It’s like really the same kind of problem, except that the 3 and 4 will all be placed by sin φ and cos φ but they are just the numbers.
Newtons laws of motion how to#
Normally, if I tell you 3 x + 4 y = 6, and 9 x + 6 y = 14, you know how to solve it. Maybe you didn’t realize that they are just simultaneous equations that you solve. Somehow, when I told you to invert the transformation, some of you had some difficulty. I gave you a law of transformation of the components namely, if the vector has components ax and ay in one reference frame and ax′ and ay′ in another reference frame, how are the two related? They come from writing I′ and J ′ in terms of I and J, then sticking it in an expression and identifying the new representation. It’s not enough to say these are the components of the vector you’ve got to tell me, “I am working with I and J, which I define in the following manner.” The components come in the minute you pick your axis. That is, the vector itself has a life of its own. So the components of the vector are not invariant characterizations of the vector. You can imagine that if a vector is viewed from an angle, then its components will vary with the perspective. If you do, the unit vectors are called I′ and J′, the components of the vector change.
Newtons laws of motion free#
I mentioned something of increasing importance only later, which is that you are free to pick another set of axes, not in the traditional x and y direction, but as an oblique direction. If you want to add two vectors, you can add the arrows by the rule I gave you or just add the components of the two guys to get the component of the sum and likewise for the y. You can either think of it as an arrow and imagine the arrow, or you can reduce it to a pair of numbers, x and y. You can deal with a vector in one of two ways. I and J are unit vectors in the x and y directions.
It’s got components which are x and y that could vary with time. The most important vector is the position vector that tells you where the object is. The typical vector is called V or A or B something with an arrow on it.
If you live in two dimensions or more, you’ve got to use vectors to describe most things. Also, people who come in early maybe should try to sit in the middle part of the classroom, so the latecomers can come in without too much disruption. I do try to start a few minutes late, but I also have to finish a few minutes early so you can go to your next class. Just come in and settle down, because it’s very hard to lecture with this amount of traffic. If you guys are coming in a little late, don’t worry about submitting the homework. By the way, I would like to make one recommendation. I picked for it two dimensions as the standard way to explain it. What I did last time was to show you how to handle motion in more than one dimension. If you say, “Can you summarize for me in a few words the main ideas?” I would like to do that. Professor Ramamurti Shankar: Let me start again by reminding you what it is that was done last time. Fundamentals of Physics I PHYS 200 - Lecture 3 - Newton's Laws of Motion
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