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Your calculus-based study guide for the College Board exam is the AP Physics C Mechanics reference sheet. All formulas and constants are included in both of the test’s 90-minute sections; however, a high score depends on knowing which equations call for integrals or derivatives and when to apply them fast.
Only 24% of American students receive a 4 or 5, so mastering the reference sheet is what sets top scorers apart. It enables students to apply calculus under pressure, obtain engineering credit, and make an impression at prestigious STEM programs.
| Resource Type | Description | Access |
| Official College Board Reference Sheet (2026) | The precise reference sheet that was given on test day is crucial for preparation. | View Online |
| Annotated Reference Sheet with Calculus Notes | Additional variable definitions and calculus applications on the official sheet | Download Guide |
| Reference Sheet Navigation Guide | Find formulas in less than ten seconds. | View Tutorial |
| Applications Reference | When using physics formulas, when to use derivatives versus integrals | Download Guide |
| Quick-Find Formula Map | A visual representation of the locations of each topic’s formulas | Download Map |
| Reference Sheet Practice Drills | Timed activities to improve navigational speed | Practice Now |
| Rotational Motion Reference Guide | specialized attention to moment of inertia, torque, and angular momentum | Download Guide |
The College Board reference sheet is comprehensive but requires students to know how and when to apply each formula. Here’s the complete breakdown:
Complete Reference Sheet Organization
| Section | What’s Included | Critical Notes |
| Constants & Conversions | G (gravitational constant), g (acceleration due to gravity) | Only 2 constants (unlike Physics 2 which has many more) |
| Kinematics with Calculus | v = dx/dt, a = dv/dt, position/velocity/acceleration relationships | Calculus forms provided, not constant-acceleration formulas |
| Dynamics | F = ma, F = dp/dt (momentum form), force relationships | Both algebraic and calculus forms shown |
| Work & Energy | KE, PE, work integrals, power formulas | W = ∫F·dx shown for variable force |
| Linear Momentum | p = mv, impulse as integral, conservation | J = ∫F dt (calculus form) |
| Rotational Motion | Torque, angular momentum, moment of inertia, rotational KE | τ = dL/dt (calculus form) provided |
| Simple Harmonic Motion | Period, frequency, angular frequency formulas | T = 2π√(m/k) and T = 2π√(L/g) |
| Universal Gravitation | F = GMm/r², gravitational PE | Standard formulas for orbital mechanics |
| Geometry & Trigonometry | Circle, triangle, sphere formulas | Basic math reference |
In addition to the cheat sheet, students have access to:
| Formula Sheet PDF | Practice FRQs and MCQs. |
| Worksheets according to topics | Comprehensive practice exams |
The AP Physics C Mechanics reference sheet emphasizes calculus relationships that distinguish it from algebra-based Physics 1:
| Relationship | Formula on Sheet | What You Must Know |
| Velocity from position | v = dx/dt | How to take derivatives of position functions |
| Acceleration from velocity | a = dv/dt | How to take derivatives of velocity functions |
| Acceleration from position | a = d²x/dt² | Second derivative concept |
| Velocity from acceleration | Shown as integral relationship | How to integrate a(t) with initial conditions |
| Position from velocity | Shown as integral relationship | How to integrate v(t) with initial conditions |
Critical Understanding:
The reference sheet shows v = dx/dt, but YOU must know how to actually take the derivative. If x(t) = 3t² + 2t, you must independently calculate v = 6t + 2.
| Concept | Formula on Sheet | Calculus Application |
| Newton’s 2nd Law | F = ma | Standard algebra form |
| Momentum form | F = dp/dt | Calculus form for variable mass or momentum |
| Impulse | J = Δp = ∫F dt | Integral form when force varies with time |
When to Use Which:
| Concept | Formula on Sheet | Calculus Requirement |
| Work (constant force) | W = F·d | Algebra sufficient |
| Work (variable force) | W = ∫F·dx | Must integrate F(x) from x₁ to x₂ |
| Power | P = dW/dt = F·v | Derivative form for instantaneous power |
| Force from potential | F = -dU/dx | Take derivative of U(x), include negative sign |
Most Frequently Tested:
F = -dU/dx appears on almost every exam. You must know how to take the derivative of a potential energy function.
| Linear → Rotational | Formula on Sheet | Calculus Form |
| Angular velocity | ω = dθ/dt | Derivative of angular position |
| Angular acceleration | α = dω/dt | Derivative of angular velocity |
| Torque (Newton’s 2nd) | τ = Iα | Algebraic form |
| Torque (angular momentum) | τ = dL/dt | Calculus form when I or ω changes |
| Angular momentum | L = Iω | Standard form |
| Rotational work | W = ∫τ dθ | Integral when torque varies |
Critical Distinction:
The reference sheet provides standard moment of inertia formulas:
| Object | Axis | Moment of Inertia (I) |
| Hoop/Ring | Through center, perpendicular to plane | MR² |
| Disk/Cylinder | Through center, along axis | ½MR² |
| Solid Sphere | Through center | ⅖MR² |
| Thin Rod | Through center, perpendicular | (1/12)ML² |
| Thin Rod | Through end, perpendicular | (1/3)ML² |
Understanding: These come from I = ∫r² dm. For non-standard shapes, you must set up and evaluate the integral yourself.
Master Physics C Formula Sheet
| Constant | Symbol | Value | Units | When You’ll Use It |
| Universal gravitational constant | G | 6.67 × 10⁻¹¹ | m³/(kg·s²) | Universal gravitation: F = GMm/r², orbital mechanics |
| Acceleration due to gravity (Earth) | g | 9.8 | m/s² | Weight, free fall, pendulums, projectile motion |
Note: Unlike AP Physics 2, Physics C Mechanics has only these 2 constants because the exam focuses exclusively on classical mechanics.
| Mistake | Why It Costs Points | How to Fix It |
| Exam day: first viewing the reference sheet | Spending five to ten minutes figuring out the layout during a timed exam | Beginning in September, study the official reference sheet layout. |
| Not understanding the meaning of variables | Formulas are available, but they cannot be used. | Make flashcards that define variables for each equation. |
| When calculus is needed, using algebra | Wrong approach loses all points | Consider calculus first if there are variations in force, velocity, or acceleration. |
| Ignoring F = -dU/dx | Missing one of most frequently tested relationships | Practice this relationship every week; it comes up on practically every test. |
| Not knowing when to apply τ = dL/dt | Using τ = Iα when moment of inertia changes | When I or ω change, use calculus form. |
| Searching without comprehending the issue | Trying random formulas hoping one works | Find the formula after carefully reading the problem and identifying the concept. |
| Ignoring the section on constants | Trying to remember G and g values | Use the precise values provided by the reference sheet. |
| Misuse of the moment of inertia | Using disk formula for rod, etc. | Verify the reference sheet table each time. |
| Not using the reference sheet for practice | Slow navigation during actual exam | Complete all assignments and practice using just the reference sheet. |
1. Do I get a reference sheet on the AP Physics C Mechanics exam?
Yes For both Section I (MCQ) and Section II (FRQ), the College Board offers an official reference sheet. It is available to you for the full 90 minutes of the test.
2. Is the Physics C reference sheet different from Physics 1 and 2?
Yes, quite different. Calculus-based formulas are used in AP Physics C Mechanics (v = dx/dt, W = ΨF·dx, τ = dL/dt), whereas algebra-based formulas are used in Physics 1 and 2.
3. What’s NOT on the AP Physics C Mechanics reference sheet?
Calculus methods (integral and derivative rules), variable definitions, formula usage guidelines, sign conventions, units, and problem-solving techniques are not included. You have to be aware of these on your own.
4. Can I write on the reference sheet during the exam?
No, the reference sheet cannot be marked up; it is only for reference. On the other hand, as you work through problems, you can write formulas from the sheet into your test booklet.
5. How should I practice with the reference sheet before the exam?
Beginning in September, only use the official College Board reference sheet for practice problems and homework. Practice finding formulas quickly and become familiar with the layout.
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