AP Physics C Mechanics Equation Sheet: 7 Unit Equation Groups, Official Download, and Exam Day Rules
The AP Physics C Mechanics equation sheet is a College Board reference listing frequently used mechanics equations, constants, and calculus rules. The College Board provides it on exam day, and students may not bring their own copy.
For the algebra-based companion reference, see AP Physics 2 Equation Sheet: 7 Equation Sections, 20 Constants and Conversion Factors, and 9 Exam Conventions Provided by the College Board.
What Is the AP Physics C Mechanics Equation Sheet?
The AP Physics C Mechanics equation sheet is the official College Board reference of equations and constants given to students during the AP Physics C: Mechanics Exam. Other names include formula sheet, equation tables, and exam reference information.
The current booklet has 3 pages:
- Page 1: the Table of Information, with constants, prefixes, unit symbols, trigonometric values, and exam conventions.
- Page 2: the Mechanics equations, with symbol definitions.
- Page 3: geometry and trigonometry formulas, vectors, calculus, and identities.
Who Publishes the Equation Sheet?
The College Board publishes the sheet on AP Central. According to the College Board, the reference information on AP Central matches the information in each subject’s course and exam description.
Where Can Students Download the Official AP Physics C Mechanics Equation Sheet?
Students download the official sheet from AP Central at apcentral.collegeboard.org/media/pdf/ap-physics-c-mechanics-equations-sheet.pdf. The College Board lists the file on its "Reference Information for Specific AP Exams" page, next to the sheets for 8 other AP subjects.
Third-party sheets exist online. Only reference information provided by the College Board is allowed during the exam.
How Do Students Receive the Equation Sheet on Exam Day?
Students receive the sheet as a printed booklet and as a reference in the Bluebook app. Five delivery rules apply:
- Schools receive printed booklets with exam shipments in spring.
- Bluebook shows the reference information in test preview and on exam day.
- Proctors distribute the booklets with the other testing materials.
- Students write scratch work on blank space in the booklet, and the writing is not scored.
- Proctors collect the booklets after the exam, and students may not remove them from the room.
Can Students Bring Their Own Equation Sheet?
No. Only the reference information provided by the College Board can be used during the exam. Students may use the official sheet throughout the school year to learn its content.
What Is the AP Physics C Mechanics Exam Format?
The AP Physics C Mechanics Exam is a 3-hour hybrid digital exam with 2 equally weighted sections: 42 multiple-choice questions and 4 free-response questions. Students answer multiple-choice questions in Bluebook. Students view free-response questions in Bluebook and handwrite answers in paper booklets.
The table below shows the exam structure. Rows list the sections, and columns show the number of questions, the time, the score weight, and the answer format.
| Section | Questions | Time | Score Weight | Answer Format |
|---|---|---|---|---|
| Section 1: Multiple Choice | 42 | 1 hour 25 minutes | 50% | Bluebook |
| Section 2: Free Response | 4 | 1 hour 35 minutes | 50% | Handwritten in paper booklet |
What Are the 4 Free-Response Question Types?
Section 2 contains one question of each type:
- Mathematical routines
- Translation between representations
- Experimental design and analysis
- Qualitative/quantitative translation
How Much Time Does Each Question Allow?
Section 1 allows about 2.0 minutes per question (85 minutes for 42 questions). Section 2 allows about 24 minutes per question (95 minutes for 4 questions).
When Is the 2027 AP Physics C Mechanics Exam?
The 2027 exam takes place on Monday, May 3, 2027, in Session 1. Each school’s AP coordinator announces the location.
Are Calculators Allowed on the Exam?
Yes, calculators are permitted. The College Board publishes a list of approved calculators in its AP Exams Calculator Policy.
What Is in the Table of Information?
The Table of Information on page 1 lists constants, prefixes, unit symbols, trigonometric values, and 3 exam conventions. The table below shows the constants for Mechanics. Rows list the constants, and columns show the symbol, the value, and the unit.
| Constant | Symbol | Value | Unit |
|---|---|---|---|
| Universal gravitational constant | G | 6.67 × 10⁻¹¹ | N·m²/kg² |
| Acceleration due to gravity at Earth’s surface | g | 9.8 | m/s² |
| Gravitational field strength at Earth’s surface | g | 9.8 | N/kg |
The table below lists the 9 prefixes. Rows list the prefixes, and columns show the factor and the symbol.
| Prefix | Factor | Symbol |
|---|---|---|
| tera | 10¹² | T |
| giga | 10⁹ | G |
| mega | 10⁶ | M |
| kilo | 10³ | k |
| centi | 10⁻² | c |
| milli | 10⁻³ | m |
| micro | 10⁻⁶ | μ |
| nano | 10⁻⁹ | n |
| pico | 10⁻¹² | p |
The sheet lists 7 unit symbols: hertz (Hz), joule (J), kilogram (kg), meter (m), newton (N), second (s), and watt (W).
What Trigonometric Values Does the Sheet Provide?
The sheet provides sine, cosine, and tangent for 7 common angles. The table below shows the values. Rows list the functions, and columns list the angles.
| Function | 0° | 30° | 37° | 45° | 53° | 60° | 90° |
|---|---|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 3/5 | √2/2 | 4/5 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 4/5 | √2/2 | 3/5 | 1/2 | 0 |
| tan θ | 0 | √3/3 | 3/4 | 1 | 4/3 | √3 | undefined |
What Conventions Does the Exam Assume?
The sheet states 3 conventions:
- The frame of reference is inertial, unless stated otherwise.
- Air resistance is negligible, unless stated otherwise.
- Springs and strings are ideal, unless stated otherwise.
What Value of g Does the Exam Expect?
The course and exam description expects g = 10 m/s² in problems that need a numerical value. Students are not penalized for correctly using 9.8 m/s² or 9.81 m/s².
What Equations Are on the AP Physics C Mechanics Equation Sheet?
The Mechanics page includes equations for each of the 7 course units, and the tables below group them by unit. The College Board updates the sheet periodically, and AP Central hosts the current version.
Which Kinematics Equations Are on the Sheet?
Unit 1 uses 3 constant-acceleration equations. These apply only when acceleration is constant.
| Equation | Name | Variables |
|---|---|---|
| vₓ = vₓ₀ + aₓt | Velocity under constant acceleration | v = velocity, a = acceleration, t = time |
| x = x₀ + vₓ₀t + ½aₓt² | Position under constant acceleration | x = position |
| vₓ² = vₓ₀² + 2aₓ(x − x₀) | Velocity-position relation | x₀ = initial position |
Which Force and Translational Dynamics Equations Are on the Sheet?
Unit 2 equations cover Newton’s second law, friction, springs, gravitation, circular motion, and center of mass.
| Equation | Name | Variables |
|---|---|---|
| a = ΣF/m | Newton’s second law | F = force, m = mass |
| F_f ≤ μF_N | Friction force limit | μ = coefficient of friction, F_N = normal force |
| F_s = −kΔx | Hooke’s law | k = spring constant, Δx = change in length |
| F_G = Gm₁m₂/r² | Law of universal gravitation (attractive) | G = gravitational constant, r = distance |
| a_c = v²/r = ω²r | Centripetal acceleration | v = speed, ω = angular speed, r = radius |
| x_cm = Σmx/Σm | Center of mass | m = mass, x = position |
Which Work, Energy, and Power Equations Are on the Sheet?
Unit 3 equations cover work, kinetic energy, potential energy, and power.
| Equation | Name | Variables |
|---|---|---|
| ΔE = W = ∫F·dr | Work-energy relation | E = energy, W = work |
| K = ½mv² | Kinetic energy | K = kinetic energy |
| P = dE/dt | Power as rate of energy transfer | P = power, t = time |
| P = F·v | Power from force and velocity | v = velocity |
| ΔU_g = mgΔy | Gravitational potential energy near Earth | U = potential energy, y = vertical position |
| U_G = −Gm₁m₂/r | Gravitational potential energy between 2 masses | r = distance |
| U_s = ½k(Δx)² | Spring potential energy | k = spring constant |
Which Linear Momentum Equations Are on the Sheet?
Unit 4 uses 3 equations.
| Equation | Name | Variables |
|---|---|---|
| p = mv | Linear momentum | p = momentum |
| F = dp/dt | Net force as rate of momentum change | F = force |
| J = ∫F dt = Δp | Impulse | J = impulse |
Which Torque and Rotational Dynamics Equations Are on the Sheet?
Unit 5 equations cover torque, rotational inertia, and rotational kinematics.
| Equation | Name | Variables |
|---|---|---|
| τ = r × F | Torque | τ = torque, r = position |
| α = Στ/I | Newton’s second law for rotation | α = angular acceleration, I = rotational inertia |
| I = ∫r² dm = Σmr² | Rotational inertia | m = mass, r = distance from the axis |
| v = rω | Tangential speed | ω = angular speed |
| ω = ω₀ + αt | Angular speed under constant angular acceleration | t = time |
| θ = θ₀ + ω₀t + ½αt² | Angular position under constant angular acceleration | θ = angular position |
Which Energy and Momentum of Rotating Systems Equations Are on the Sheet?
Unit 6 uses 2 core equations.
| Equation | Name | Variables |
|---|---|---|
| L = r × p = Iω | Angular momentum | L = angular momentum |
| K = ½Iω² | Rotational kinetic energy | K = kinetic energy |
Which Oscillation Equations Are on the Sheet?
Unit 7 equations cover simple harmonic motion and periods.
| Equation | Name | Variables |
|---|---|---|
| x = x_max cos(ωt + φ) | Position in simple harmonic motion | ω = angular frequency, φ = phase angle |
| T = 2π/ω = 1/f | Period | T = period, f = frequency |
| T_s = 2π√(m/k) | Period of a mass on a spring | m = mass, k = spring constant |
| T_p = 2π√(ℓ/g) | Period of a simple pendulum | ℓ = length |
What Do the Symbols on the Sheet Mean?
The Mechanics page defines symbols in 2 separate lists, and some symbols serve more than one role. The table below shows selected definitions. Rows list the symbols, and columns show the meaning on the sheet.
| Symbol | Meaning on the Sheet |
|---|---|
| ω | angular frequency or angular speed |
| r | radius, distance, or position |
| x | position or distance |
| y | vertical position |
| m, M | mass |
| λ | linear mass density |
| μ | coefficient of friction |
| E | energy |
| U | potential energy |
| J | impulse |
| φ | phase angle |
| ℓ | length |
Which Equations Are Not on the Sheet?
Derived equations are equations that the course and exam description lists as expected results of derivations and that the sheet omits. Students derive them from listed equations. Examples include the 8 results below. Rows list the equations, and columns show the meaning and the course topic.
| Derived Equation | Meaning | Course Topic |
|---|---|---|
| ΣF = 0 | Translational equilibrium | 2.4 Newton’s First Law |
| g = F_G/m = GM/r² | Gravitational field strength | 2.6 Gravitational Force |
| F_g = mg | Weight near a planet’s surface | 2.6 Gravitational Force |
| F_f,s,max = μ_s F_N | Maximum static friction | 2.7 Kinetic and Static Friction |
| 1/k_eq = Σ(1/kᵢ) | Equivalent spring constant in series | 2.8 Spring Forces |
| k_eq = Σkᵢ | Equivalent spring constant in parallel | 2.8 Spring Forces |
| v = √(gr) | Minimum speed at the top of a vertical loop | 2.10 Circular Motion |
| T² = 4π²r³/(GM) | Kepler’s third law for circular orbits | 2.10 Circular Motion |
The course description also states that the sheet omits many equations that combine or specialize listed equations. Students are responsible for knowing the conditions under which each equation applies.
How Do Students Use the Equation Sheet on the Exam?
Use the sheet by matching the unknown quantity to an equation and confirming the equation’s conditions. The method has 6 steps:
- List the known and unknown quantities.
- Identify the course unit that contains the unknown.
- Select the equation that links the known and unknown quantities.
- Confirm the conditions, such as constant acceleration or an inertial frame.
- Solve symbolically, then substitute numbers.
- Check units and direction.
How Do You Calculate the Period of a Mass on a Spring?
Use T_s = 2π√(m/k) from Unit 7. A 0.50 kg mass hangs on a spring with k = 200 N/m.
- Period: T = 2π√(0.50 ÷ 200) = 2π(0.050) = 0.314 s
- Frequency: f = 1/T = 3.18 Hz
- Angular frequency: ω = 2π/T = 20 rad/s
How Do You Calculate Rotational Motion From Torque?
Use α = Στ/I, ω = ω₀ + αt, and K = ½Iω² from Units 5 and 6. A wheel with I = 2.0 kg·m² starts from rest under a net torque of 6.0 N·m for 4.0 s.
- Angular acceleration: α = 6.0 ÷ 2.0 = 3.0 rad/s²
- Final angular speed: ω = 0 + 3.0 × 4.0 = 12 rad/s
- Rotational kinetic energy: K = ½ × 2.0 × 12² = 144 J
Which Units Carry the Most Weight on the Multiple-Choice Section?
Unit 2, Force and Translational Dynamics, carries the highest weighting range at 20 to 25% of the multiple-choice section. The table below shows the 7 units. Rows list the units, and columns show the multiple-choice weighting.
| Unit | Topic | Multiple-Choice Weighting |
|---|---|---|
| 1 | Kinematics | 10-15% |
| 2 | Force and Translational Dynamics | 20-25% |
| 3 | Work, Energy, and Power | 15-25% |
| 4 | Linear Momentum | 10-20% |
| 5 | Torque and Rotational Dynamics | 10-15% |
| 6 | Energy and Momentum of Rotating Systems | 10-15% |
| 7 | Oscillations | 10-15% |
How Does the Mechanics Sheet Differ From Other AP Physics Reference Sheets?
Each of the 4 AP Physics exams has its own reference information. The table below compares the exams. Rows list the exams, and columns show the course basis and the reference sheet.
| Exam | Course Basis | Reference Sheet |
|---|---|---|
| AP Physics 1 | Algebra-based | Separate sheet |
| AP Physics 2 | Algebra-based | Separate sheet |
| AP Physics C: Mechanics | Calculus-based | Separate sheet |
| AP Physics C: Electricity and Magnetism | Calculus-based | Separate sheet |
Which Study Methods Help Students Learn the Equation Sheet?
Practice with the official sheet during the course to learn where each equation sits and which conditions apply. Roediger and Karpicke (2006) found that students who practiced retrieval recalled about 61% of material after 1 week, compared with about 40% for students who only restudied.
Six methods improve fluency with the sheet:
- Download the official PDF and use it for every practice problem.
- Derive each kinematic equation with calculus to learn its conditions.
- Sort equations by unit and by the quantity solved for.
- Complete the 7 Progress Checks in AP Classroom, one for each unit.
- Solve past free-response questions posted on AP Central.
- Preview the Bluebook interface in test preview before exam day.
What Are Common Mistakes When Using the Equation Sheet?
Five mistakes occur often. The table below lists each mistake with its correct fact. Rows show the mistakes, and columns show the mistake and the correct fact.
| Mistake | Correct Fact |
|---|---|
| Applying kinematic equations when acceleration changes | The 3 equations apply only to constant acceleration, and varying acceleration requires integration |
| Writing F_f = μF_N for static friction at all times | The sheet gives F_f ≤ μF_N, and equality holds only at the maximum static friction |
| Treating torque and angular momentum as scalars | τ = r × F and L = r × p are vector cross products |
| Switching between g = 10, 9.8, and 9.81 m/s² within one problem | One value applies throughout a problem, and the 3 values are all accepted |
| Reading ω as angular speed only | The sheet defines ω as angular frequency or angular speed, depending on the equation |
People Also Ask About the AP Physics C Mechanics Equation Sheet
Is an Equation Sheet Provided for AP Physics C Mechanics?
Yes, the College Board provides the sheet as a printed booklet and as a reference in Bluebook.
Can Students Bring a Personal Formula Sheet?
No, only reference information provided by the College Board is allowed.
Where Can Students Download the Official Sheet?
Students download it from AP Central, on the Reference Information for Specific AP Exams page.
How Many Questions Are on the Exam?
The exam has 42 multiple-choice questions and 4 free-response questions.
Is a Calculator Allowed?
Yes, calculators on the College Board approved list are permitted.
What Value of g Does the Exam Expect?
The course description expects g = 10 m/s², and correct use of 9.8 or 9.81 m/s² is not penalized.
Does the Sheet Include Every Equation Needed?
No, the sheet omits derived equations and special cases, and students derive them from listed equations.
What Is the Main Summary of the AP Physics C Mechanics Equation Sheet?
The AP Physics C Mechanics equation sheet is the College Board reference provided on exam day. There are 6 key facts:
- The booklet has 3 pages: Table of Information, Mechanics equations, and geometry, vectors, and calculus.
- The College Board provides the sheet in print and in Bluebook, and students may not bring their own.
- The exam has 42 multiple-choice questions in 85 minutes and 4 free-response questions in 95 minutes.
- The equations map to 7 units, and Unit 2 carries the highest weighting at 20 to 25%.
- Derived equations, such as v = √(gr), are not on the sheet.
- The 2027 exam is on Monday, May 3, 2027.
Sources:
- College Board, AP Physics C: Mechanics Exam (AP Students)
- College Board, Reference Information for Specific AP Exams (AP Central)
- College Board, AP Physics C: Mechanics Exam Reference Information (2025 booklet)
- College Board, AP Physics C: Mechanics Course and Exam Description (effective Fall 2024)
- Roediger, H. L., and Karpicke, J. D. (2006), "Test-Enhanced Learning," Psychological Science, volume 17
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