lecture2 - Lecture 2 Kinematics 1 Review from Last Time...

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Lecture 2 Kinematics 1 Review from Last Time Vector Manipulation Important point: the magnitude of the difference between two vectors is not equal to the difference of their magnitudes!!! (Section III on Vector Worksheet). Example: Two people push on the desk from opposite sides. If we want to know how the desk moves under the net force acting on it, we need to add the forces. But force is a vector and includes direction! If each person exerts a force of magnitude 5N, but they push in opposite directions, obviously the desk won’t accelerate. This is because if we add the two vectors , the magnitude of the sum of the two forces is zero. Conceptually, it’s obvious that the desk won’t accelerate, but vectors allow us to keep track of direction (which is clearly important) and get the right answer mathematically. This will help us solve problems that are more complicated and not quite so obvious as this example! 2 Kinematic Definitions A few final preliminaries .... you’ve all been introduced to concepts like velocity and acceleration before (either in a physics class or just everyday life). We have very precise definitions of these in physics that are important (and somewhat suprisingly subtle). In order to describe the motion of an object, we need to be clear on these definitions. That’s the basic idea of kinematics - a mathematical description of an object’s motion. A bunch of people thought the relation between displacement, velocity, and acceleration was interesting. So, I’ll define them here again using vectors so you can get comfy with notation. I’ll also point out what I think is interesting! 2.1 Displacement We describe the position of an object by a single point. Of course, an object like a car or a person is not a single point! But, we describe their position that way anyway. We might think of representing the position of the car by the location of its center, for example. (DRAW person with pt at center) the position vector of an object, vector r , has a length (magnitude) equal to the distance of the object from the origin, and it points from the origin to the object. Thus the position vector depend on the choice of coordinate system!
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