio_only.txt | well good stole the ball episode 6f well I have very question I don't think I'll go over them now anything like that there were some be more that intention those were from the kind of thing to do and you dare popular names russ was about to poverty the other to do and the neighbors are having an airing up so you don't ... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_16_audio_only.txt | just certain activities involve the exercise of higher faculties which those have the dominant place and then in chapter 4 of utilitarianism he makes the argument you can Michael over that argument that the only thing desirable and that is happening and that all things are desirable either as means to or as a part of h... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_9_audio_only.txt | well I don't know the explanation why it won't turn [Applause] on so I just have to can you hear me at all I I just might make one comment about the last time you recall I gave the example of trying to explain the notion of adjusted procedural Justice gave the example of the PO game right where we took something out of... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_21_audio_only.txt | I should say forward again we have some macabre teacher not sure how to set it should be good it's got into English oh I mean it'll be good well actually that's anyway there's a package of it up here those do we didn't get it sexy well this is a third last class or Marco capatch alphabet mark and I always feel as I do ... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_19_audio_only.txt | well today we remember the law taking a change in trade makin up near contemporary Pacioretty know who was 12 years old and I'm I went in the remarks that we read we could provide a knuckle cloud the birth by the early essays and philosophical writings in 1840 example on the good question 143 from economic and philosop... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_10_audio_only.txt | last time to see how thankful I can make it all actually there's something in that because I think if it's not hurting stuff but I think before I get onto that I probably should say some things about Y which we call the procedure for flying tomorrow and since of we feel tomorrow loads it is spring there is a categorica... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_15_audio_only.txt | sighs I'm this is a good beginning once again in the vacation so I will see actually I ought to say in advance believing actually away April's 12 and 14 so have a lecture but here that wednesday because somebody shuffling I'll talk to y'all about how to work that way I thought what I would do is it over yet what I went... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_17_audio_only.txt | take up the patient everything's that I discussed in chapter 4 and make today just a very general point about those actually because I want to lead into that by talking some more about a mill the kind of audience rice gets up at the last time and I want to draw some contracts and someone have suggestions of pathetic ad... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_4_audio_only.txt | now on the first day I'm not going to today remember we need somebody we want to think what question is he attempting the extra and open that takes understanding that's some idea and I'll illustrate the point I mean with the contractor now in the case of hog he was concerned with the civil war between this contract opp... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_6_audio_only.txt | oh no no chance to do that but now you hear something it's about okay well I'll leave it the way it is all know it's up a full body hope it doesn't sudden the wrong well monday i should say before we begin that i will go back to pj in the game part of a chapter to the sections will discuss world two times next week 11 ... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_3_audio_only.txt | well what we're doing and then I think of doing that as an attempt to to gain some kind of orientation so that in tikrit we don't get lost by the detail it's easy to get lost by the detail and I think it's a case from seeing what happened take it the wrong way so whatever happened some explaining how these fundamental ... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_7_audio_only.txt | graduate study group we got a room in Emerson 305 it will be meeting on Wednesday 2 the 3 that's from our graduate section anybody who wants to come to that welcome Emerson 305 Wednesday the 3 um is this loud enough you hear anything hi are are you not hearing anything I don't know what the settle down all up you shoul... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_8_audio_only.txt | I thought I might ask before the class begins because they want to know what the C I was told that we appear to be out of Mark text and there no context yet I guess I'll have to get enough of the I have done up to hand out for next week but I assume there are copies of the ground work many of you need copies of the gro... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_11_audio_only.txt | well a neck 22 to 25 gray and I want to make some remarks about that indicates and i hope you will find helpful anyway I'm over two years perhaps that I hope not and I make women took before again about two elections were classes I always feel it's hard to say anything youthful over conflicts book their time so packs t... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_23_audio_only.txt | I won't be able to pair of hands out the machine so if I will hand it out 31 what we will do as I mentioned national last time notice a number of people seems somewhat shocked I thought it couldn't come with a dreadful product that the damn question it will hand out ahead of time and the following scent will be about 1... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_22_audio_only.txt | this is the second we can survive it isn't anywhere think so yes this factory workers everyone else hears is a lot i did you know mate ok well it's actually notice on the sheet of topics that we've had to go over we're not going to be able to do everything so had to make some decision about how to cut it short and I'll... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_5_audio_only.txt | which we are to for next week and here and I'll talk about that actually week from today because it's callay on Monday so it will get behind but if we get any further behind I'll have to make it up sometime the but if you don't have that you be copies available upstairs is it c um come to my office okay to dany's offic... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_1_audio_only.txt | those of you who don't have the the class readings and the schedule of the lectures and so on we will hand some of those out after the class we have run out of those but I hope majority of you have that uh schedu of group and it gives the assignments and so forth and I might talk about that for a moment and say some th... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_13_audio_only.txt | thank you Jesus go Oh later a last time you saw what we did was a regular braid what I call the setup and by that I met the guys that are going over in Section 25 where we describe the nature of the argument with the police and information and the motivation of a party is on and the alternatives that they have availabl... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_20_audio_only.txt | anything I met to bring in I've had enough copies open and like the cookiecutter program is intended by the whole thing that are higher than I extra to mimic felon and a fam a little accident for getting it but it would be available two sections I'll hope if I don't forget wednesday and i hope we will pick it up then i... |
Modern_Political_Philosophy_John_Rawls_PhD_1984 | John_RawlsModern_Political_PhilosophyLecture_12_audio_only.txt | I'm sorry the other day that I went over kills view it bad what I was calling a judicious spectator whenever that very fast and i don't know if i will try to give a proper account of it yeah but I i should say that i think that that idea is one of the most interesting important ideas moral philosophy and it's really wo... |
Introduction_to_Psychology_with_Paul_Bloom | 12_Evolution_Emotion_and_Reason_Emotions_Part_II.txt | Professor Paul Bloom: So what we're doing today is continuing on the theme of emotions. "Emotions" is a two-part lecture and we're continuing along certain themes. I want to begin by responding to a question which was raised in the last class concerning smiling and nonhuman primates. It was a very good question. The is... |
Introduction_to_Psychology_with_Paul_Bloom | 1_Introduction.txt | Professor Paul Bloom: I'd like to welcome people to this course, Introduction to Psychology. My name is Dr. Paul Bloom. I'm professor of this course. And what this is going to be is a comprehensive introduction to the study of the human mind. So, we are going to cover a very, very wide range of topics including brains,... |
Introduction_to_Psychology_with_Paul_Bloom | 8_Conscious_of_the_Present_Conscious_of_the_Past.txt | Professor Paul Bloom: I'll begin the class officially with a different sort of demonstration. I want to just show you one of the change-blindness studies that has been done in the real world. And these videotapes are not available publicly. We get them from the web and see them as little Java scripts. So, this is one o... |
Introduction_to_Psychology_with_Paul_Bloom | 10_Evolution_Emotion_and_Reason_Evolution_and_Rationality.txt | Professor Paul Bloom: We began the course by talking about one of the foundational ideas of modern psychology. This is what Francis Crick described as "The Astonishing Hypothesis," the idea that our mental life, our consciousness, our morality, our capacity to make decisions and judgments is the product of a material p... |
Introduction_to_Psychology_with_Paul_Bloom | 3_Foundations_Freud.txt | Professor Paul Bloom: Okay. The last class we talked about the brain. Now we're going to talk a little bit about some foundations. So today and Monday we're going to talk about two very big ideas and these ideas are associated with Sigmund Freud and B. F. Skinner and are psychoanalysis and behaviorism. And I want to ta... |
Introduction_to_Psychology_with_Paul_Bloom | 14_What_Motivates_Us_Sex.txt | Professor Paul Bloom: Sex is really strange. You ask people, "What's your favorite activity?" and if you ask people, particularly college students, particularly just fresh from spring break – I've seen teen movies – they'll often answer, "Sex." or some word that is synonymous with sex. But there's a kind of a puzzle ab... |
Introduction_to_Psychology_with_Paul_Bloom | 15_A_Person_in_the_World_of_People_Morality.txt | Professor Paul Bloom: Let me begin by just reminding us where we are in this course, reminding us of what we've done and what we have yet to do. We started by talking about the brain, the physical basis of thought. And then we moved to some general introductions to some foundational ideas in the study of psychology, Fr... |
Introduction_to_Psychology_with_Paul_Bloom | 20_The_Good_Life_Happiness.txt | This lecture will be a some slightly shorter lecture than usual. What I first want to do is finish off the discussion of clinical psychology from last lecture and then have a little brief discussion about some very interesting research on happiness. We talked--we ended last lecture with a discussion of some early--some... |
Introduction_to_Psychology_with_Paul_Bloom | 17_A_Person_in_the_World_of_People_Self_and_Other_Part_II.txt | Professor Paul Bloom: Just to review, here's where we left off. The discussion from last lecture and for about half of this lecture is going to be social psychology. And so, we started off by talking about certain fundamental biases in how we see ourselves. We then turned to talk about a bias and how we see other peopl... |
Introduction_to_Psychology_with_Paul_Bloom | 9_Evolution_Emotion_and_Reason_Love_Guest_Lecture_by.txt | Professor Paul Bloom: I'm delighted to introduce the first guest lecturer for this Introduction to Psychology course, Dean Peter Salovey. Peter is an old friend and colleague. Many of you--I think everybody here knows of him through his role as Dean of Yale College. I'll just, in this context of this introduction, ment... |
Introduction_to_Psychology_with_Paul_Bloom | 16_A_Person_in_the_World_of_People_Self_and_Other_Part_I.txt | Professor Paul Bloom: This is going to begin a two-lecture sequence on social psychology on how we think about ourselves, how we think about other people, how we think about other groups of people. We've talked a lot about the capacities of the human mind and some of these capacities involve adapting and dealing with t... |
Introduction_to_Psychology_with_Paul_Bloom | 5_What_Is_It_Like_to_Be_a_Baby_The_Development_of_Thought.txt | Professor Paul Bloom: So, most of what we do these days – our methods, our theories, our ideas – are shaped, to some extent, by Piaget's influence. And so, what I want to do is begin this class that's going to talk about cognitive development by talking about his ideas. His idea was that children are active thinkers; t... |
Introduction_to_Psychology_with_Paul_Bloom | 4_Foundations_Skinner.txt | Professor Paul Bloom: I actually want to begin by going back to Freud and hitting a couple of loose ends. There was a point in my lecture on Wednesday where I skipped over some parts. I said, "We don't have time for this" and I just whipped past it. And I couldn't sleep over the weekend. I've been tormented. I shouldn'... |
Introduction_to_Psychology_with_Paul_Bloom | 7_Conscious_of_the_Present_Conscious_of_the_Past_Language.txt | Professor Paul Bloom: Two follow-ups on yesterday's--I'm sorry, on Monday's lecture. One is that somebody came up after class and asked when the preference for your own language emerges in development and fortunately, studies pretty much exactly this sort of infant understanding. She knew the answer. There's been studi... |
Introduction_to_Psychology_with_Paul_Bloom | 2_Foundations_This_Is_Your_Brain.txt | Professor Paul Bloom: We're going to begin the class proper, Introduction to Psychology, with a discussion about the brain. And, in particular, I want to lead off the class with an idea that the Nobel Prize winning biologist, Francis Crick, described as "The Astonishing Hypothesis." And The Astonishing Hypothesis is su... |
Introduction_to_Psychology_with_Paul_Bloom | 13_Why_Are_People_Different_Differences.txt | Professor Paul Bloom: What we've been talking about so far in the course are human universals, what everybody shares. So, we've been talking about language, about rationality, about perception, about the emotions, about universals of development, and we've been talking about what people share. But honestly, what a lot ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS22_Worked_Example_Stacked_Blocks_Choosing_the_System_of_2_Blocks_Together.txt | When we analyze the problem about putting two blocks along a frictionless surface and pushing one and asking, what is the maximum force such that block 2 does not slip? We have three different systems. And now I want to focus a little bit on what would happen if we just naively chose our systems as both blocks together... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 120_Week_4_Introduction.txt | This week, we will examine some more advanced topics in the application of Newton's laws of motion. First, we will look at more examples of constrained motion, where the motion is forced to obey some particular condition in addition to Newton's laws of motion. These conditions usually specify some particular relationsh... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 182_Set_up_a_Recoil_Problem.txt | We would like to now apply the momentum principle to examples of recoil. So recall that the momentum principle is that the external force causes the momentum of the system to change. Now, this is a vector equation. So for example, if the external force in the x direction is 0, then the momentum of the system in the x d... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 151_Momentum_and_Impulse.txt | So suppose we have a point mass particle of mass m moving with a velocity vector, v. We can introduce a quantity we call the momentum of that particle. I'll label it with the symbol p. And it's equal to the product of the mass times the velocity. This is something you've undoubtedly seen before. Now, let's think about ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS31_Worked_Example_Orbital_Circular_Motion_Radius.txt | The little prince's asteroid B612 is being orbited by a small body. It has a mass m. And it goes around this asteroid B612 that has a mass m1. We should add a coordinate system. We always know about r-hat goes radially outward. And we know from the universal law of gravitation that we have mutual attraction between the... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 171_Definition_of_the_Center_of_Mass.txt | Today we'd like to explore the idea of the center of mass, or the center of gravity, of a rigid object. For instance, take this rod. And if I try to balance it on my finger at a certain point in that rod, I'm balancing it via the gravitational force. And this point is often referred to as the center of gravity of the r... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS31_Worked_Example_Orbital_Circular_Motion_Period.txt | The little prince has really come to like this little body that's orbiting him. He knows at what distance it orbits and knows how fast it goes. And I think the little prince fell in love with that little body. And now he wants to see it all the time as it goes around the asteroid. But the little prince just wants to ke... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 61_Contact_Forces.txt | Let's consider what happens when we have an object that's moving on a horizontal surface. So here's our object, and here's our surface. Now, we want to look at a special case where we're applying a force F to the object, and the object is moving at a constant speed. Then what we see here is that there has to be some ty... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 83_Angular_Velocity.txt | Now we'd like to talk about angular velocity. So for a particle traveling in a circle, we've seen that the velocity can be written as r d theta dt. In the theta hat direction. And we've also seen that d theta dt can be positive, in which case, theta is increasing. And so the particle is traveling around the circle in t... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 17_Worked_Example_Derivatives_in_Kinematics.txt | Let's consider a one dimensional motion that has a non-uniform acceleration. What we'd like to do is explore how do you differentiate position functions, to get velocity functions, to get acceleration functions. So what we're going to consider is a rocket. So I'm going to choose a coordinate system y. And here's my roc... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS22_Worked_Example_Stacked_Blocks_Solve_for_the_Maximum_Force.txt | And now I'm in position to talk about what is the maximum force. If I push F harder, as if I push F and the blocks go together, the accelerations are the same. I push F harder. Accelerations are the same. I push F harder, and I push F so hard, that the static friction no longer reaches its maximum value. And if I push ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 133_Differential_Elements.txt | In many problems throughout this class, we will find it useful to consider how the mass of an object is distributed throughout the object. To do this, we will define a small piece of that object and then consider the mass that's contained within that small piece. For an object in one dimension, the differential element... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 02_Vector_Operators.txt | We begin with multiplication of a vector by a scalar. When you multiply a vector, A, by a scalar, this multiplicative factor just rescales the magnitude or the length of the vector. Let us look at the vector 2 times A. This is in the same direction as the vector A, but is twice as long. This is vector B. A vector is de... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 111_Newtons_2nd_Law_and_Circular_Motion.txt | Let's examine again an object that's undergoing circular motion. And we'll choose our polar coordinates r hat, theta hat. We'll make it cylindrical with a k hat. Now that we've completed our kinematic description of the motion, now let's see how we apply Newton's second law to circular motion. Well, when we write Newto... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 11_Coordinate_Systems_and_Unit_Vectors_in_1D.txt | We will now like to begin our analysis of motion. And we'll start with one dimensional motion. Let's just consider a person running along a road. And so here's our runner, and here's our road. And what we want to do is be able to describe the position, the velocity, the acceleration of this runner. In order to do that,... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 123_Virtual_Displacement.txt | When we did our analytic analysis of the constraint conditions between the accelerations of objects 1 and 2, we came up with the condition that a1 was equal to minus 2 a2. Now let's do something which we call a virtual displacement argument. Suppose that b and 2 move down a certain amount. Let's imagine-- and I'm going... |
MIT_801SC_Classical_Mechanics_Fall_2016 | P14_Sketch_the_Motion.txt | Let's consider a kinematics problem. And in this problem, we want to focus on special conditions-- how to think about that. So what I'm going to consider is some charged plates, and I have a charged particle, and it enters into this region of charged plates. And in this problem, there's two types of forces that are goi... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 131_Rope_Hanging_Between_Trees.txt | OK. Well, I like to lay in the hammock in the summer. And this is our version of that hammock. So we're having one rope, or perhaps two ropes, hanging between two trees here. And they span an angle theta on each side here. And we want to know what is the tension in this rope at the midpoint and here, right where it is ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 172_Worked_Example_Center_of_Mass_of_3_Objects.txt | The little prince is sitting on his little planet, and he's watching the planets go by. And so suddenly, he's seeing three of them. One, two, three. And he wonders, hmm, what would the center of mass of these three planets be? So let's calculate it. We have one planet here that's three times the mass of this guy. And t... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 74_Hookes_Law.txt | We now would like to analyze the force law on an idealized spring, a force law called Hooke's law. Let's begin by drawing a ideal spring connected to an object on a frictionless surface. So we'll draw our object. We'll draw our idealized spring. This surface here is going to be frictionless. And this is a wall, and we'... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 155_Force_on_a_System_of_Particles.txt | Now we'd like to analyze in more depth our result that for a system of particles-- so let's indicate our system. We had particle 1. We have our jth particle. And we have a particle N. So here's our system of particles where the total force caused the momentum of the system of particles to change. Now, I'd like to exami... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 134_Density.txt | We want to relate the small length, area, or volume element to delta m, the amount of mass contained within. In one dimension, this relation is called the linear density, lambda, which is delta m over delta l. For a uniform rod of length L and total mass M, lambda is equal to M over L. In two dimensions, the area eleme... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 102_Angular_Acceleration.txt | Now we'd like to discuss angular acceleration for circular motion. So suppose we have our angle theta, radius r, and r hat and theta hat. Recall that we described the angular velocity as the derivative of d theta dt, and we made this perpendicular to our right-handed coordinate system, direction k hat. Now let's differ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 51_Universal_Law_of_Gravitation.txt | The motion of objects in space is governed by the universal law of gravity. So let's consider how this works. We have two objects here, object one and two. And that could be two planets or two asteroids or two white dwarfs, black holes, any kind of objects you can imagine. And they are mutually attracted by each other ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 153_Worked_Example_Bouncing_Ball.txt | Let's consider a ball that is dropped from a certain height, h i, above the ground and this ball is falling. It hits the ground and it bounces up until it reaches some final height, h final. Now when the ball is colliding with the ground, there are collision forces. And in this problem what we like to do is figure out ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 181_Relative_Velocity.txt | We will practice going between reference frames to look at relative velocities in one dimension. Let's say that an observer is standing on the sidewalk and that observer sees a car drive past to the right at a speed of v car. The observer also sees a bike that's riding to the left at a slower speed, v bike. Now, I'm in... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 33_Instantaneous_Acceleration_in_2D.txt | Let's now consider two dimensional motion, and let's try to analyze how to describe the change in velocity. So again, let's choose a coordinate system. We have an origin plus y plus x. And let's draw the trajectory of our object. And now let's draw the object at two different times. So for instance, if I call this the ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 161_Cases_of_Constant_Momentum.txt | Let's examine when the momentum of a system is constant, and apply that to solving problems. First, we'll revisit the impulse equation. On the left, we have the impulse, the integral of the total external force acting on a system between some initial and final times. And on the right, we have the change in the total mo... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 143_Resistive_forces_high_speed_case.txt | Now we're going to analyze a more complicated example of drag forces, where we have an object falling in a gravitational field with gravity. We have a resistive force. And this is an object in air. And so our model will be for the resistive force that it's going to be proportional to the velocity squared. Now to get it... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 44_Noninertial_Reference_Frames.txt | Now that we've seen how coordinates are related between two inertial frames, I want to consider a slightly more advanced example for a moment, which is supposed that capital V, the vector velocity of frame S prime relative to inertial frame S, is not a constant. So in this case, suppose that frame S prime has an accele... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS31_Worked_Example_Orbital_Circular_Motion_Velocity.txt | Now the little prince wants to know how fast this little body is going around. And well, we can just do f equals ma analysis again, but use a different option here for the description of the circle of motion. So we are going to get minus Gm m1 over r squared equals minus mv squared over r. And here one r cancels, and t... |
MIT_801SC_Classical_Mechanics_Fall_2016 | P15_Worked_Example_Pedestrian_and_Bike_at_Intersection.txt | You're standing at a traffic intersection. And you start to accelerate when the light turns green. Suppose that your acceleration as a function of time is a constant for some time interval t less than t one. And after that, it's zero for a time after t one less than t less than some time t two. At the exact same instan... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS11_Three_Questions_Before_Starting.txt | I'd like to talk to you about solving these kinematics problems. So we're going to actually start by asking ourselves three separate questions anytime we start one of these kinematics problems and this will help us really figure out what's happening in the motion. So the first question that we want to ask is, how many ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 52_Worked_Example_Gravity_Superposition.txt | The little prince lives on his asteroid B-612. And he really likes to watch the stars. And what he really wishes for is to watch the stars while floating, to have the best possible view and to just immerse himself in the stars. And so the little prince has to think if there is a position in space with respect to other ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 141_Intro_to_resistive_forces.txt | We would now like to discuss drag forces in a fluid. Now remember that fluids can be both a liquid or air. And drag forces are actually quite complicated depending on a lot of factors. If we had an object falling in a fluid, the drag forces can depend on both the properties of the object-- and in that case, it might be... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 31_Coordinate_System_and_Position_Vector_in_2D.txt | Let's consider a two dimensional motion. Suppose we have something like projectile motion. And we have an object moving. Let's now describe how we can describe this motion with vectors. So the first thing we always want to do, and let's remind ourselves of the steps, is we want to choose a coordinate system. Now what d... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 41_Newtons_First_and_Second_Laws.txt | Newton's first law tells us about the motion of isolated bodies. By an "isolated body," we mean one on which the net force is 0, one that's isolated from all interactions to as great a degree as possible. Newton's first law states that an isolated body moves in a straight line at constant velocity and will continue to ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 24_Integration.txt | If we know the position x of t of an object as a function of time, we can use differentiation to calculate its velocity and its acceleration at later times. Essentially, by taking the derivatives of the position, we know everything there is to know about the motion. Sometimes, however, we'll want to go in the other dir... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 173_Center_of_Mass_of_a_Continuous_System.txt | Let's try to find the center of mass of a uniform object like a uniform rod. And let's assume this rod is length L, and we want to find the center of mass. Now, before I begin this calculation, you can probably already guess that it's going to be exactly in the middle, and we'll verify that, but let's first define what... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS23_Window_Washer_Solution.txt | So now that we've combined pulley A, string 2, platform, and washer as our system, we can now address our question. If we measure the acceleration of the person, what is the force that the person pulls the rope down with? Well, of course, that will just be the tension in the string. And with this simple system, we can ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | Newtons_3rd_Law_Pairs.txt | Where do forces come from? All forces arise from the interaction of two objects with each other. In this example, we have two objects, One and Two, interacting with each other in this case because their surfaces are in contact with each other-- one sitting on top of the other. And the interaction between the two object... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 91_Uniform_Circular_Motion.txt | When we analyzed how the position vector changed, we know that the velocity for circular motion is given by the radius times the rate that the angle is changing. And it points tangential to the circle. So let's draw a few characteristic arrows to show that. At this point, we'll draw these pictures with d theta dt posit... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 124_Solve_the_System_of_Equations.txt | We are now in position to find the accelerations a1, a2, and the tension, because we have Newton's second law and our constraint condition for the acceleration. Let's recall the equations that we found. We had m1g minus t was m1a1. And we had m2g minus 2t was equal to m2a2. And we also had the condition-- constraint co... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 162_Momentum_Diagrams.txt | We would like to now introduce a new methodological tool for analyzing problems that involve momentum transfers. And we call that tool momentum diagrams. Now, what we'd like to do is look at our fundamental idea, which was, for discrete objects, we have that-- involved in a collision-- we have that the external force i... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS23_Window_Washer_Free_Body_Diagrams.txt | Let's consider what we call the window washer problem. What we have is suspended from some ceiling. We have a pulley. And the pulley is suspended by a rope, which we're going to call this string 3. And we have a rope that is wrapping around this pulley. And then it wraps around another pulley. So this rope is going aro... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 14_Average_Velocity_in_1D.txt | Now that we've described the displacement of our object-- remember that our displacement vector delta r in this time interval was x(t) plus t minus x(t) i hat, which we denoted as delta x i hat. Now, let's just remind ourselves that this distance here, that's delta x, and this whole distance from here over to there-- t... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 801SC_Classical_Mechanics_Introduction.txt | Welcome to Physics 8.01, MIT's introductory course in classical mechanics for first year undergraduates. Im Deepto Chakrabarty. And I'm Peter Dourmashkin. We're the faculty members in charge of this course. The science of classical mechanics establishes an important principle of cause and effect, wherein the changes in... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 06_Going_Between_Representations.txt | Let's look at going between representations. We'll start in i, j, k representation going to the magnitude and angle representation. So if we have our vector, the arbitrary vector could be written as Ax i hat plus Ay j hat. In this particular case, we're given a vector minus 2i hat plus 3 hat. And we'd like to go to the... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 42_Newtons_Third_Law.txt | Newton's third law states that forces always come in equal and opposite pairs. One way we can write that is if you imagine two objects, object one and object two, the force exerted by object one on object two is equal and opposite to the force exerted by object two on object one. This makes explicit that real forces al... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 05_Vector_Decomposition_into_components.txt | Vectors can be represented through their components. If we have a vector A, we can decompose it into its components in the x and y-directions by finding the vectors, one along x and one along y, that add up to the vector A. This is the same thing as finding the projections of the vector A along the x and y-axes. Here i... |
MIT_801SC_Classical_Mechanics_Fall_2016 | Internal_and_External_Forces.txt | Newton's second law states that the sum of the forces on an object is equal to the acceleration of that object times the mass. But what if instead this object is actually two objects? Do I now need to consider the forces that are acting between each of these parts? Or what if I consider the object to be made out of eve... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 154_Momentum_of_a_System_of_Point_Particles.txt | Let's now extend our concept of momentum to a system of particles. Again, we need to choose a reference frame. So we'll have a ground frame. And let's consider N particles. Now when we have a lot of particles, we need some type of notation. So let's use the symbol j. And it will goes from 1 to N. And then our arbitrary... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 121_Pulley_Problems.txt | Let's look at a typical application of Newton's second law for a system of objects. So what I want to consider is a system of pulleys and masses. So I'll have a fixed surface here, a ceiling. And from the ceiling, we'll hang a pulley, which I'm going to call pulley A. And this pulley will have a rope attached to it, wr... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 125_Worked_Example_2_Blocks_and_2_Pulleys.txt | We want to look at this pulley system. We want to find out what this force here is, for example, with which this block is being pulled. Now we have two massless pulleys here and two moving parts. And one key component of this problem is to derive the acceleration constraint. How are we going to do that? Well, we have t... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 136_Summary_for_Differential_Analysis.txt | So let me summarize what the steps that we've taken are to do this differential analysis. So when you're trying to analyze a continuous mass distribution, the first step is to pick some arbitrary mass element, a small but finite size mass element somewhere in the middle of the mass distribution. You don't want to pick ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 82_Circular_Motion_Position_and_Velocity_Vectors.txt | When we're looking at polar coordinates, one of the important issues is to understand the unit vectors. Let's describe our coordinate system, again. We have a point where there is an object. And at this point, we have a pair of unit vectors, r hat and theta hat. Now those unit vectors will change, depending on where yo... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 23_Worked_Example_Acceleration_from_Position.txt | Let's consider a very simple example of a runner in which our position function x of t is given as a quadratic function in time. It will be a constant b times t squared. Here, b is a constant. Now it's always important in SI units to consider what the units of this constant is. Because a position function is measured i... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 32_Instantaneous_Velocity_in_2D.txt | Recall, when we were examining the motion an object, in two dimensions, we introduced Cartesian coordinates and a position vector. Now let's suppose the object has moved to a new point, along the orbit. Well, we'll write another vector r of t. And let's say this took a time delta t to the new point. And what we want to... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 71_Pushing_Pulling_and_Tension.txt | Here we have a little block that sits on that surface. And well, what can one do with a block? You can push it, or you can pull it. And that's exactly what we're going to look at now. So I can exert a pushing force onto this block here, F push. But I could also pull it like this, F pull. And the question is, how can we... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 180_Week_6_Introduction.txt | This week, we will use the concept of momentum to analyze some more advanced situations. Namely, systems in which there is a continuous flow of mass rather than just the motion of discrete objects. The classic example of this is the thrust due to exhaust from a rocket engine. Once again, we will appeal to a differentia... |
MIT_801SC_Classical_Mechanics_Fall_2016 | PS22_Worked_Example_Stacked_Blocks_Free_Body_Diagrams_and_Applying_Newtons_2nd_Law.txt | One of the big difficulties students have in a problem that involves many objects is to successfully identify third law interaction pairs. So today, I'd like to look at a problem which shows us how to think about that. So what we're going to look at is third law interaction pairs. Now, the problem I'd like to consider ... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 40_Week_2_Introduction.txt | Last week, we discussed the kinematics of motion. How one describes the motion of an object by specifying its position, velocity, and acceleration as a function of time. This week, we will continue by discussing the dynamics of motion. How the application of forces on an object changes the geometry or trajectory of its... |
MIT_801SC_Classical_Mechanics_Fall_2016 | 112_Worked_Example_Car_on_a_Banked_Turn.txt | Let's consider the motion of a car on a circular track, and the track is frictionless. And it's also banked. So this is the overhead view of our circular track. It has radius, r. And here's our car moving at a constant velocity. Now, from the side view when we want to look at that bank turn-- let's draw a side view. So... |
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