Force and Motion: An Illustrated Guide to Newton's Laws

6 Introducing Acceleration

CHAPTER 6 Introducing Acceleration You may think that you already know what acceleration means. Get ready for a new definition! Here is what acceleration means: Acceleration is ⎧ ⎪ ⎨ ⎪ ⎩ speeding up slowing down or turning. (63) The word acceleration means something different in physics than it does in everyday speech. In everyday speech, acceleration means only “speeding up.” But in physics, speeding up is just one of the meanings of the word acceleration. Strangely enough, in physics acceleration can also mean slowing down! In common speech, slowing down is sometimes called “deceleration .” But we shall never use this word. Deceleration is not a physics term. If we mean slowing down, we’ll say “slowing down.” Finally, and even stranger still, in physics acceleration can also mean turning! Acceleration is a big word that covers many situations that may seem unrelated at first. Let me emphasize five points: 1. If you are speeding up, you are accelerating. 2. If you are slowing down, you are accelerating. 3. If you are going at a constant speed but turning, you are accelerating. 4. If you are speeding up and turning at the same time, you are accelerating. 87 88 PART I DESCRIBING MOTION v v v FIGURE 84. The trajectory of a falcon that is turning at each instant of time shown. 5. If you are slowing down and turning at the same time, you are accelerating. In fact, there are only two ways not to accelerate. One is to move in a perfectly straight line at a perfectly constant speed. The other is to stand still. How to Tell When an Object Is Turning Before we proceed with our discussion of acceleration, let me take a moment to clarify the word turning. By turning I mean moving with any degree of curvature in an object’s trajectory. For example, if you are driving in a car and going around a bend, at that moment your trajectory is curved, and therefore you are turning. Turning doesn’t have to be a right-or-left thing. It can also be an up-or-down thing. Picture a falcon pulling out of a dive. The falcon in Figure 84 is turning at each moment shown because its trajectory is curved at each moment. As another example, think about riding a bike. Is it possible for you to be “turning” even as you hold your handlebars perfectly straight? Sure—if you are riding on a hilly road! See Figure 85. Students often have trouble identifying curvature in a trajectory . Identifying curvature is not as easy as it sounds. After all, if you “zoom in” on any curve far enough, it will look straight. So the trick is not to zoom in too much. When in doubt, draw a tangent line to the trajectory at the moment in question. If the trajectory falls away from the line to one side, the trajectory is curved at that point, and the object is turning at the moment in Chapter 6 Introducing Acceleration 89 FIGURE 85. The trajectory of a bicycle rider who is turning at the moment shown because her trajectory is curving in the vertical dimension. It doesn’t matter that her trajectory would appear straight if viewed from directly overhead. question. But if the trajectory “hugs” the tangent line and doesn’t fall away—or if it falls away in different directions before and after the moment in question—the trajectory is straight, or at least momentarily straight, and the object is not turning at the moment in question. An example is in order.» WORKED EXAMPLE 1 A fly travels on the trajectory shown in Figure 86. For each moment of time indicated by a black dot, say whether the fly is turning at that moment or not. FIGURE 86. Worked Example 1. The trajectory of a fly in flight, with moments in time represented by black dots.» SOLUTION 1 In Figure 87, I have overlaid tangent lines on the trajectory from Figure 86. The fly is turning at moments 1, 2, 3, 5, 6, 7, 9, and 11. Observe how the trajectory falls away from the tangent line to one side at these moments. 90 PART I DESCRIBING MOTION 1 2 3 4 5 6 7 8 9 10 11 12 FIGURE 87. Solving Worked Example 1. The trajectory in Figure 86 with “overlaid” tangent lines that help us decide whether the fly is turning...