- 1. Units
- 2. Linear Motion
- 3. Vectors
- 4. Force
- 5. Energy
- 6. Number
- 7. Operations
- 8. Heat
- 9. Electrostatics
- 10. Electrical Circuits
- 11. Oscillation
- 12. Sound and Waves
- 13. Electromagnetic Radiation
- 14. Momentum
- 15. Final Review

Math goal: Symbolic manipulation - be comfortable doing algebra even when you have to work with variables rather than numbers.

Why you should care: Math is a language. When you take a language like Latin or Spanish, you learn how to converse in that language and how to translate in and out of that language. Math, on the other hand, has probably always been taught to you as somethign entirely abstract. Physics is different - it uses the language of mathematics to describe reality, and to allow us to predict how the world works.

In the end, the reason this should matter to you is that mathematics is power. I'm not really talking about social or economic power, although it's true that in our society math is the gatekeeper that locks many people out of high-paying jobs. Rather,

Units

Math goal: Reading graphs - by looking at a graph, be able to determine the value of one variable for any given value of the other, be able to describe how one variable changes as the other changes, and find the slope at any point.

Why you should care: The linear motion equations are the simplest way to describe the motion of an object. Phrases like "speed up," "slow down," and so on are really based on ideas in physics, so to really understand how, for example, a car moves, you need to know the physics behind it.

Reading graphs is an essential skill in life. You have to be able to pick out individual data points and identify trends in order to track the performance of a company (say, before accepting a job there or buying stock). Graphs can also help you to organize information and notice trends and patterns.

Rate of change is the most important single idea in physics, so important that the founder of physics, Isaac Newton, developed an entirely new type of math (Calculus) just to deal with it. All the quantities that we will deal with in this first part of physics are related either by some conversion using their mass, or by a rate of change relation.

Linear Motion

Math goal: Vectors: A vector is how, in math, we represent some measurement that goes in more than one direction at once. In this unit, you will learn how to add, subtract, and scale vectors, and how to use these simple procedures to solve problems.

Why you should care: Two dimensional motion is what is used to describe the motion of a space ship slinging around the moon, or of a trebuchet's boulder flying through the air. Once you have learned how to deal with vector motion, you will be able to figure out things like what angle a baseball should best be hit at.

Vectors are another really big idea in math that you will be introduced to in physics. We will be using them for the rest of the class, expecially in the next unit, Force. It is possible you won't see them anywhere else in high school unless you take AP physics, but when you get off into college or the real world you will find them everywhere (They are particularly useful in computer games, which are Mr. Z.'s other passion).

Vectors

Math goal: Trigonometry. There are many forces acting on any object, from many different directions. In order to find the vector form of a force at an angle, we need to be able to find the components given the angle. For this, we use trigonometry, the math functions that convert from angles to lengths.

Why you should care: One thing force diagrams are often used for is in research into sports such as hockey and figure skating, basketball, football, or auto racing. A trainer with a good understanding of how force works can teach someone how to jump higher, how to block better, or how to take a car around a turn while maintaining as much speed as possible.

Trigonometry is an indispensable tool in engineering and science, because it is very common to need to convert something from an angle into a length and vice versa. I remember being very frustrated in eight grade math because I could tell that something like the trigonometric functions ought to exist, and that if they did, it would open up a whole new world of possibilities in geometry, but I wan't able to figure out, using eigth grade math, how to calculate the trig functions. Once you know the trig functions, you can solve almost any problem that involves angles and measurements.

Force

Math goal: Reading graphs. In addition to all the skills from the linear motion unit (reading a graph, finding slope, finding area) you need to know how to look at several "stacked" graphs and identify what part belongs to what quantity.

Why you should care: This is probably your first formal introduction to the idea of

The graphical skills you will use in this chapter are the same that are used when planning out a budget, determining the result of a chemical reaction, or tracking the population of a school district. If you get into any sort of business as a career, you will need to be comfortable looking at a graph and understanding what information it conveys.

Energy

Math goal: Learn to use a number line as the foundation of your understanding of numbers and operations.

Why you should care: Students as intelligent as you all are shouldn't have to struggle with basic math concepts. The fact that you do is a result of bad math education in elementary and middle school, not a result of any failing on your part. I want you to be able to come out of this class with the confidence that you can tackle any sort of science or engineering problem and really understand the math behind it. In order to do that, we need to go back to the foundations of algebra and re-learn everything from the ground up in a way that will finally make sense to you.

Number

Math goal: Learn to understand the various mathematical operators as transformation of numbers on a number line, and use this to make sense of functions and manipulate them in various ways.

Why you should care: As you develop an intuitive sense of the effect of both individual operations and entire functions, you are taking the first steps toward encountering math as a language, rather than an abstract collection of rules and symbols. This unit will help you to discover what is going on in the mind of a math expert when they analyze a mathematical expression: instead of teaching you what it looks like on the surface to solve a problem and expecting you to derive from that the deep structure, we will use tools like function notation that help you to deal consciously and concretely with the representations of math that you will eventually internalize. You will come out of this section having taken a big step toward becoming yourself an expert in mathematics.

Operations

Math goal: Reading exponential graphs. When heat transfers between objects, their temperatures want to match. How quickly the temperature changes has to do with how insulated the objects are and how different their temperatures are.

Why you should care: This is probably the most practical unit in our whole physics course. Heat is something that you encounter all the time in your life: trying to keep warm in winter and cool in summer, cooking food, trying to avoid getting stuck to a cold object or burned by a hot one.

Heat

Math goal: One of the fun parts of this chapter is that there is hardly any math involved at all, in the traditional sense of number and mathematical operations. However, it does teach an important skill: being able to think about two things, like the charges in an object, being either balanced, or having an excess one way or the other.

Why you should care: Electrostatics, and the interaction of protons and electrons, are the basis for chemistry, electrical engineering, and several other fields. Being able to think of matter as made up of a careful balance of positive and negative electrical charges, and being able to understand what makes those charges behave as they do, gives you a much better idea of how the world is put together.

Electrostatics

Math goal: Solving systems of linear equations. Often a math problem does not start out all nicely put together in a single, solvable equation with a single variable. If you understand how to use substitution, you can write as equations the things that you know, and then follow a math process to get an answer.

Why you should care: At the very least, coming out of this unit you'll be less likely to electrocute yourself or short-circuit a battery. You will also probably have teh tools that you need to do some basic repairs on electrical appliances. Nearly all the tools you depend on are electrical in nature; it's a good idea to understand how they work.

Electrical Circuits

Math goal: Again, we will be focusing on symbolic manipulation. This time, the goal is to be able to take information, put it into an equation, and then rearrange that equation so that it is in a particular form, all using variables instead of numbers.

Why you should care: Resonance and harmonic oscillation are ideas you use all the time, whether you realize it or not. Swinging on a swing is an exercise in both. Symbolic manipulation, too, is a skill you really need; one of the things that most distinguishes college level math, science, and engineering classes from high school classes is that instead of being given an equation and being asked to plug in numbers, you are asked to derive the equation, and not even bother with numbers.

Oscillation

Math goal: This chapter deals a lot with ratios and fractions. You will learn that rational numbers are the basic of harmony in music, and you will learn how to recognize what fraction of a wave will fit into a given string or pipe.

Why you should care: The rules that you learn in this chapter are what is behind all musical instruments, including things like voice and drums. You will be able to understand these instruments in enough detail that you could make a stringed instrument like a guitar or a wind instrument like a pan pipes or a recorder.

Sound and Waves

Math goal: Scientific notation: yes, it's back, and you'll be stuck with it for the rest of your life, so we're going to make absolutely sure that everyone understands it. We will also do some fun stuff with

Why you should care: Every part of the electromagnetic spectrum is useful to us as modern human beings. This unit will help you to understand what things like ultraviolet light are and how we use them. What you learn about electron energy levels will also be important to you in chemistry.

Electromagnetic Radiation

Math goal: Vectors: We will be dealing again with objects that are moving in two dimensions, so we need to review what we know about multiplying and adding vectors and resolving their components.

Why you should care: First of all, this unit is a great review of what we've done at the start of the year, because momentum fits in nicely with all the other units like force, energy, and velocity that we studied. Secondly, it's useful to be able to envision how collisions take place: people who play games like football or pool need to think about collision physics all the time.

Momentum