AP Physics Symbols: What Every Variable Means

Which table you actually want

The AP appendix carries two different things that both get called a symbols table, and they answer different questions.

If you are looking at a number and want to know what its unit is, for example the N in "12 N", you want the unit symbols table. That box is a short alphabetical list of abbreviations: N is newton, Pa is pascal, and so on.

If you are looking at an italic letter inside an equation and want to know what quantity it stands for, for example the $J$ in $J = F_{avg} \Delta t$, you want this page. Those definitions are not in a single box. They are printed as narrow lists down the side of each block of equations, one list per block, and the same letter can be defined differently in two blocks that sit inches apart.

The booklet separates the two by typeface. Variables are italic, unit symbols are upright roman. That works in print and not at all in handwriting, which is why so many of these letters cause trouble.

The letters that mean three or more different things

Five letters carry three or more distinct definitions across the four booklets. These are worth knowing before you meet them cold.

$L$ is the worst of them with four meanings. In a rotation problem $L = I\omega$ is angular momentum. In the Physics 2 thermal block $L$ is the length in the conduction equation $Q/\Delta t = kA\Delta T/L$. In the Physics 2 optics block $L$ is the distance from the slits to the screen. In C: E&M it is inductance, in henrys, and $U_L = \frac{1}{2}LI^2$.

Two more letters pick up a third meaning from the constants box rather than a symbol list. $k$ is the spring constant on every mechanics list and thermal conductivity on the Physics 2 thermal list, and it is also the Coulomb constant in the Physics 2 and C: E&M constants boxes, which is why Boltzmann's constant has to be written $k_B$ with a subscript. $\mu$ is the coefficient of friction on the mechanics lists and magnetic permeability on the C: E&M magnetism list, plus $\mu_0$ in the constants box.

Rho, and the six lines where the sheet defines one symbol two ways

In six places the booklet gives a symbol two unrelated meanings on a single printed line, joined by the word "or". It is not being sloppy. It is telling you that the block you are reading uses that letter for both, and you have to work out which from context.

The $\rho$ line is the one people search for, because it looks like an error. It is not. The C: E&M electricity block prints both $R = \rho \ell / A$, where $\rho$ is resistivity in ohm meters, and $Q_{total} = \int \rho(r)\,dV$, where $\rho$ is a volume charge density in coulombs per cubic meter. Both equations are on the same page, and the symbol list has to cover both. Read the equation, not the letter: if $\rho$ is multiplying a length over an area you are doing resistance, and if it is being integrated over a volume you are doing charge.

And remember that on the mechanics pages of the very same C: E&M booklet, $\rho$ is neither of those. It does not appear there at all, but on the Physics 1 and Physics 2 mechanics pages $\rho = m/V$ is mass density.

The $m$ = order or mass line has a similar flavor. In $\Delta D = m\lambda$ the $m$ is an integer counting interference maxima, and in $v_{string} = \sqrt{F_T/(m/\ell)}$ on the same page it is a mass. Nothing marks the difference except what the equation is about.

Mechanics and fluids, the list you will use most

AP Physics 1 and AP Physics 2 print an identical mechanics and fluids page, with two symbol lists on it. The first goes with kinematics, forces, energy and momentum. The second goes with rotation, oscillations and fluids.

Kinematics, forces, energy, momentum. Nineteen entries.

Rotation, oscillations, fluids. Twenty seven entries.

Notice what happens across those two lists. $P$ is power in the first and pressure in the second, on the same printed page. $m$ and $M$ both mean mass, with no stated difference beyond the convention that $M$ is usually the larger or the whole body. And $A$ is amplitude or area, which is why the fluids equations and the oscillation equations can share one list at all.

The Physics C mechanics lists are similar but not the same. The C version of the first list runs to twenty three entries: it adds $f$ for frequency, $\ell$ for length, $M$ for mass, $T$ for period and $\lambda$ for linear mass density, and it drops $\theta$. The C version of the second list also runs to twenty three: it adds $p$ for momentum and $\phi$ for phase angle, and it drops $A$, $h$, $P$, $V$, $y$ and $\rho$, because C: Mechanics has no fluids content and states amplitude as $x_{max}$ rather than $A$.

Electricity, magnetism, thermal, waves and modern physics

AP Physics 2, electricity. Eighteen entries. $A$ area, $C$ capacitance, $d$ distance, $E$ electric field, $F$ force, $I$ current, $\ell$ length, $P$ power, $q$ charge, $Q$ charge, $r$ distance, radius, or position, $R$ resistance, $t$ time, $U$ potential energy, $V$ electric potential, $\kappa$ dielectric constant, $\rho$ resistivity, $\tau$ time constant.

AP Physics 2, magnetism. Twelve entries. $A$ area, $B$ magnetic field, $F$ force, $I$ current, $\ell$ length, $q$ charge, $r$ distance, radius, or position, $t$ time, $v$ velocity or speed, $\varepsilon$ emf, $\theta$ angle, $\Phi$ flux.

AP Physics 2, thermal physics. Seventeen entries. $A$ area, $c$ specific heat, $F$ force, $k$ thermal conductivity, $K$ kinetic energy, $L$ length, $m$ mass, $n$ number of moles, $N$ number of atoms, $P$ pressure, $Q$ energy transferred to a system by heating, $t$ time, $T$ temperature, $U$ internal energy, $v$ velocity or speed, $V$ volume, $W$ work done on a system.

AP Physics 2, waves, sound, and optics. Twenty one entries. $a$ width, $A$ amplitude, $d$ separation, $D$ path length, $f$ frequency or focal length, $F$ force, $h$ height, $\ell$ length, $L$ distance, $m$ order or mass, $M$ magnification, $n$ index of refraction, $s$ position, $t$ time, $T$ period, $v$ speed, $x$ position, $y$ position, $\lambda$ wavelength, $\theta$ angle, $\omega$ angular frequency.

AP Physics 2, modern physics. Thirteen entries. $A$ area, $E$ energy, $f$ frequency, $K$ kinetic energy, $m$ mass, $N$ number of particles, $p$ momentum, $P$ power, $t$ time, $T$ absolute temperature, $\theta$ angle, $\lambda$ wavelength or decay constant, $\phi$ work function.

AP Physics C: E&M, electricity. Twenty entries. $A$ area, $C$ capacitance, $d$ distance, $E$ electric field, $F$ force, $I$ current, $J$ current density, $\ell$ length, $P$ power, $q$ charge, $Q$ charge, $r$ radius, distance, or position, $R$ resistance, $t$ time, $U$ potential energy, $V$ electric potential or volume, $\varepsilon$ electric permittivity, $\rho$ resistivity or charge density, $\kappa$ dielectric constant, $\Phi$ flux.

AP Physics C: E&M, magnetism. Twenty one entries. $A$ area, $B$ magnetic field, $C$ capacitance, $E$ electric field, $F$ force, $I$ current, $\ell$ length, $L$ inductance, $n$ number of loops per unit length, $N$ number of loops, $q$ charge, $r$ radius, distance, or position, $R$ resistance, $t$ time, $U$ potential energy, $v$ velocity or speed, $\varepsilon$ emf, $\mu$ magnetic permeability, $\tau$ time constant, $\Phi$ magnetic flux, $\omega$ angular frequency.

A few of those deserve a second look. $a$ is width in the optics block, and acceleration everywhere else in physics. $T$ is period in optics, temperature in thermal, and absolute temperature in modern physics. $Q$ is charge in both electricity blocks and "energy transferred to a system by heating" in the thermal block, which is heat by another name. And AP Physics 2 defines $\rho$ as resistivity only, while C: E&M defines it as resistivity or charge density, because only the calculus course integrates a charge density.

Eight letters mean two things inside the C: E&M booklet alone

The AP Physics C: Electricity and Magnetism appendix reprints the entire C: Mechanics equation page, because the exam can ask a mechanics question in an electric field. That means one booklet, four pages, carries mechanics definitions and electromagnetism definitions a page apart, and eight letters end up with two different printed meanings inside the same appendix.

The $\varepsilon$ row is the strangest of them, because both meanings are on the same two facing lists rather than split between mechanics and electromagnetism. The electricity list defines $\varepsilon$ as electric permittivity, and the magnetism list, printed alongside it, defines the same glyph as emf. The equations disambiguate: $\kappa = \varepsilon / \varepsilon_0$ is clearly a permittivity ratio, and $\varepsilon = -L\,dI/dt$ is clearly an emf.

One more trap in that booklet that is not a repeat: lowercase $\phi$ is the phase angle on the mechanics rotation list, and uppercase $\Phi$ is flux on both electromagnetism lists. Two cases of the same Greek letter, two unrelated quantities, one appendix. Write your phis carefully.

The Greek letters, all of them

Every Greek symbol the four booklets define, in one place, because these are the ones students cannot look up by typing.

Twelve Greek letters carry a defined meaning in the appendix, and one, capital omega, is only ever a unit symbol. Two of them come in a lowercase and uppercase pair with unrelated meanings: $\phi$ against $\Phi$, and $\omega$ against the unit $\Omega$. Also note that $\pi$ appears constantly in the equations without being defined in any symbol list, because it is a number rather than a physical quantity.

The capital sigma $\Sigma$ and the integral sign are operators, not variables, and are likewise undefined in the lists. The Physics C booklets print the derivative and integral rules they expect you to apply, in a separate calculus box. $\Delta$ in front of a symbol always means a change in that quantity, final minus initial, and the booklet never spells that out either.

How to use this on a free response question

The lists are printed on the exam, so nothing here needs memorizing. What you should build is the habit of resolving a symbol from its equation rather than from memory.

When a symbol is ambiguous, three things disambiguate it, in order of reliability:

1. The equation it sits in. $\rho$ divided into $\ell / A$ is resistivity. $\rho$ times $V$ giving a mass is density. The algebra is unambiguous even when the letter is not.
2. The block of the sheet you are working in. Every symbol list belongs to one block, and a symbol means what its own block says it means. An $L$ found in the optics block is a distance, no matter what it means three pages earlier.
3. The units. If your $L$ has to come out in henrys, it is an inductance.

On a free response answer, define your own symbols the first time you use one, particularly if you introduce a letter the sheet does not use. Graders read a lot of scripts, and "where $\rho$ is the linear charge density" costs you four seconds and removes every doubt. The same applies to subscripts: the sheet writes $F_{net}$, $v_{cm}$, $R_{eq}$, $K_{max}$ and $x_{max}$ rather than inventing new letters, and copying that convention keeps your work readable.