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Ch0_Jan11

Ch0_Jan11 - PHYS 121 Mechanics Chapter 0 Chapter 0...

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PHYS 121 Mechanics Chapter 0 Chapter 0 MECHANICS: The Motion of Bodies and how the Motion Depends on the Forces Acting on those Bodies WHAT IS A BODY ? For this course, we usually refer to blocks of wood, cars, air particles, planets, even people, etc. This is something fairly solidly held together (even rigid) so that when we talk about its position, we have some idea of where the body is. The location or position of a blob of ink spilled onto the floor is harder to describe, although we will talk about flexible bodies like ropes before long (and short ropes before long ones). WHAT IS MOTION ? To talk about motion, we start with the body’s position and how it changes in time. So we need the velocity (the time rate of change of position), and, because of the interaction story you’ll read below, we also need the acceleration (the time rate of change of velocity) of the body. By the way, the position implies the coordinate location of some point defined on the body (a great choice will be the “center of mass” – see much later). This also brings us to digress about basic units of position and time measurements (meters, seconds, and all that). Units: The primary units are SI meters m , seconds s , and kilograms kg for lengths, times, and masses (SI System Internationale where we will use “ ” to mean “defined by” or “equivalent to” or “means”). The littler units come in the “cgs” system and are centimeters cm, seconds, and grams g (1m = 100cm, 1kg=1000g). We’ll say more about units in a moment, including a really ugly discussion that many people even avoid because it seems so awful. WHAT IS FORCE ? Well, a body accelerates (changes its velocity, as we said) because there is some interaction between it and another body (some influence on its motion due to another body). Why? Well, this is what is behind Newton’s laws. We think a neat way to start this introductory physics course in mechanics is to show you Newton’s three laws straightaway. Why? Well, because everything we do in this course can be explained, can be derived, from them. We describe the strength and direction of this interaction by "numbers." In our full three- dimensional (3D) world, there are three numbers needed for each position, velocity, and acceleration, in view of the three directions, which defines “vectors” for each. (We will have a more detailed discussion of vectors as we go.) We thus have a vector associated with the interactions; force is the name we use for this vector. The vector corresponding to the three interaction numbers is the "force" vector . [ F F G G is a nice notation connected to the fact that the 3 numbers (the “components” in all three directions) also can be described in terms of a direction and a magnitude. So we often use , r G v G , a G for the position, velocity, and acceleration, too.] The idea that a body accelerates only if there is some interaction on it can be rephrased in two equivalent ways: VECTOR STATEMENT:

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Ch0_Jan11 - PHYS 121 Mechanics Chapter 0 Chapter 0...

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