5 Steps to a 5: AP Physics C - Greg Jacobs 2019
Appendices
Constants
Physics C Equations
Four-Minute Drill Prompts
Web Sites
Glossary
Bibliography
The Pantheon of Pizza
Constants
Physics c equations
Read Chapter 6 about memorizing equations for more help with learning not only what the equations say, but also what they mean.
You’ll notice that the C equation sheet often expresses relationships in calculus terms. Don’t let that confuse you; for example, though impulse is expressed as an integral of force with respect to time, you should also interpret that as force times time if the force is constant, or as the area under a force vs. time graph.
Remember, your textbook might use slightly different symbols.
MECHANICS
ELECTRICITY AND MAGNETISM
Four-minute drill prompts
The lists that follow are designed to help you study equations. Each prompt refers to a specific equation on the AP Equations sheet (we’ve listed the prompts in the same order in which the equations appear on the Equations sheet). So, for example, the prompt “Net force” refers to the equation, “Fnet = ma.”
There are several ways to use these prompts. First, you can use them as a self-test: For each prompt, write down the corresponding equation on a separate sheet of paper. Then check the equations you wrote down against the AP Equations sheet to see if you got any wrong. You can also use these prompts when you study with a friend: Have your friend read the prompts to you, and you respond by reciting the appropriate equation. Try to go through the list as fast as possible without making a mistake. Last, your physics teacher can use these prompts to lead your class through a four-minute drill, which is an activity we describe in Chapter 6.
Mechanics
1st kinematics equation
2nd kinematics equation
3rd kinematics equation
Net force
Force in terms of momentum
Impulse
Definition of momentum
Force of friction
Work
Kinetic energy
Power
Power—alternate expression
Gravitational potential energy near a planet
Centripetal acceleration
Torque
Newton’s second law for rotation
Definition of rotational inertia
Position of the center of mass
Conversion between linear and angular velocity
Angular momentum
Rotational kinetic energy
1st rotational kinematics equation
2nd rotational kinematics equation
Force of a spring (The negative sign reminds you that the spring force is a restoring force, always acting toward the equilibrium point.)
Potential energy of a spring
Period in terms of angular frequency and standard frequency
Period of a mass on a spring
Period of a pendulum
Gravitational force between two massive objects
Gravitational potential energy between two massive objects (Don’t use unless an object is far away from a planet’s surface.)
Electricity and Magnetism
Electric force between two point charges
Definition of electric field
Gauss’s law (Though you should never actually take an integral when using this.)
How to find electric field in terms of potential
Potential energy in terms of potential, and then potential energy between two point charges (This line on the equation sheet really has two different equations. PE = qV is always valid, but PE = kqq/r is only valid between two point charges.)
The electric potential at some point due to surrounding point charges
Definition of capacitance
Capacitance of a parallel-plate capacitor with a dielectric substance of constant κ added
How to add parallel capacitors
How to add series capacitors
Definition of current
Energy stored on a capacitor
Resistance of a wire
Ohm’s law
How to add series resistors
How to add parallel resistors
Power in an electrical circuit
Magnetic force on a charge
Ampère’s law
Magnetic force on a wire
Magnetic field of a solenoid
Magnetic flux
Induced EMF
Voltage across an inductor
Energy stored in an inductor
Web sites
The Internet offers some great resources for preparing for the AP Physics exam.
Your textbook may have an associated Web site … if so, check it out! For example, Paul A. Tipler’s Physics C-level text provides this Web site: http://www.whfreeman.com/tipler4e/
• Of course, the official site of the College Board, www.collegeboard.com, has administrative information and test-taking hints, as well as contact information for the organization that actually is in charge of the exam.
• Did you enjoy your first taste of physics? If so, you can try your hand at physics debating. The United States Association for Young Physicists Tournaments hosts a national tournament which consists of “physics fights,” or debates, over experimental research projects. Check out www.usaypt.org for details.
• The author writes the country’s leading physics teaching blog, available at jacobsphysics.blogspot.com. Students and teachers can obtain and share ideas at this site.
• Having trouble solving calculus problems associated with Physics C, especially differential equations? Don’t spend a lot of time solving these. Use www.wolfranalpha.com to get the solution spit out for you. Sure, you can’t use this on the exam, but it’s worth using on homework to speed or check your solutions. Physics is generally more about setting up the problem correctly than carrying out the mathematics anyway.
Glossary
acceleration—the change in an object’s velocity divided by the time it took to make that change; equal to the derivative (slope) of an object’s velocity—time function
amplitude—the maximum displacement from the equilibrium position during a cycle of periodic motion; also, the height of a wave
angular momentum—the amount of effort it would take to make a rotating object stop spinning
atom—the fundamental unit of matter; includes protons and neutrons in a small nucleus, surrounded by electrons
atomic mass unit (amu)—the mass of a proton; also the mass of a neutron
average speed—the distance an object travels divided by the time it took to travel that distance
capacitor—a charge-storage device, often used in circuits
centrifugal force—a made-up force; when discussing circular motion, only talk about “centripetal” forces
centripetal force—the force keeping an object in uniform circular motion
coefficient of friction—the ratio of the friction force to the normal force. The coefficient of static friction is used when an object has no velocity relative to the surface it is in contact with; the coefficient of kinetic friction is used for a moving object
concave lens—a translucent object that makes the light rays passing through it diverge
conservative force—a force that acts on an object without causing the dissipation of that object’s energy in the form of heat
current—the flow of positive charge in a circuit; the amount of charge passing a given point per unit time
dipole—something, usually a set of charges, with two nonidentical ends
direction—the orientation of a vector
displacement—a vector quantity describing how far an object moved
elastic collision—a collision in which kinetic energy is conserved
electric field—a property of a region of space that affects charged objects in that particular region
electric flux—the amount of electric field that penetrates a certain area
electric potential—potential energy provided by an electric field per unit charge
electromagnetic induction—the production of a current by a changing magnetic field
electron—a subatomic particle that carries a negative charge
energy—the ability to do work
equilibrium—when the net force and net torque on an object equal zero
equipotential lines—lines that illustrate every point at which a charged particle would experience a given potential
field—a property of a region of space that can affect objects found in that particular region
free-body diagram—a picture that represents one or more objects, along with the forces acting on those objects
frequency—the number of cycles per second of periodic motion; also, the number of wavelengths of a wave passing a certain point per second
friction—a force acting parallel to two surfaces in contact; if an object moves, the friction force always acts opposite the direction of motion
fulcrum—the point about which an object rotates g—free-fall acceleration near the Earth’s surface, about 10 m/s2
induced EMF—the potential difference created by a changing magnetic flux that causes a current to flow in a wire; EMF stands for “electro-motive force,” but the units of EMF are volts.
inductance—the property of an inductor that describes how good it is at resisting changes in current in a circuit
inductor—a coil in a circuit that makes use of induced EMF to resist changes in current in the circuit
inelastic collision—a collision in which kinetic energy is not conserved, as opposed to an elastic collision, in which the total kinetic energy of all objects is the same before and after the collision
inertia—the tendency for a massive object to resist a change in its velocity
internal energy—the sum of the kinetic energies of each molecule of a substance
ion—an electrically charged atom or molecule
kinetic energy—energy of motion
Kirchoff’s laws—in a circuit, 1) at any junction, the current entering equals the current leaving; 2) the sum of the voltages around a closed loop is zero
Lenz’s law—the direction of the current induced by a changing magnetic flux creates a magnetic field that opposes the change in flux
magnetic field—a property of a region of space that causes magnets and moving charges to experience a force
magnetic flux—the amount of magnetic field that penetrates an area
magnitude—how much of a quantity is present; see “scalar” and “vector”
mass spectrometer—a device used to determine the mass of a particle
rotational inertia—the rotational equivalent of mass
momentum—the amount of “oomph” an object has in a collision, equal to an object’s mass multiplied by that object’s velocity
net force—the vector sum of all the forces acting on an object
normal force—a force that acts perpendicular to the surface on which an object rests
nucleus—the small, dense core of an atom, made of protons and neutrons
oscillation—motion of an object that regularly repeats itself over the same path
parallel—the arrangement of elements in a circuit so that the charge that flows through one element does not flow through the others
perfectly inelastic collision—a collision in which the colliding objects stick together after impact
period—the time it takes for an object to pass through one cycle of periodic motion; also, the time for a wave to propagate by a distance of one wavelength
potential energy—energy of position
power—the amount of work done divided by the time it took to do that work; also, in a circuit, equal to the product of the current flowing through a resistor and the voltage drop across that resistor
resistance—a property of a circuit that resists the flow of current
resistor—something put in a circuit to increase its resistance
restoring force—a force that restores an oscillating object to its equilibrium position
scalar—a quantity that has a magnitude but no direction
series—the arrangement of elements in a circuit so that they are connected in a line, one after the other
time constant—a value related to how long it takes to charge or discharge a capacitor, or for current to flow in an inductor
torque—the application of a force at some distance from a fulcrum; if the net torque on an object isn’t zero, the object’s rotational velocity will change
vector—a quantity that has both magnitude and direction
velocity—how fast an object’s displacement changes; equal to the derivative (slope) of an object’s position—time function
weight—the force due to gravity; equal to the mass of an object times g, the gravitational field
work—the product of the distance an object travels and the components of the force acting on that object directed parallel to the object’s direction of motion
work-energy theorem—the net work done on an object equals that object’s change in kinetic energy
Bibliography
Your AP Physics textbook may have seemed difficult to read early in the year. But now that you have heard lectures, solved problems, and read our guide, try reading your text again—you’ll be amazed at how much more clear the text has become.
If you’d like to look at another textbook, here is one that we recommend:
• Tipler, P. A., Mosca, G. (2007). Physics for Scientists and Engineers (6th ed.). New York: W. H. Freeman.
You might also find this book helpful:
• Hewitt, P. G. (2009). Conceptual Physics (11th ed.). San Francisco: Addison Wesley.
(Hewitt’s is the classic text for readable, non-mathematical expositions of physics principles. If you are having trouble seeing the meaning behind the mathematics, check out this book.)
Just for fun, we also recommend these books … they might not help you too much for the AP exam, but they’re great reads.
• Feynman, R. (1997). Surely you’re joking, Mr. Feynman! New York: W. W. Norton. (Collected stories of the 20th century’s most charismatic physicist. If you ever thought that physicists were a bunch of stuffy nerds without personality, you should definitely read this book. One of our all-time favorites!)
• Hawking, S. (1998). A Brief History of Time. New York: Bantam. (The canonical introduction to cosmology at a layperson’s level.)
• Lederman, L. (1993). The God Particle. New York: Dell. (Written by a Nobel Prize—winning experimental physicist, this book not only discusses what kinds of strange subatomic particles exist, but goes through the amazing and interesting details of how these particles are discovered.)
• Walker, J. (2007). The Flying Circus of Physics (2nd ed.). New Jersey: Wiley. (This book provides numerous conceptual explanations of physics phenomena that you have observed. The classic “Physics of the world around you” book.)
The pantheon of pizza
Pizza is the traditional food of the physics study group. Why? Probably because it’s widely available, relatively inexpensive, easily shareable, and doesn’t cause arguments the way “let’s order bean curd” might.
If you have not yet experienced the late-night physics group study session, you should. Physics is more fun with friends than alone, and you learn more productively with other people around. Ideally, you’ll find a mix of people in which sometimes they are explaining things to you, but sometimes you are explaining things to them. Explaining physics to friends is the absolute best way to cement your own knowledge.
But if you don’t already have a regular study group, how do you go about creating one? Use pizza as bait. “Hey, let’s get together in my mom’s basement to do the problem set” is like a party invitation from Bill Nye the science guy. But, “Hey, we’re ordering seven large pizzas with extra cheese and a variety of toppings, why don’t you come by and do your problem set with us?” sounds more like you’re headed to Encore on the Vegas Strip.1
Over the years I’ve eaten enough pizza to fill several dozen dumpsters—and dumpsters have been an appropriate receptacle for much of that pizza. Given the choice between a five-star restaurant and a pizza place, I’d usually choose the five stars. Usually. I know of four—just four—pizza places I would prefer to anything recommended by Squilliam Fancyson.
These four make up the Pantheon of Pizza.
Please understand the rules of access to the Pantheon:
1. I must have eaten at a member restaurant at least twice. This unfortunately rules out the heavenly Pepper’s Pizza in Chapel Hill, North Carolina.2
2. I must have such an affinity for their pepperoni-and-extra-cheese pizza that my mouth waters upon the mere mention of a potential visit to the restaurant.
That’s it. It’s my pantheon, so it’s my choice who gets in.
That said, please do send your own corrections, additions, oversights, etc. You can contact me via Woodberry Forest School. If you make a good enough case for a particular pizza place possibly joining the Pantheon, I may attempt to make a pilgrimage.
The Pantheon
4. Broadway Joe’s Pizza, Riverdale, New York. This tiny shop below the #1 line train station in the North Bronx has everything you could ask for in a New York pizzeria—street noise, no air conditioning but instead a fan running all summer, the Yankees game on the television, and Broadway Joe himself behind the counter. Okay, I’m sure that there are hundreds of such places throughout New York City, all of which probably have tremendous pizza. But Broadway Joe’s is the one I walk to every year during the AP Physics Teachers’ Summer Institute that I run at Manhattan College. Bonus points to Mr. Joe for recognizing me each year: “Hey, you’re the teacher who wants a small3 pepperoni and extra cheese.” Ten minutes later, out pops the classic New York—style pie with deciliters of cheese piled on top of a foldable crust. I can never finish the small by myself, but I so, so want to.
3. Thyme Market, Culpeper, Virginia. When I moved to central Virginia, I initially despaired at the food choices. But then we discovered Pizza Monday at Thyme Market. Even an unjuiced Alex Rodriguez4 could knock a baseball across the length of Culpeper’s Main Street, but it contains the heavenly brick oven from which its $5 pies spring forth each Monday, plus a lot of money for toppings, plus another $5 if you come on a day other than Monday. But it’s well worth the cash and the trip. This is one of the few pizza places ever in which “extra cheese” provides a bit too much gooeyness. The pepperoni itself is the best of any in the Pantheon—just the right size, on top of the cheese, a bit of thickness to it, and baked until the edges begin to get crispy. While you’re in the restaurant, try a bite of the “Culpeper Crack” branded cheese spread that’s always available to sample. The pizza may be only $5 per pie, but you’ll spend an order of magnitude more than that after you buy up multiple tubs of the Crack to take home.
2. Big Ed’s Pizza, Oak Ridge, Tennessee. I encountered Big Ed’s in conjunction with the United States Invitational Young Physicists Tournament, which was held in Oak Ridge for several years due to the presence of Oak Ridge National Laboratory. My friend and fellow physics teacher Peggy insisted that it was worth waiting in the crowd outside the door for a table, and she was right. The pizza was, of course, fabulous: New York—style foldable crust, with plenty of cheese and a multitude thereof of pepperonis. What sold me on Big Ed’s, more so than even the T-shirts with a cartoony drawing of Big Ed himself, was the Kneeling Bench. The kitchen is separated from the dining area by a high wooden façade. But in the middle of the façade are two holes, with benches underneath. I was instructed to kneel on a bench, cup my hands communion-style, and put them through the hole. Lo, a generous portion of shredded mozzarella was placed in my hands by unknown beneficiaries. I had to go through this ritual a second time—I probably had as much cheese from my trips to the Kneeling Bench as from the pizza itself.
1. Langel’s Pizza, Highland, Indiana. Most people who sample Chicago-style deep-dish pizza go to the big chains that have sprouted up across the Chicagoland area. Burrito Girl5 grew up in a small suburb in northwest Indiana, and so she is well aware of the famous, fancy chains. Yet the first pizza place that Burrito Girl took me to consisted of about six booths sandwiched between an exotic reptiles store and a sports bar. I ordered, and I endured the requisite progression of helpfulness, skepticism, and then outright horror that waitresses in Chicago pizza places bestow upon me when I order extra cheese. Yes, I want extra cheese, even though the pizza is stuffed with seemingly an entire cow-day’s worth of cheese already. Really. I’ve done this before, and lived to tell the tale. Please?
At Langel’s, the extra cheese oozes and stretches beyond the mere constraints of slices.
It takes a full 20 minutes before the cheese is congealed enough to hold the shape in which you cut it. But it’s the sauce that makes Langel’s the best pizza in the known universe. This deep-dish pizza does not come in layers, but rather mixed all about, which means that the sauce can be appreciated throughout every bite. The pepperoni is fine, but I actually recommend just getting a pure extra-cheese pie. You’ll have enough for lunch right now, dinner tonight, and probably breakfast tomorrow. Too bad they don’t deliver within a 1,200 km radius.
1Sorry. I certainly do not intend to dis Bill Nye the Science Guy. He is demonstrably cool.
2Now, alas, I hear they’ve closed down for good. Sigh.
3Don’t be deceived. A “small” pie at Broadway Joe’s could last for three straight late nights of Minecraft. Just one extralarge could sustain the entire rat population along the banks of the East River.
4… if such a thing exists
5My wife and sidekick, also known as the mild-mannered Shari.
