## 5 Steps to a 5: AP Physics C (2016)

### STEP __3__

### Develop Strategies for Success

__CHAPTER__ **6 Memorizing Equations in the Shower**

__CHAPTER__ **7 How to Approach Each Question Type**

__CHAPTER__ **8 Extra Drill on Difficult but Frequently Tested Topics**

### CHAPTER 6

### Memorizing Equations in the Shower

**IN THIS CHAPTER**

**Summary:** Learn how to memorize all the equations you absolutely need to know to ace the AP Physics exam.

**Key Ideas**

Learn why memorizing equations is so critical.

Learn equations by using them: practice solving problems without looking up the equations you need.

Use mnemonic devices to help you remember.

Practice speed: see how many equations you can say in four minutes.

Use visual reminders: put a copy of the equation sheet somewhere you”ll see it often.

**Can You Ace This Quiz?**

__Instructions:__ We”ll give you a prompt, you tell us the equation. Once you”ve finished, check your answers with the key at the end of this chapter.

** 1 .** Coefficient of friction in terms of

*F*

_{f}** 2 .** Momentum

** 3 .** Two equations for impulse

** 4 .** Two equations for mechanical power

** 5 .** Two equations for work

** 6 .** Period of a mass on a spring

** 7 .** Three kinematics equations for constant acceleration

** 8 .** Centripetal acceleration

** 9 .** Kinetic energy

** 10 .** Gravitational force of one planet on another

** 11 .** Ohm”s Law

** 12 .** Power in a circuit

** 13 .** Magnetic force on a charge

** 14 .** Magnetic force on a wire

** 15 .** Electric force on a charge

** 16 .** Electric potential energy

** 17 .** Magnetic field around a long, straight, current-carrying wire

** 18 .** Time constant for an RC circuit

** 19 .** Resistance of a wire in terms of its dimensions

** 20 .** Electric field due to a point charge

**So, How Did You Do?**

Grade yourself according to this scale.

You may think we”re joking about our grading system, but we”re completely serious. Knowing your equations is absolutely imperative. Even if you missed one question on the quiz, you need to study your equations. Right now! A student who is ready to take the AP exam is one who can ace an “equations quiz” without even thinking about it. How ready are you?

**Equations Are Crucial**

It”s easy to make an argument against memorizing equations. For starters, you”re given all the equations you need on the exam. And besides, you can miss a whole bunch of questions on the test and still get a 5.

But equations are the nuts and bolts of physics. They”re the fundamentals. They should be the foundation on which your understanding of physics is built. Not knowing an equation—even one—shows that your knowledge of physics is incomplete. And every question on the AP exam assumes *complete* knowledge of physics.

Now you get equation sheets on the multiple choice section, too.

**What About the Free-Response Section?**

The free-response questions test your ability to solve complex, multistep problems. They also test your understanding of equations. You need to figure out which equations to use when and how. The makers of the test are being nice by giving you the equation sheet—they”re reminding you of all the equations you already know in case you cannot think of that certain equation that you *know* would be just perfect to solve a certain problem. But the sheet is intended to be nothing more than a reminder. It will not tell you when to use an equation or which equation would be best in solving a particular problem. You have to know that. And you will know that only if you have intimate knowledge of every equation.

**Exam tip from an AP Physics veteran:**

Don”t use the equation sheet to “hunt and peck.” The sheet can remind you of subtle things; for example, does the magnetic field due to a wire have an *r* or an *r* ^{2} in the denominator? But if you don”t have the general idea that the magnetic field depends on current and gets weaker farther away from a wire, then you won”t recognize

even if you go hunting for it.

—*Wyatt, college freshman in engineering*

**Some Examples**

We mentioned in __Step 2__ that some questions on the AP exam are designed solely to test your knowledge of equations. If you know your equations, you will get the question right. Here”s an example.

A pendulum of length *L* swings with a period of 3 s. If the pendulum”s length is increased to 2*L* , what will its new period be?

(A) 3/ *s*

(B) 3 *s*

(C) 3 *s*

(D) 6 *s*

(E) 12 *s*

The answer is (C). The equation for a pendulum”s period is

since *L* is in the numerator and under the square root, multiplying *L* by 2 multiplies the period by .

Of course, the multiple-choice section will not be the only part of the exam that tests your knowledge of equations. Often, a part of a free-response question will also test your ability to use an equation. For example, check out this problem.

Four charges +Q are arranged in a square of side length *l* .

(a) What is the magnitude of the electric field due to just one of these charges at the center of the square?

Yes, later in the problem you”ll be asked to add vectors to find *E* due to a bunch of charges. Ugh. But you can still score some easy points here if you simply remember that old standby, .

Memorizing equations will earn you points. It”s that simple.

**Treat Equations Like Vocabulary**

Think about how you would memorize a vocabulary word: for example, “boondoggle.” There are several ways to memorize this word. The first way is to say the word out loud and then spell it: “Boondoggle: B-O-O-N-D-O-G-G-L-E.” The second way is to say the word and then say its definition: “Boondoggle: An unproductive or impractical project, often involving graft.” If you were to use the first method of memorizing our word, you would become a great speller, but you would have no clue what “boondoggle” means. As long as you are not preparing for a spelling bee, it seems that the second method is the better one.

This judgment may appear obvious. Who ever learned vocabulary by spelling it? The fact is, this is the method most people use when studying equations.

Let”s take a simple equation, *v _{f} *=

*v*+

_{o}*at*. An average physics student will memorize this equation by saying it aloud several times, and that”s it. All this student has done is “spelled” the equation.

But you”re not average. __ ^{1}__ Instead, you look at the equation as a whole, pronouncing it like a sentence: “

*V f*equals

*v*naught plus

*at*.” You then memorize what it means and when to use it: “This equation relates initial velocity with final velocity. It is valid only when acceleration is constant.” If you are really motivated, you will also try to develop some intuitive sense of why the equation works. “Of course,” you say, “this makes perfect sense! Acceleration is just the change in velocity divided by the change in time. If acceleration is multiplied by the change in time, then all that”s left is the change in velocity

So the final velocity of an object equals its initial velocity plus the change in velocity.”

The first step in memorizing equations, then, is to learn them as if you were studying for a vocabulary test, and not as if you were studying for a spelling bee.

**Helpful Tips**

Memorizing equations takes a lot of time, so you cannot plan on studying your equations the night before the AP exam. If you want to really know your equations like the back of your hand, you will have to spend months practicing. But it”s really not that bad. Here are four tips to help you out.

**Tip 1:** Learn through use. Practice solving homework problems without looking up equations.

Just as with vocabulary words, you will only learn physics equations if you use them on a regular basis. The more you use your equations, the more comfortable you will be with them, and that comfort level will help you on the AP test.

The reason you should try solving homework problems without looking up equations is that this will alert you to trouble spots. When you can look at an equations sheet, it”s easy to fool yourself into a false sense of confidence: “Oh, yeah, I *knew* that spring potential energy is ½*kx* ^{2} .” But when you don”t have an equations sheet to look at, you realize that either you know an equation or you don”t. So if you solve homework problems without looking up equations, you”ll quickly figure out which ones you know and which you don”t; and then you can focus your studying on those equations that need more review.

**Tip 2:** Use mnemonic devices.

Use whatever tricks necessary to learn an equation. For example, it is often hard to remember that the period of a pendulum is

and *not*

So make up some trick, like “The terms go in backward alphabetical order: **T** wo-pi **r** oot ** L **over

**.” Be creative.**

*g***Tip 3:** The Four-Minute Drill.

Practice speed. Say the equations as fast as you can, then say them faster. Start at the top of the AP equations sheet __ ^{2}__ and work your way down. Have someone quiz you. Let that person give you a lead, like “Period of a pendulum,” and you respond “Two-pi root

*L*over

*g*.” See how many equations you can rattle off in four minutes. We call it the Four-Minute Drill.

This is much more fun with a group; for example, try to persuade your teacher to lead the class in a four-minute drill. Not only will you get out of four minutes of lecture, but you may also be able to bargain with your teacher: “Sir, if we can rattle off 50 equations in the Four-Minute Drill, will you exempt us from doing tonight”s problems?” ^{3}

**Tip 4:** Put a copy of the equations sheet somewhere visible.

See how the equations sheet looks next to your bathroom mirror. Or in your shower (laminated, of course). Or taped to your door. Or hung from your ceiling. You”d be surprised how much sparkle it can add to your décor. You”d also be surprised how easy it will be to memorize equations if you are constantly looking at the equations sheet.

So what are you waiting for? Start memorizing!

** Answer Key to Practice Quiz**

__1__ .

__2__ .*p* = *mv*

__3__ .*I* = Δ*p* and *I* = *F* Δ*t*

__4__ .

__5__ .*W* = *Fd* and *W* _{net} = Δ*KE*

__6__ .

__7__ .

__8__ .

** 9 .** KE = ½

*mv*

^{2}

__10__ .

__11__ .*V* = *IR*

__12__ .*P* = *IV*

__13__ .*F* = *qvB* sin *θ*

__14__ .*F* = *ILB* sin *θ*

__15__ .*F* = *qE*

__16__ .*U* = *qV*

__17__ .

__18__ .*τ* = *RC*

__19__ .

__20__ .

__ ^{1}__ In fact, just because you bought this book, we think that you”re way better than average. “Stupendous” comes to mind. “Extraordinary, Gullible.” Er … uh … cross that third one out.

__ ^{2}__ We”ve included a copy of this sheet at the end of the book, along with a sheet of prompts to guide you through a four-minute drill.