MIT OpenCourseWare http://ocw.mit.edu 8.01 Physics I: Classical Mechanics, Fall 1999 Please use the following citation format: Walter Lewin, 8.01 Physics I: Classical Mechanics, Fall 1999. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/termsMIT OpenCourseWare http://ocw.mit.edu 8.01 Physics I: Classical Mechanics, Fall 1999 Transcript – Lecture 6 Last time we discussed that an acceleration is caused by a push or by a pull. Today we will express this more qualitatively in three laws which are called Newton's Laws. The first law really goes back to the first part of the 17th century. It was Galileo who expressed what he called the law of inertia and I will read you his law. "A body at rest remains at rest "and a body in motion continues to move "at constant velocity along a straight line unless acted upon by an external force." And now I will read to you Newton's own words in his famous book, Principia. "Every body perseveres in its state of rest "or of uniform motion in a right line "unless it is compelled to change that state by forces impressed upon it." Now, Newton's First Law is clearly against our daily experiences. Things that move don't move along a straight line and don't continue to move, and the reason is, there's gravity. And there is another reason. Even if you remove gravity then there is friction, there's air drag. And so things will always come to a halt. But we believe, though, that in the absence of any forces indeed an object, if it had a certain velocity would continue along a straight line forever and ever and ever. Now, this law, this very fundamental law does not hold in all reference frames. For instance, it doesn't hold in a reference frame which itself is being accelerated. Imagine that I accelerate myself right here. Either I jump on my horse, or I take my bicycle or my motorcycle or my car and you see me being accelerated in this direction. And you sit there and you say, "Aha, his velocity is changing. "Therefore, according to the First Law, there must be a force on him." And you say, "Hey, there, do you feel that force?" And I said, "Yeah, I do! "I really feel that, I feel someone's pushing me." Consistent with the first law.Perfect, the First Law works for you. Now I'm here. I'm being accelerated in this direction and you all come towards me being accelerated in this direction. I say, "Aha, the First Law should work so these people should feel a push." I say, "Hey, there! Do you feel the push?" And you say, "I feel nothing. There is no push, there is no pull." Therefore, the First Law doesn't work from my frame of reference if I'm being accelerated towards you. So now comes the question, when does the First Law work? Well, the First Law works when the frame of reference is what we call an "inertial" frame of reference. And an inertial frame of reference would then be a frame in which there are no accelerations of any kind. Is that possible? Is 26.100... is this lecture hall an inertial reference frame? For one, the earth rotates about its own axis and 26.100 goes with it. That gives you a centripetal acceleration. Number two, the earth goes around the sun. That gives it a centripetal acceleration including the earth, including you, including 26.100. The sun goes around the Milky Way, and you can go on and on. So clearly 26.100 is not an inertial reference frame. We can try to make an estimate on how large these accelerations are that we experience here in 26.100 and let's start with the one that is due to the earth's rotation. So here's the earth... rotating with angular velocity omega and here is the equator, and the earth has a certain radius. The radius of the earth... this is the symbol for earth. Now, I know that 26.100 is here but let's just take the worst case that you're on the equator. You're...[no audio] You go around like this and in order to do that you need a centripetal acceleration, a c which, as we have seen last time, equals omega squared R. How large is that one? Well, the period of rotation for the earth is 24 hours times 3,600 seconds so omega equals two pi divided by 24 times 3,600 and that would then be in radians per second. And so you can calculate now what omega squared R earth is if you know that the radius of the earth is about 6,400 kilometers. Make sure you convert this to meters, of course. And you will find, then that the centripetal acceleration at the equator which is the worst case-- it's less here-- is 0.034 meters per second squared. And this is way, way less-- this is 300 times smaller than the gravitational acceleration that you experience here on Earth. And if we take the motion of the earth around the sun then it is an additional factor of five times lower. In other words, these accelerations even though they're real and they can be measured easily with today's high-tech instrumentation-- they are much, much lower than what we are used to which is the gravitational acceleration. And therefore, in spite of these accelerations we will accept this hall as a reasonably good inertial frame of reference in which the First Law then should hold. Can Newton's Law be proven? The answer is no, because it's impossible to be sure that your reference frame is without any accelerations. Do we believe in this? Yes, we do. We believe in it since it is consistent within the uncertainty of the measurements with all experiments that have been done. Now we come to the Second Law, Newton's Second Law. I have a spring... Forget gravity for now-- you can do this somewhere in outer space.This is the relaxed length of the spring and I extend the spring. I extend it over a certain amount, a certain distance-- unimportant how much. And I know that I when I do that that there will be a pull-- non-negotiable. I put a mass, m1, here, and I measure the acceleration that this pull causes on this mass immediately after I release it. I can measure that. So I measure an acceleration, a1. Now I replace this object by mass m2 but the extension is the same, so the pull must be same. The spring doesn't know what the mass is at the other end, right? So the pull is the same. I put m2 there, different mass and I measure the new acceleration, a2. It is now an
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