To find the angle
If you need a more in-depth refresher, check out Trigonometry For Dummies, by Mary Jane Sterling (Wiley).
Interpreting Equations as Real-World Ideas
Physics instructors are very familiar with one of the biggest problems college students face — getting lost in, and being intimidated by, the math.
BE A GENIUS: DON’T FOCUS ON THE MATH
Richard Feynman was a famous Nobel Prize winner in physics who had a reputation during the 1950s and ’60s of being an amazing genius. He later explained his method: He attached the problem at hand to a real-life scenario, creating a mental image, while others got caught in the math. When someone would show him a long derivation that had gone wrong, for example, he’d think of some physical phenomenon that the derivation was supposed to explain. As he followed along, he’d get to the point where he suddenly realized the derivation no longer matched what happened in the real world, and he’d say, “No, that’s the problem.” He was always right, which mystified people who, awestruck, took him for a supergenius. Want to be a supergenius? Do the same thing: Don’t let the math scare you.
In physics, the ideas and observations of the physical world are the things that are important. Math operations are really only a simplified language for accurately describing what is going on. For example, here’s a simple equation for speed:
In this equation, v is the speed, s is the distance, and t is the time. You can examine this equation’s terms to see how this equation embodies simple common-sense notions of speed. Say that you travel a larger distance in the same amount of time. In that case, the right side of the equation must be larger, which means that your speed, on the left, is also greater. If you travel the same distance but it takes you more time, then the right side of this equation becomes smaller, which means that your speed is lower. The relationship between all the different components makes sense.
You can think of all the equations you come across in a similar way to make sure they make sense in the real world. If your equation behaves in a way that doesn’t make physical sense, then you know that something must be wrong with the equation.
Bottom line: In physics, math is your friend. You don’t need to get lost in it. Instead, you use it to formulate the problem and help guide you in its solution. Alone, each of these mathematical operations is very simple, but when you put them together, they’re very powerful.
Chapter 3
Exploring the Need for Speed
IN THIS CHAPTER
There you are in your Formula 1 racecar, speeding toward glory. You have the speed you need, and the pylons are whipping past on either side. You’re confident that you can win, and coming into the final turn, you’re far ahead. Or at least you think you are. Seems that another racer is also making a big effort, because you see a gleam of silver in your mirror. You get a better look and realize that you need to do something — last year’s winner is gaining on you fast.
It’s a good thing you know all about velocity and acceleration. With such knowledge, you know just what to do: You floor the gas pedal, accelerating out of trouble. Your knowledge of velocity lets you handle the final curve with ease. The checkered flag is a blur as you cross the finish line in record time. Not bad. You can thank your understanding of the issues in this chapter: displacement, velocity, and acceleration.
You already have an intuitive feeling for what we discuss in this chapter, or you wouldn’t be able to drive or even ride a bike. Displacement is about where you are, speed is about how fast you’re going, and anyone who’s ever been in a car knows about acceleration. These characteristics of motion concern people every day, and physics has made an organized study of them. This knowledge has helped people to plan roads, build spacecraft, organize traffic patterns, fly, track the motion of planets, predict the weather, and even get mad in slow-moving traffic jams. Understanding movement is a vital part of understanding physics, and that’s the topic of this chapter. Time to move on.
Going the Distance with Displacement
When something moves from Point A to Point B, displacement takes place in physics terms. In plain English, displacement is a distance in a particular direction.
In this section, we cover position and displacement in one to three dimensions.
Understanding displacement and position
You find displacement by finding the distance between an object’s initial position and its final position. Say, for example, that you have a fine new golf ball that’s prone to rolling around, as shown in Figure 3-1. This particular golf ball likes to roll around on top of a large measuring stick. You place the golf ball at the 0 position on the measuring stick, as you see in Figure 3-1, diagram A.
