The AP Physics C Mechanics reference sheet gives you specific formulas and constants, but not the reasoning behind them
The College Board provides a one-page reference sheet during the AP Physics C Mechanics exam. It contains kinematic equations, Newton's laws in equation form, work and energy formulas, momentum equations, rotational motion formulas, and gravitational constants. The sheet does not include derivations, does not tell you when to use each formula, and does not solve problems for you — it is a lookup tool for equations you already know how the process works.
Understanding what is on the sheet and what is not matters because it shapes how you should study. If you memorize every formula on the sheet, you have wasted time. If you arrive at the exam without knowing which formula solves which type of problem, the sheet will not help you. The sheet assumes you know physics; it just saves you from writing down equations from memory.
Key Takeaways
- The reference sheet contains kinematic equations, force and motion formulas, work-energy relationships, momentum equations, rotational dynamics, and universal gravitation — but not every formula you might need.
- Formulas for straightforward harmonic motion, springs, and some rotational relationships are not on the sheet, so you must memorize those.
- The sheet does not include problem-solving steps, decision trees, or hints about which formula to use when — you must know that from practice.
- Studying the sheet before the exam means learning what is there and what is missing, not memorizing what is already printed.
What formulas are actually printed on the sheet
The reference sheet is organized by topic. The kinematics section includes the four standard equations for motion with constant acceleration: v = v₀ + at, x = x₀ + v₀t + ½at², v² = v₀² + 2a(x − x₀), and x = x₀ + ½(v₀ + v)t. These are the equations you use to find position, velocity, or time when acceleration is constant.
The dynamics section lists F = ma (Newton's second law), the definition of weight as F_g = mg, the friction equations f_s ≤ μ_s N and f_k = μ_k N, and the centripetal force formula F_c = mv²/r. It also includes the universal gravitation formula F = Gm₁m₂/r² and the gravitational field strength g = GM/r².
Work and energy formulas on the sheet include W = F·d·cos(θ) for work, KE = ½mv² for kinetic energy, PE_g = mgh for gravitational potential energy, W_net = ΔKE (the work-energy theorem), and P = W/t for power. The sheet also includes the conservation of mechanical energy statement: E_total = KE + PE = constant (when no non-conservative forces act).
Momentum and impulse appear as p = mv, F_avg·Δt = Δp (impulse-momentum theorem), and the conservation of momentum for collisions. Rotational motion formulas include τ = r·F·sin(θ) for torque, α = τ/I (rotational Newton's second law), ω = ω₀ + αt and θ = ω₀t + ½αt² for rotational kinematics, KE_rot = ½Iω² for rotational kinetic energy, and L = Iω for angular momentum.
Formulas you must memorize because they are not on the sheet
The reference sheet does not include the spring force equation F = −kx or the elastic potential energy formula PE_spring = ½kx². These appear frequently on the exam, so you must know them cold. Similarly, the sheet does not list the straightforward harmonic motion equations x = A·cos(ωt) or T = 2π√(m/k) for a mass on a spring, or T = 2π√(L/g) for a pendulum.
Moment of inertia formulas for specific shapes (rod, disk, sphere, hoop) are not on the sheet. You may be given the moment of inertia in a problem, or you may need to look it up in a table provided with that specific question, but you cannot rely on the reference sheet to have it. The parallel axis theorem I = I_cm + Md² is also not included.
Equations for rolling motion without slipping, such as v_cm = ωr and the relationship between translational and rotational kinetic energy, are not explicitly on the sheet. You must derive or remember that a rolling object's total kinetic energy is KE_total = ½mv_cm² + ½Iω². Orbital mechanics formulas, such as the relationship between orbital radius and period, are also not on the sheet.
How the sheet changes your study strategy
Knowing what is on the sheet means you should not spend exam time writing down equations you can straightforward read. Instead, use the sheet to check the exact form of an equation if you are uncertain about a sign or a constant. This saves a few seconds per problem and reduces transcription errors.
The sheet also tells you what to prioritize in your studying. Formulas that appear on the sheet still require practice — you need to know when to use them, how to combine them, and how to interpret the variables. But formulas not on the sheet demand deeper memorization. If you have limited study time, memorize the spring and straightforward harmonic motion equations before you memorize the exact form of the centripetal force equation.
Many students make the mistake of thinking the reference sheet means they do not need to memorize anything. The opposite is true. The sheet is a safety net for formulas you have already learned; it is not a substitute for learning. Problems that require you to combine multiple equations, or that ask you to derive a relationship, will not be solved by straightforward reading the sheet.
How to use the sheet during the exam
During the exam, the reference sheet is most useful when you have narrowed down which formula you need but are uncertain about the exact form. For example, if you know you need to use the work-energy theorem but cannot remember whether it is W_net = ΔKE or W_net = ΔPE, you can glance at the sheet and confirm. This takes five seconds and prevents a careless error.
The sheet is less useful for deciding which formula to use in the first place. If you read a problem and do not know whether it is a kinematics problem, a dynamics problem, or an energy problem, the reference sheet will not help you make that decision. That judgment comes from practice and understanding the physics concepts, not from the sheet.
Some students waste time during the exam by reading through the entire reference sheet looking for inspiration. Avoid this. Read the problem, decide what physics principle applies, then check the sheet only if you need to confirm the exact equation. Treat the sheet as a reference, not as a study guide during the test.
What constants and conversions are included
The reference sheet includes the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², the acceleration due to gravity at Earth's surface g = 9.8 m/s² (or sometimes 10 m/s² for estimates), and the mass and radius of Earth. It also includes the mass and radius of the Moon if gravitational problems involve the Moon. Some versions include the conversion factor between degrees and radians.
The sheet does not include conversion factors between metric units (like meters to centimeters) because those are assumed to be known. It does not include the speed of light, Planck's constant, or any constants from electricity and magnetism, because this is the mechanics sheet only. If you are taking AP Physics C Electricity and Magnetism, that exam has its own separate reference sheet.
How to prepare using the reference sheet before test day
One week before the exam, obtain a copy of the actual reference sheet from the College Board website or from your teacher. Print it and work through practice problems with it in front of you, just as you will during the exam. This teaches you where to find each formula and how long it takes to locate it under pressure.
As you work practice problems, mark which formulas you use most often and which ones you never seem to need. The formulas you use constantly should be memorized so thoroughly that you do not need to look them up. The formulas you rarely use can be looked up during the exam without penalty.
Do not use the reference sheet as an excuse to skip memorization. Instead, use it to focus your memorization on the formulas that are not there. Spend your study time on spring forces, straightforward harmonic motion, moment of inertia, and the decision-making process of which formula to use when. Let the reference sheet handle the rest.
Frequently Asked Questions
Is the reference sheet the same for both the AP Physics C Mechanics and Electricity and Magnetism exams?
No. Each exam has its own reference sheet. The Mechanics sheet contains kinematics, dynamics, energy, momentum, and rotation formulas. The Electricity and Magnetism sheet contains formulas for electric fields, magnetic fields, circuits, and electromagnetic induction. You receive only the sheet for the exam you are taking.
Can I write notes or formulas on the reference sheet before the exam?
No. You receive a blank copy of the reference sheet at the start of the exam. You cannot bring your own annotated version into the testing room. You can, however, study from an annotated copy during your preparation.
If a formula is on the reference sheet, do I still need to know how to derive it?
Not always. The exam tests whether you can use formulas to solve problems, not whether you can derive them from first principles. However, some free-response questions ask you to derive a relationship or explain your reasoning, which may require you to show where a formula comes from. Practice both using and deriving the main formulas.
What should I do if I cannot find a formula I need on the reference sheet?
First, check whether you have the right formula in mind. Many students look for a formula that does not exist. If you have confirmed that the formula is not on the sheet, you either need to memorize it (like the spring force equation) or derive it from other formulas on the sheet. Look at what you know and what you are trying to find, then combine equations logically.
Does the reference sheet include formulas for circular motion and orbits?
The sheet includes the centripetal force formula and centripetal acceleration. It includes the universal gravitation formula, which you can use to solve orbital problems. However, it does not include pre-derived orbital formulas like Kepler's third law in its standard form. You can derive these from the formulas that are on the sheet.