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Physics C: Mech

AP Physics C: Mechanics

Calculus-based mechanics: derive it from a law, graph it, test it in a lab, and justify every claim the way AP readers score it.

Category
Sciences
Units
7 units
Exam
Exam May 3, 2027 (in 218 days)
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What the course covers

A first-semester, calculus-based college mechanics course built on the current framework (CED effective Fall 2024, with the exam changes that take effect in May 2027). Seven units run from kinematics through Newton's laws, work and energy, linear momentum, torque and rotational dynamics, rotating systems and orbits, to oscillations. Calculus is used as a working tool, not decoration: velocity-dependent drag leads to a differential equation, variable forces to work and impulse integrals, nonuniform rods to integrals for center of mass and rotational inertia, and simple harmonic motion to a second-order differential equation. Every lesson trains the four free-response tasks by name (Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, and Qualitative/Quantitative Translation), including derivations that start from a fundamental principle, free-body and energy bar representations, linearized lab graphs, and justifications with reasoning beyond algebra. The May 3, 2027 exam has 42 four-choice multiple-choice questions in Bluebook (85 minutes) and four handwritten free-response questions (95 minutes), with a calculator and the official equation sheet throughout.

7 units, with exam weights

  1. Unit 1

    Kinematics

    10-15% of examFree
    The language of motion, with calculus from day one. Vectors and unit-vector notation, position, velocity, and acceleration as derivatives and integrals of one another, reading slopes and areas on motion graphs, the constant-acceleration equations, relative velocity between inertial frames, and two-dimensional motion including projectiles.
    5 topics
    1. 1.1Scalars and Vectors
    2. 1.2Displacement, Velocity, and Acceleration
    3. 1.3Representing Motion
    4. 1.4Reference Frames and Relative Motion
    5. 1.5Motion in Two or Three Dimensions

  2. Unit 2

    Force and Translational Dynamics

    20-25% of exam
    The heaviest unit on the exam. Systems and center of mass (including integrals over nonuniform rods), forces as interactions, free-body diagrams, all three of Newton's laws, gravitation with the shell theorem and apparent weight, static and kinetic friction, springs in series and parallel, velocity-dependent resistive forces that lead to differential equations and terminal velocity, and circular motion with Kepler's third law.
    10 topics
    1. 2.1Systems and Center of Mass
    2. 2.2Forces and Free-Body Diagrams
    3. 2.3Newton's Third Law
    4. 2.4Newton's First Law
    5. 2.5Newton's Second Law
    6. 2.6Gravitational Force
    7. 2.7Kinetic and Static Friction
    8. 2.8Spring Forces
    9. 2.9Resistive Forces
    10. 2.10Circular Motion

  3. Unit 3

    Work, Energy, and Power

    15-25% of exam
    Energy as a second route through mechanics. Kinetic energy, work as a dot product and as the integral of force over displacement, the work-energy theorem, conservative and nonconservative forces, potential energy from a force integral and force from a potential-energy slope, stable and unstable equilibrium on U(x) graphs, choosing a system so that energy is constant, and power as a rate of energy transfer.
    5 topics
    1. 3.1Translational Kinetic Energy
    2. 3.2Work
    3. 3.3Potential Energy
    4. 3.4Conservation of Energy
    5. 3.5Power

  4. Unit 4

    Linear Momentum

    10-20% of exam
    Momentum and the impulse that changes it. Impulse as the time integral of force and the area under a force-time graph, net force as the slope of a momentum-time graph, the impulse-momentum theorem including changing-mass systems, conservation of momentum with system choice, the velocity of the center of mass, and elastic, inelastic, and perfectly inelastic collisions in one and two dimensions.
    4 topics
    1. 4.1Linear Momentum
    2. 4.2Change in Momentum and Impulse
    3. 4.3Conservation of Linear Momentum
    4. 4.4Elastic and Inelastic Collisions

  5. Unit 5

    Torque and Rotational Dynamics

    10-15% of exam
    Rigid systems that rotate. Angular kinematics and its link to the linear motion of points on the body, torque as a cross product and as force times lever arm, rotational inertia from sums, from the integral of r squared dm, and from the parallel-axis theorem, rotational equilibrium, and Newton's second law in rotational form, often solved together with the translational form for pulleys and rolling objects.
    6 topics
    1. 5.1Rotational Kinematics
    2. 5.2Connecting Linear and Rotational Motion
    3. 5.3Torque
    4. 5.4Rotational Inertia
    5. 5.5Rotational Equilibrium and Newton's First Law in Rotational Form
    6. 5.6Newton's Second Law in Rotational Form

  6. Unit 6

    Energy and Momentum of Rotating Systems

    10-15% of exam
    The conservation laws for rotation. Rotational kinetic energy, work done by torques, angular momentum of particles and rigid bodies, angular impulse, conservation of angular momentum for systems that change shape, rolling with and without slipping, and orbits: energy and angular momentum of satellites in circular and elliptical orbits, and escape velocity.
    6 topics
    1. 6.1Rotational Kinetic Energy
    2. 6.2Torque and Work
    3. 6.3Angular Momentum and Angular Impulse
    4. 6.4Conservation of Angular Momentum
    5. 6.5Rolling
    6. 6.6Motion of Orbiting Satellites

  7. Unit 7

    Oscillations

    10-15% of exam
    Simple harmonic motion from the ground up. Restoring forces proportional to displacement, the period of a mass on a spring and of a simple pendulum, the cosine solution of the SHM differential equation and its velocity and acceleration, resonance, energy exchange in an oscillator, and physical and torsion pendulums from Newton's second law in rotational form with the small-angle approximation.
    5 topics
    1. 7.1Defining Simple Harmonic Motion (SHM)
    2. 7.2Frequency and Period of SHM
    3. 7.3Representing and Analyzing SHM
    4. 7.4Energy of Simple Harmonic Oscillators
    5. 7.5Simple and Physical Pendulums

The exam, part by part

5 parts, 3 h in all.

  • Section I: Multiple Choice

    Questions
    42
    Time
    1 h 25 min
    Weight
    50%

    Calculator allowed

    Format details

    Answered in the Bluebook app. Four answer choices (A-D). Discrete questions and short question sets that share a stimulus or a data set. All seven units appear, weighted Unit 1 10-15%, Unit 2 20-25%, Unit 3 15-25%, Unit 4 10-20%, Unit 5 10-15%, Unit 6 10-15%, Unit 7 10-15%. By skill: 2.A derive 25-30%, 2.B calculate 20-25%, 2.C compare 10-15%, 2.D predict factors of change 10-15%, 3.B apply a law to make a claim 15-25%, 3.C justify with evidence 5-10%. Science Practice 1 (creating representations) is not assessed in this section. A four-function, scientific, or graphing calculator is allowed, and the equation sheet is available in print and in Bluebook.

  • Section II, Question 1: Mathematical Routines (MR)

    Questions
    1
    Time
    22.5 min
    Weight
    12.5%

    Calculator allowed

    Format details

    Task types: Mathematical Routines

    Section II is one 95-minute block of four questions in a fixed order, viewed in Bluebook and handwritten in a paper booklet. The CED suggests 20-25 minutes for this question; 22.5 is the midpoint. College Board does not publish per-question weights; the 50% section weight is split here in proportion to raw points (10 of 40).

  • Section II, Question 2: Translation Between Representations (TBR)

    Questions
    1
    Time
    27.5 min
    Weight
    15%

    Calculator allowed

    Format details

    Task types: Translation Between Representations

    Suggested time 25-30 minutes (midpoint 27.5). Weight in proportion to raw points (12 of 40).

  • Section II, Question 3: Experimental Design and Analysis (LAB)

    Questions
    1
    Time
    27.5 min
    Weight
    12.5%

    Calculator allowed

    Format details

    Task types: Experimental Design and Analysis

    Suggested time 25-30 minutes (midpoint 27.5). Weight in proportion to raw points (10 of 40). Students plot data by hand on a provided grid; a ruler or straightedge is allowed.

  • Section II, Question 4: Qualitative/Quantitative Translation (QQT)

    Questions
    1
    Time
    17.5 min
    Weight
    10%

    Calculator allowed

    Format details

    Task types: Qualitative/Quantitative Translation

    Suggested time 15-20 minutes (midpoint 17.5). Weight in proportion to raw points (8 of 40). Historically the lowest-scoring question: the 2025 mean was 2.30 of 8.

How the 1 to 5 score is set

Section I (42 multiple-choice questions, no penalty for wrong answers) and Section II (four free-response questions, 40 raw points: MR 10, TBR 12, LAB 10, QQT 8) each count for half of a weighted composite score. College Board converts the composite to the 1-5 AP score with cut points set each year from statistical equating and college-grade comparability studies; the cuts are not published. On the May 2025 exam, 21.7% of students earned a 5, 24.0% a 4, and 27.5% a 3 (mean 3.30). Free-response points are awarded row by row, each row worth 1 point, and a correct final answer with no supporting derivation typically earns only the answer point.

What you bring and get

The AP Physics C: Mechanics Table of Information (constants and conversion factors, prefixes, trig values for common angles, the Mechanics equation table, geometry and trigonometry, vectors, calculus rules, and identities) is printed for every student and also available in Bluebook for both sections. A four-function, scientific, or graphing calculator is allowed on both sections, and Bluebook includes a built-in graphing calculator. A ruler or straightedge is allowed for free response. Exam conventions: frames are inertial, air resistance is negligible, and springs and strings are ideal unless a question says otherwise. The sheet lists g=9.8 m/s2g = 9.8\ \mathrm{m/s^2}; the CED says students are not penalized for using 10 m/s210\ \mathrm{m/s^2} or 9.81 m/s29.81\ \mathrm{m/s^2} correctly.

Skills the exam scores

  • 1.ACreate diagrams, tables, charts, or schematics

    Science Practice 1, Creating Representations (20-35% of free response, not assessed in multiple choice). Represent a physical situation with a free-body or force diagram, an energy bar chart, a momentum chart, a motion map, or a schematic, drawn to the exam conventions (each force a separate straight arrow from the dot, relative lengths meaningful).

  • 1.BCreate quantitative graphs and plot data

    Science Practice 1, Creating Representations (free response only). Choose quantities, label axes with units, pick a linear numerical scale, plot data points accurately, and draw a best-fit line, most often in the LAB question.

  • 1.CSketch qualitative graphs of a model or system

    Science Practice 1, Creating Representations (free response only). Sketch how a quantity behaves over time or position so that the graph shows the right starting value, sign, slope, concavity, discontinuities, and limiting behavior of the model.

  • 2.ADerive a symbolic expression

    Science Practice 2, Mathematical Routines (25-30% of multiple choice; Practice 2 is 40-45% of free response). Start from a fundamental law or a reference-sheet equation and follow a logical algebraic or calculus pathway to an expression in the allowed variables.

  • 2.BCalculate or estimate a quantity with units

    Science Practice 2, Mathematical Routines (20-25% of multiple choice). Compute a numerical value from known quantities by a logical computational pathway, with correct units and sensible significant figures.

  • 2.CCompare quantities across scenarios or times

    Science Practice 2, Mathematical Routines (10-15% of multiple choice). Compare a physical quantity between two or more scenarios, or at different times or places in one scenario, by magnitude, ratio, or ranking.

  • 2.DPredict values or factors of change from functional dependence

    Science Practice 2, Mathematical Routines (10-15% of multiple choice). Use how one variable depends on another (linear, inverse, square, square root) to predict a new value or the factor by which a quantity changes.

  • 3.ACreate an experimental procedure for a question

    Science Practice 3, Scientific Questioning and Argumentation (free response only; Practice 3 is 30-35% of free response). Design a procedure a high school lab could run: vary one parameter, measure its effect on one quantity with realistic equipment, reduce uncertainty, and say how the data answer the question.

  • 3.BApply a law, definition, or model to make a claim

    Science Practice 3, Scientific Questioning and Argumentation (15-25% of multiple choice). Choose the principle that governs a situation (Newton's laws, conservation of energy or momentum, the rotational analogs) and use it to reach a claim.

  • 3.CJustify a claim with evidence or principles

    Science Practice 3, Scientific Questioning and Argumentation (5-10% of multiple choice). Support or refute a claim with experimental data, a representation, or a physical law, using conceptual reasoning that goes beyond restating an equation.