AP Physics C Mechanics Formula Sheet 2027
A reference-first Mechanics equation system with current exam-reference relationships separated from derived calculus models, variables, units, conditions, and equation-selection guidance.
What is actually given—and what you still have to know?
The exam supplies reference information, so this resource is organized around a more useful distinction than “memorize everything.” Exam reference marks relationships present in the current course reference information. Derived / course marks relationships, special cases, or model extensions that are useful for the course but are not being treated here as printed equation entries.
Before substitution, identify the system or source, representation/geometry, governing law, assumptions, sign convention, and limiting behavior. On Physics C problems, the missing step is often deciding what to differentiate or integrate—not recalling the final algebraic form.
Mechanics equation-selection map
Motion first
Use derivatives and integrals for general motion. Constant-acceleration equations are special cases, not universal kinematics.
System and interaction
Choose the object/system before applying force, momentum, energy, or center-of-mass relationships.
Rotation needs an axis
Torque, rotational inertia, angular momentum, and angular impulse depend on the chosen origin/axis.
Energy is scalar
Track the system boundary and distinguish potential-energy changes from external transfer/work.
Momentum is vector
Conserve components only when external impulse in that direction is negligible.
SHM needs a restoring law
Use sinusoidal and period formulas only after the dynamics reduce to the SHM differential-equation form.
More than an equation list: know the reference information around the equations
The current Physics C reference information supplied for exam use includes equations plus supporting constants, unit symbols, prefixes, standard modeling conventions, vector/calculus identities, and geometry/trigonometry. This page reorganizes those tools for learning rather than copying the official booklet layout.
Constants you can rely on
G = 6.67×10⁻¹¹ N·m²/kg²; near Earth, g = 9.8 m/s² and equivalently 9.8 N/kg. The reference information also supplies SI prefixes, common-angle trig values, and standard unit symbols.
Default Mechanics assumptions
Unless a problem states otherwise, use an inertial frame, neglect air resistance, and treat springs and strings as ideal. A special-case equation still needs its own additional conditions, such as constant acceleration or rolling without slipping.
Vector identities
Resolve components first. Dot products control work/flux-type projections; cross products control torque and magnetic-force directions. Magnitude and unit-vector notation are part of the supplied mathematical toolkit.
Calculus identities
The reference information supports standard derivative/integral identities, but it does not choose limits, signs, paths, surfaces, or the physical integrand for you. Those decisions remain part of the physics.
Geometry + trigonometry
Area/volume relations, right-triangle relations, arc-length geometry, and common-angle trig values are reference aids. They are most useful after you draw and label the geometry correctly.
Formula-family coverage on this sheet
| Formula family | Exam-reference | Derived / course | Role |
|---|---|---|---|
| Energy | 6 | 7 | Searchable formula family |
| Linear Momentum | 5 | 7 | Searchable formula family |
| Kinematics | 3 | 6 | Searchable formula family |
| Rotational Inertia | 3 | 3 | Searchable formula family |
| SHM Period | 2 | 2 | Searchable formula family |
| SHM Energy | 1 | 4 | Searchable formula family |
| Circular Motion | 1 | 4 | Searchable formula family |
| Dynamics | 3 | 3 | Searchable formula family |
| Rolling | 1 | 3 | Searchable formula family |
| Angular Momentum | 1 | 2 | Searchable formula family |
| Systems | 1 | 2 | Searchable formula family |
| Linear-Rotational Bridge | 2 | 1 | Searchable formula family |
| Rotation | 1 | 1 | Searchable formula family |
| Rotational Work | 1 | 1 | Searchable formula family |
The table shows the largest formula families first. Use the category filter below to reach every smaller family without scrolling through the full library.
High-value derivation routes
Kinematics chain
Start from v=dx/dt and a=dv/dt. Integrate only after deciding whether acceleration is constant or variable; the familiar constant-acceleration equations are special cases.
Force → momentum
F⃗_net=dp⃗/dt. Integrating in time gives impulse and momentum change; constant mass reduces the differential law to ΣF⃗=ma⃗.
Force → energy
Work is ∫F⃗·dr⃗. Combine it with ΔK=W_net or define conservative potential through F_x=−dU/dx. This is the route to spring/gravitational energy, not a separate memorization list.
Translation → rotation
Map x↔θ, v↔ω, a↔α, m↔I, F↔τ, p↔L, impulse↔angular impulse. Then state the axis and constraint before using the analogy.
Restoring law → SHM
Show that the equation of motion has the form x¨=−ω²x (or angular equivalent). Only then use sinusoidal solutions and period formulas.
Orbit models
Combine gravity with circular dynamics or energy/angular momentum. Circular-orbit and escape-speed results should be derived from the more general laws and checked against their conditions.
Symbol collisions that cause avoidable errors
| Symbol | Meaning here | How to disambiguate |
|---|---|---|
| I | rotational inertia | Not current here; units kg·m². |
| k | spring constant | N/m in Mechanics; do not import Coulomb-constant meaning from E&M. |
| L / ℓ | angular momentum vs length | Typography matters. State units when handwriting could be ambiguous. |
| P | power | W = J/s; distinguish from momentum p. |
| T / τ | period vs torque | T is seconds; τ is N·m. |
| r | radius, distance, or position | The same symbol can mean a scalar distance or enter a position vector; define the geometry. |
Interactive equation library
Search by quantity, equation, unit, model, or purpose. Switch between exam-reference and derived/course relationships, isolate a formula family, or hide equations for active-recall practice.
Five-step equation check before you calculate
Represent
Draw or label the graph, free-body diagram, field/circuit geometry, axis, path, surface, or state variables.
Choose the model
Name the governing law or definition before choosing a special-case result.
State conditions
Check symmetry, constancy, idealizations, system isolation, no-slip constraints, or transient endpoint assumptions.
Set signs/orientation
Fix axes, loop directions, area vectors, torque signs, current directions, and potential references before substitution.
Verify
Check units, direction, t=0/∞ endpoints, zero-angle/zero-field limits, and whether the result matches the original qualitative prediction.
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