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

### STEP __1__

### Set Up Your Study Program

### CHAPTER 3

### How to Plan Your Time

**IN THIS CHAPTER**

**Summary:** What to study for the Physics C exam, plus three schedules to help you plan.

**Key Ideas**

Focus your attention and study time on those topics that are most likely to increase your score.

Study the topics that you”re *afraid* will appear, and relax about those that you”re best at.

Don”t study so widely that you don”t get good at some specific type of problem.

The AP Physics exam is held on a Monday afternoon in mid-May. You may think that you just started your exam preparation today, when you opened this book … but, in reality, you have been getting ready for the AP test all year. The AP exam is an authentic test of your physics knowledge and skills. Your AP Physics *class* presumably is set up to teach those skills. So, don”t give your class short shrift. Diligent attention to your class lectures, demonstrations, and assignments can only save you preparation time in the long run.

Of course, you may not be satisfied with the quantity or quality of your in-class instruction. And even if your class is the best in the country, you will still need a reminder of what you covered way back at the beginning of the year. That”s where this book, and extracurricular AP exam preparation, are useful.

**What Should I Study?**

You will hear plenty of poorly-thought-out advice about how to deal with the vast amounts of material on the AP Physics exams, especially if you are taking both Mechanics and E and M. Fact is, in the month or two before the exam, you do not have enough time to re-teach yourself the entire course. So, you ask a presumed expert, “What should I study?”

**Bad Answer Number 1: “Everything.”**

This logic says, every topic listed in the AP course description is guaranteed to show up somewhere on the exam, whether in the free-response or the multiple-choice sections. So, you must study everything. That”s ridiculous, I say to my students. You”ve been studying “everything” all year. You need to focus your last-month study on those topics that are most likely to increase your score.

**Bad Answer Number 2: “Let me use my crystal ball to tell you exactly what types of problems will show up on this year”s free-response exam. Study these.”**

I know teachers who think they”re oracles … “An RC circuit was on last year”s test, so it won”t be on this year”s. And, we haven”t seen point charges for two straight years, so we”ll definitely see one this year.”^{ }^{1}^{ }Suffice it to say that a teacher who is not on the test development committee has no possible way of divining which specific types of problems will appear on the exam, any more than a college basketball “expert” can say with confidence which teams will make the final four. And, even if you *did* know which topics would be covered on the free-response section, all of the other topics must appear on the multiple-choice section! So don”t choose your study strategy based on an oracle”s word.

**Good Answer: Do a Cost-Benefit Analysis**

You know how much time you have left. Use that limited time to study the topics that are most likely to increase your score. The trick is identifying those topics. Start with honest, hyperbole-free answers to two questions, in the following manner.

Imagine that the AP Physics Genie^{ }^{2}^{ }has granted you two boons. You may choose one type of problem that *will* be tested on the free-response exam; and you may choose one type of problem that will *not* appear on the free response. Now, answer:

- What topic or problem type do you ask the genie to put on the exam?
- What topic or problem type do you forbid the genie to put on the exam?

If you are extremely comfortable, say, solving kinematics and projectile problems, why would you spend any time on those? It won”t hurt to give yourself a quick reminder of fundamental concepts, but in-depth study of what you know well is a waste of valuable time. On the other hand, if you”re *un* comfortable with, say, Energy-Position diagrams, then spend a couple of evenings learning how to deal with them. Study the topics you”re afraid will appear; relax about those you”re best at.^{ }^{3}

This is an important point—don”t study so broadly that you don”t get good at some specific type of problem. Use __Chapter 8__ ”s drill exercises, or the end-of-chapter examples in this book, or some similar handout from your teacher, or a subset of your textbook”s end-of-chapter problems, to keep practicing until you actually are *hoping* to see certain types of problems on your test. That”s far more useful than just skimming around.

For the mechanics exam, focus your preparation on __Chapter 16__ , Rotational Motion. For the E&M exam, understand how to use Gauss”s law and the time-varying circuits: RC, RL, and LC.

Though there are other subtopics that are unique to Physics C, extra preparation on these topics will probably benefit you the most, because they are (a) far enough removed from first-year material that they truly require extra work and (b) understandable with a reasonable amount of supplemental study.

**Have a Plan for the Exam**

When it comes to the last few days before the exam, think about your mental approach. You can do very well on the exam even if you have difficulty with a few of the topics. But, know ahead of time which topics you are weak on. If you have trouble, say, with electric fields, plan on skipping electric fields multiple-choice questions so as to concentrate on those that you”ll have more success on. Don”t fret about this decision—just make it ahead of time, and follow your plan. On the free-response test, though, be sure to approach every problem. Sure, it”s okay to decide that you will not waste time on electric fields due to point charges. But if you read the entire problem, you might find that parts (d) and (e) are simple *F* = *qE* questions, or ask about some aspect of electricity that you understand just fine.

**Understand Physics First, Then AP Physics C**

Be sure you understand physics before preparing specifically for the AP Physics C exams.

I”ve taught Physics C with great success for many years. But, not just anyone can sign up for my Physics C class. I only take students who have completed Physics 1, and for good reason. The C course is very deep. It requires that you have not just an idea about, but a true *mastery* of, Physics 1- and 2-level material.

Now, your first physics course might not have formally been labeled “Advanced Placement.” Any rigorous introductory class is sufficient preparation for Physics C. Nevertheless, before you even begin to discuss a calculus-based approach to problem-solving, you MUST have a solid conceptual understanding of physics at the introductory level.

My advice to my Physics C students has always been to know the basics. An average difficulty Physics C question is equivalent to an above-average (and more calculational) Physics 1 or 2 question. Someone who knows physics cold at the 1/2 level could do reasonably well on the Physics C exam.

Therefore, you start your preparation by answering the following with brutal honesty: “Could I solve *any* Physics 1 level mechanics, or Physics 2 E&M, problem? Would I recognize the appropriate equations, relationships, and definitions instantly, without wrinkling my forehead for more than a few seconds?”

If the answer is “no,” then the most efficient way to improve your Physics C performance is to learn the fundamentals. Use your algebra-based physics textbook or *5 Steps to a 5: AP Physics 1* . There”s no substitute for a thorough knowledge of basic physics principles. Don”t worry about calculus concepts, don”t worry about the special Physics C–specific material, just work until you have the material down at the introductory level. Even if this is the only exam preparation you have time for, you will be far better served by shoring up your fundamentals than by grasping at more difficult concepts.

Once you are rock-solid on your algebra-based physics, then it”s time to think about the advanced topics on the C exam.

**A Word About Calculus**

Yes, Physics C is “calculus-based” physics. And yes, you will be asked to evaluate a few integrals and/or derivatives here and there. But it is vitally important that you understand that Physics C is *not* a math course. The development committee is not trying to find out whether you know how to evaluate ∫ sin *x* · *dx* . Rather, they are looking to see whether you understand how to apply calculus concepts to physics problems. What do we mean by calculus concepts? Two things.

**Recognizing When a Calculus Approach Is Necessary**

In algebra-based physics you learned that the work done by a force is equal to that force times parallel displacement. You will use that relationship in Physics C, too. However, in Physics C, you must recognize the limitations of that relationship: you can only multiply force times parallel displacement *when the force is constant* . If the force is changing, you must use calculus concepts, knowing that work is the integral of force with respect to distance.

Physics 1-style situations, in which calculus is not necessary, *will* appear on the Physics C exam. Your challenge is to recognize when a quantity is changing in such a way that calculus must be used.

**Understanding the Conceptual and Graphical Meanings of Integrals and Derivatives**

On a graph, an integral is the area under the graph; a derivative is the slope of a graph at a given point. Consider a problem in which you”re asked to find the work done by a non-constant force. If you”re given a graph of that force vs. position, then all you”ve got to do is find the area under the graph—*no integration necessary* .

You should have an idea of the meaning of a derivative or integral, even without evaluating it, or without graphing the function in question. This isn”t as hard as it looks! Consider the following multiple-choice problem:

A box is pushed across a frictionless table a distance of 9 m. The horizontal force pushing the box obeys the function *F* (*x* ) = 50(5 – ), where *F* is in newtons and *x* is in meters. How much work is done by the pushing force?

(A) 2500 J

(B) 1700 J

(C) 900 J

(D) 250 J

(E) 90 J

“Whoa,” you say. “This is a nasty calculus problem, especially without a calculator.” Your first instinct is to take the integral . That becomes nasty toot sweet. No

chance you can get that done in the minute or so you have on a multiple-choice problem.

So, what to do?

You know in your bones that if this force were constant, then all you”d have to do is multiply the force by 9 m. This force is not constant. But, we can approximate an *average* force from the function, can”t we? Sure … the initial force is 50(5 – 0) = 250 N. The force at the end of the push is 50(5 – ) = 100 N. So, the average force is somewhere in between 100 N and 250 N.^{ }^{4}^{ }Guess that this average force is, say, 200 N … then, the work would be (200 N)(9 m) = 1800 J. So the answer is **B** .

Note that ANY kind of estimate of the average force would still get you close to the correct answer. This is a classic calculus *concepts* question … it”s not about evaluating the integral, it”s about understanding the meaning of work.

**What Specific Calculus Methods Do I Have to Know?**

You will be expected to evaluate straightforward integrals and derivatives. Remember, this is not a math test—the exam is not trying to test your math skills but rather your ability to apply calculus to physical situations. This means the actual integrals and derivatives will not be from the most difficult questions on your AP Calculus BC test!

You should know:

- Derivatives and integrals of polynomial functions
- Derivatives and integrals of sin
*x*and cos*x*—but we”ve never seen questions that require trigonometric identities on the exam - Derivatives and integrals with ln
*x*or*e*^{x} - Derivatives using the chain rule
- Integration with
*u*-substitution

If you need a review of these topics, take a look at your calculus book or at *5 Steps to a 5: AP Calculus AB* .

Two other mathematical techniques are necessary on the Physics C exam:

- Basic first- and second-order differential equations
- Integrals involving linear density

These topics are covered briefly in this book.

**Three Different Study Schedules**

**Plan A: You Have a Full School Year to Prepare**

Although its primary purpose is to prepare you for the AP Physics exam you will take in May, this book can enrich your study of physics, your analytical skills, and your problem-solving abilities.

**SEPTEMBER–OCTOBER** (Check off the activities as you complete them.)

— Determine the study mode (A, B, or C) that applies to you.

— Carefully read __Steps 1__ and __2__ of this book.

— Work through the diagnostic exam.

— Get on the web and take a look at the AP Web site(s).

— Skim __Step 4__ . (Reviewing the topics covered in this section will be part of your year-long preparation.)

— Buy a few color highlighters.

— Flip through the entire book. Break the book in. Write in it. Highlight it.

— Get a clear picture of what your own school”s AP Physics curriculum is.

— Begin to use this book as a resource to supplement the classroom learning.

**NOVEMBER** (The first 10 weeks have elapsed.)

— Read and study __Chapter 9__ , A Bit About Vectors.

— Read and study __Chapter 10__ , Free-Body Diagrams and Equilibrium.

— Read __Chapter 6__ , Memorizing Equations in the Shower.

**DECEMBER**

— Read and study __Chapter 11__ , Kinematics.

— Read and study __Chapter 12__ , Newton”s Second Law, *F* _{net} = *ma* .

— Read and study __Chapter 13__ , Momentum.

— Review __Chapters 9__ –__10__ .

**JANUARY** (20 weeks have elapsed.)

— Read and study __Chapter 14__ , Energy Conservation.

— Read and study __Chapter 15__ , Gravitation and Circular Motion.

— Review __Chapters 9__ –__13__ .

**FEBRUARY**

— Read and study __Chapter 16__ , Rotational Motion (for Physics C students only).

— Read and study __Chapter 17__ , Simple Harmonic Motion.

— Review __Chapters 9__ –__15__ .

**MARCH** (30 weeks have now elapsed.)

— Read and study __Chapter 18__ , Electrostatics.

— Read and study __Chapter 19__ , Circuits.

— Review __Chapters 9__ –__20__ .

**APRIL**

— Read and study __Chapter 20__ , Magnetism.

— Review __Chapters 9__ –__19__ .

— Read __Chapters 7__ –__8__ carefully!

**MAY** (first 2 weeks) (THIS IS IT!)

— Review __Chapters 9__ –__20__ —all the material!!!

— Take the Practice Exams, and score yourself.

— Get a good night”s sleep before the exam. Fall asleep knowing that you are well prepared.

GOOD LUCK ON THE TEST.

**Plan B: You Have One Semester to Prepare**

Working under the assumption that you”ve completed one semester of your physics course, the following calendar will use those skills you”ve been practicing to prepare you for the May exam.

**JANUARY–FEBRUARY**

— Carefully read __Steps 1__ and __2__ of this book.

— Work through the diagnostic exam.

— Read and study __Chapter 9__ , A Bit About Vectors.

— Read and study __Chapter 10__ , Free-Body Diagrams and Equilibrium.

— Read and study __Chapter 11__ , Kinematics.

— Read and study __Chapter 12__ , Newton”s Second Law, *F* _{net} = *ma* .

— Read and study __Chapter 13__ , Momentum.

— Read __Chapter 6__ , Memorizing Equations in the Shower.

**MARCH** (10 weeks to go.)

— Read and study __Chapter 14__ , Energy Conservation.

— Read and study __Chapter 15__ , Gravitation and Circular Motion.

— Read and study __Chapter 16__ , Rotational Motion.

— Read and study __Chapter 17__ , Simple Harmonic Motion.

— Review __Chapters 9__ –__13__ .

**APRIL**

— Read and study __Chapter 18__ , Electrostatics.

— Read and study __Chapter 19__ , Circuits.

— Read and study __Chapter 20__ , Magnetism.

— Review __Chapters 9__ –__17__ .

**MAY** (first 2 weeks) (THIS IS IT!)

— Review __Chapters 9__ –__20__ —all the material!!!

— Read __Chapters 7__ –__8__ carefully!

— Take the Practice Exams and score yourself.

— Get a good night”s sleep before the exam. Fall asleep knowing that you are well prepared.

GOOD LUCK ON THE TEST.

**Plan C: You Have Six Weeks to Prepare**

At this point, we assume that you have been building your physics knowledge base for more than six months (if you”re a Physics C student, you”ve probably been studying physics for more than a year). You will, therefore, use this book primarily as a specific guide to the AP Physics exam. Given the time constraints, now is not the time to try to expand your AP Physics knowledge. Rather, you should focus on and refine what you already do know.

**APRIL 1–15**

— Skim __Steps 1__ and __2__ of this book.

— Skim __Chapters 9__ –__13__ .

— Skim and highlight the Glossary at the end of the book.

— Read __Chapter 6__ , and work on memorizing equations.

**APRIL 16–MAY 1**

— Skim __Chapters 14__ –__18__ .

— Continue to work on memorizing equations.

**MAY** (first 2 weeks) (THIS IS IT!)

— Skim __Chapters 19__ –__20__ .

— Carefully go over the Rapid Review sections of __Chapters 10__ –__20__ .

— Read __Chapter 7__ .

— Take the Practice Exams and score yourself.

— Get a good night”s sleep before the exam. Fall asleep knowing that you are well prepared.

GOOD LUCK ON THE TEST.

^{1}^{ }A moment”s thought will find some inconsistency in the above logic.

^{2}^{ }… who is not a real person …

^{3}^{ }I know many wiseguys will say, “There”s nothing I”m comfortable with; I”m bad at everything.” That”s called defeatism, and you shouldn”t tolerate that from yourself. If you were to tell your softball coach, “Hey, I”m going to strike out at the plate, let grounders go through my legs, and drop all the fly balls hit to me,” would the coach let you play? More likely, he or she would kick you off the team! When you pretend that you can”t do anything in physics, you do yourself a tremendous disservice. Pick *something* that you can figure out, *some* topic you can develop confidence in, and go from there.

^{4}^{ }Not *exactly* in between, because this function is not linear. However, you”ll see that any approximation of the average force will do here.