# AP Physics C: Mechanics exam guide > Calculus-based mechanics across the seven units of the revised framework, from kinematics to oscillations. - Canonical page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics - Markdown source: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/llms.txt - Exam family: AP exams - Governing body: College Board - Official exam information: https://apstudents.collegeboard.org/courses/ap-physics-c-mechanics - Who takes it: High school students taking calculus concurrently or already, usually those heading toward engineering, physics, or another quantitative major. - Follows the fall 2024 course and exam description, from 14 May 2025 - Guide structure last checked against official sources: August 30, 2026 ## Overview AP Physics C: Mechanics is a calculus-based college physics course covering the same physical territory as AP Physics 1 at a higher mathematical level. Derivatives and integrals are used throughout: velocity and acceleration come from differentiating position, work comes from integrating force over displacement, and rotational inertia comes from integrating over a mass distribution. The framework was revised effective fall 2024. It is organized into seven units that parallel the first seven units of AP Physics 1, and the exam grew from a 90-minute assessment to a full three hours with a longer multiple-choice section and four free-response questions. Gravitation is now developed within the dynamics and energy units rather than standing alone. Arcade Academy is an independent study workspace. Because the framework and exam were revised recently, treat the official Course and Exam Description and exam page as authoritative for unit organization, published weightings, and current timing, and use the unit pages below to organize problem practice. ## Exam format - **Total time:** 3 hours - **Section I:** 42 multiple-choice questions in 1 hour 25 minutes, 50% of the exam score - **Section II:** 4 free-response questions, 50% of the exam score - **Format update:** The multiple-choice count and per-section timing changed beginning with the May 2027 exam; confirm the current numbers on the official exam page - **Delivery:** Hybrid digital: multiple-choice questions are answered and free-response prompts are read in College Board's Bluebook app, and free-response answers are handwritten in a paper booklet - **Calculator:** Permitted on the exam; an equations and reference information sheet is provided - **Mathematics:** Calculus is used throughout, and calculus is a corequisite for the course - **Score scale:** 1 to 5 ## Scoring The multiple-choice and free-response sections each contribute half of a composite score, which College Board converts to the reported 1 to 5 scale using cut points set for that year's exam. Because AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism are separate exams, each receives its own score, and colleges may grant credit for one without the other. ## Units AP Physics C: Mechanics is organized into 7 units. Each one below lists its published weighting where the governing body publishes one, the topics it covers, and study tips specific to it. ### 1. Unit 1: Kinematics - Position: 1 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-1-kinematics Unit 1 recasts motion in the language of calculus. Position, velocity, and acceleration are related by differentiation and integration rather than by a fixed set of equations, which lets the course handle non-constant acceleration from the start. Two-dimensional motion and reference frames complete the unit. #### Topics - **Describing motion with calculus** — Velocity as the derivative of position and acceleration as the derivative of velocity, with the integrals that reverse them. - **Kinematics with constant acceleration** — Deriving the constant-acceleration relationships rather than memorizing them, including free fall. - **Non-constant acceleration** — Handling acceleration given as a function of time, position, or velocity, and separating variables when needed. - **Motion graphs** — Reading slope and area on position, velocity, and acceleration graphs and translating between them. - **Two-dimensional and relative motion** — Vector decomposition, projectile motion, and describing motion from a different reference frame. #### Study tips - Derive the constant-acceleration equations from the integrals once so you can rebuild them if memory fails. - Practice problems where acceleration depends on velocity, since that is where the calculus-based course diverges most from the algebra-based one. - Keep the graph relationships (slope and area) explicit; they appear in both multiple-choice and free-response questions. ### 2. Unit 2: Force and Translational Dynamics - Position: 2 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-2-force-and-translational-dynamics Unit 2 develops Newton's laws with calculus-capable force models. Resistive forces that depend on velocity, such as air drag, are the signature addition, along with terminal velocity as the solution of a differential equation. Gravitation appears here as a force law rather than as a separate unit. #### Topics - **Systems, forces, and free-body diagrams** — Choosing a system, identifying all interactions, and translating a diagram into equations of motion. - **Newton's laws applied** — Connected bodies, inclines, pulleys, and force pairs analyzed with consistent coordinate choices. - **Friction and spring forces** — Static and kinetic friction, and the linear restoring force of an ideal spring. - **Resistive forces and terminal velocity** — Velocity-dependent drag, the resulting differential equation, and the approach to terminal speed. - **Gravitation** — The universal law of gravitation, gravitational field, and the force inside and outside a spherical body. - **Circular motion** — Centripetal acceleration, the net inward force requirement, and applications including orbital motion. #### Study tips - Set up the drag differential equation from a free-body diagram at least a few times; recognizing the setup is most of the work. - Sketch the velocity-versus-time curve approaching terminal velocity and be able to explain its shape. - Choose coordinate axes along the acceleration direction on inclines; it removes most of the algebra. ### 3. Unit 3: Work, Energy, and Power - Position: 3 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-3-work-energy-and-power Unit 3 defines work as an integral of force over displacement, which lets the course handle position-dependent forces cleanly. Conservative forces, potential energy functions, and the relationship between force and the derivative of potential energy are central. Energy diagrams are a recurring representation. #### Topics - **Work as an integral** — Computing work for variable forces, and reading work as area under a force-versus-position graph. - **Kinetic energy and the work-energy relationship** — Relating net work to the change in kinetic energy for both constant and variable forces. - **Conservative forces and potential energy** — Which forces have an associated potential energy function, and how that function is defined. - **Force from potential energy** — Recovering force as the negative derivative of the potential energy function. - **Conservation of energy** — Tracking mechanical energy through a system, including dissipation by nonconservative forces. - **Power** — Instantaneous and average power, and the relationship between power, force, and velocity. #### Study tips - Practice both directions of the force and potential-energy relationship: differentiate a potential to get force, and integrate a force to get potential. - Use energy diagrams to identify equilibrium points and classify them as stable or unstable. - Choose energy over force methods when the force varies with position; it is usually far less work. ### 4. Unit 4: Linear Momentum - Position: 4 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-4-linear-momentum Unit 4 develops momentum, impulse as the integral of force over time, and conservation of momentum for systems. Center-of-mass motion is treated carefully, including the fact that the center of mass of an isolated system moves at constant velocity regardless of internal interactions. Collisions in two dimensions appear here. #### Topics - **Momentum and impulse** — Momentum as mass times velocity, and impulse as the time integral of force or the area under a force-time graph. - **Conservation of momentum** — The conditions for conservation, and how the choice of system determines whether forces are internal or external. - **Center of mass** — Locating the center of mass for discrete and continuous distributions, and its motion under internal forces. - **Collisions** — Elastic, inelastic, and perfectly inelastic collisions, in one and two dimensions. - **Systems with changing mass** — Analyzing situations where mass enters or leaves the system, such as a chain or a stream of particles. #### Study tips - Compute the center of mass of a continuous rod or plate by integration a few times so the setup is familiar. - Work two-dimensional collisions strictly component by component, writing both equations before solving. - State what is conserved and why before any calculation; the justification carries points on free-response questions. ### 5. Unit 5: Torque and Rotational Dynamics - Position: 5 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-5-torque-and-rotational-dynamics Unit 5 rebuilds dynamics for rotating rigid bodies. Rotational inertia is computed by integration for continuous bodies, the parallel-axis idea extends those results, and torque plays the role of force in the rotational form of Newton's second law. Equilibrium problems with extended bodies also live here. #### Topics - **Rotational kinematics** — Angular position, velocity, and acceleration, related by differentiation and integration. - **Connecting linear and rotational motion** — Relating tangential and angular quantities, and the rolling constraint between them. - **Torque** — Torque from force and lever arm, net torque on an extended body, and the sign convention for rotation. - **Rotational inertia** — Computing rotational inertia by integration for rods, disks, and spheres, and combining bodies. - **Rotational equilibrium** — Balanced forces and torques for beams and supported bars, including choosing a convenient pivot. - **Newton's second law for rotation** — Net torque equal to rotational inertia times angular acceleration, applied to rigid-body problems. #### Study tips - Derive the rotational inertia of a uniform rod about its end and its center; those two derivations cover most of the technique. - Maintain a translational-to-rotational analogy table and add to it as the unit progresses. - Pick the pivot to eliminate an unknown force in equilibrium problems, and say why you chose it. ### 6. Unit 6: Energy and Momentum of Rotating Systems - Position: 6 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-6-energy-and-momentum-of-rotating-systems Unit 6 applies conservation laws to rotation. Rotational kinetic energy, work done by a torque, angular momentum, and angular impulse are defined, and conservation of angular momentum handles problems that force analysis cannot reach easily. Rolling motion and orbital mechanics are the standard applications. #### Topics - **Rotational kinetic energy** — Energy of rotation, and combining rotational with translational kinetic energy for rolling bodies. - **Work and power in rotation** — Work as the integral of torque over angular displacement, and rotational power. - **Angular momentum and angular impulse** — Angular momentum for particles and rigid bodies, and its change under an applied torque. - **Conservation of angular momentum** — Identifying when external torques vanish, and analyzing systems whose rotational inertia changes. - **Rolling motion** — Rolling without slipping, the role of static friction, and energy partition between translation and rotation. - **Orbits and gravitational systems** — Applying energy and angular momentum conservation to circular and elliptical orbits. #### Study tips - Work the classic rolling-race problem and be able to explain the ordering from rotational inertia alone. - Check for external torques explicitly before invoking conservation of angular momentum. - Solve orbit problems with energy and angular momentum together rather than with force alone. ### 7. Unit 7: Oscillations - Position: 7 of 7 - Page: https://www.arcadesacademy.com/exams/ap-physics-c-mechanics/unit-7-oscillations Unit 7 treats simple harmonic motion as the solution of a differential equation rather than as a set of memorized results. Mass-spring systems, simple pendulums, and physical pendulums are analyzed, and the energy exchange over a cycle is described quantitatively. Recognizing when a restoring force is approximately linear is the key skill. #### Topics - **Conditions for simple harmonic motion** — A restoring force proportional to displacement, and the differential equation it produces. - **Mass-spring systems** — Angular frequency, period, and the position, velocity, and acceleration functions over time. - **Simple and physical pendulums** — The small-angle approximation, and how rotational inertia sets the period of a physical pendulum. - **Energy in oscillating systems** — Exchange between kinetic and potential energy, and the dependence of total energy on amplitude. #### Study tips - Show that a given restoring force is linear in displacement before applying any simple harmonic result. - Practice physical pendulum problems, since they combine rotational inertia with oscillation and appear frequently. - Sketch position, velocity, and acceleration on shared axes and be able to state the phase relationships. ## Study strategies - Practice using calculus as the default tool rather than as a special case, since problems with non-constant forces and continuous mass distributions are where this exam separates from the algebra-based courses. - Derive rather than memorize wherever the derivation is short; the exam rewards students who can rebuild a relationship when the situation is unfamiliar. - Work free-response questions in full under a timer, showing setup and reasoning, because partial credit follows the visible steps. - Rehearse the standard derivations (rotational inertia by integration, terminal velocity, work from a variable force) until they can be reproduced quickly. - Solve symbolically and check limiting cases, which catches errors and matches how many exam questions are framed. - Treat the official Course and Exam Description as the source for unit organization and published weightings, since the framework was revised recently. ## Frequently asked questions ### How is the AP Physics C: Mechanics Exam structured? The exam runs 3 hours and is split evenly between a multiple-choice section worth 50% of the score and a free-response section of 4 questions worth the other 50%. The exam was lengthened in the revised framework, and the multiple-choice count and section timing changed again beginning with the May 2027 exam, so confirm current numbers on the official exam page. ### How much calculus does the course actually require? Calculus is used throughout and is a corequisite, meaning students are expected to take it concurrently if they have not already. Differentiation and integration appear in kinematics, work, rotational inertia, and oscillations, so comfort with both is more important than advanced technique. ### Which parts do students find most challenging? College Board does not rank difficulty. Students commonly report that velocity-dependent resistive forces, rotational inertia by integration, and combined rolling problems require the most practice. Use your own practice results to set priorities. ### How is the exam scored, and is it separate from the Electricity and Magnetism exam? The two sections combine into a composite score converted to the reported 1 to 5 scale using cut points set each year. AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism are separate exams with separate scores, and colleges may grant credit for one without the other. ### When do students usually start exam preparation? A common approach is to work problems continuously through the year and then begin cumulative timed practice roughly two months before the exam. Since the course leans on calculus, keeping calculus skills current matters as much as reviewing physics content. ### Is Arcade Academy affiliated with College Board? No. AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. Arcade Academy is an independent educational resource. ## Related exam guides - [AP Physics C: Electricity and Magnetism](https://www.arcadesacademy.com/exams/ap-physics-c-electricity-and-magnetism): Calculus-based electricity and magnetism across the six units of the revised framework, from Gauss's law to induction. - [AP Physics 1: Algebra-Based](https://www.arcadesacademy.com/exams/ap-physics-1): Work through all eight units of the revised AP Physics 1 framework, kinematics through fluids, with published exam weightings. - [AP Calculus BC](https://www.arcadesacademy.com/exams/ap-calculus-bc): All ten AP Calculus BC units with published exam weightings, including parametric and polar functions and infinite series. - [AP Calculus AB](https://www.arcadesacademy.com/exams/ap-calculus-ab): All eight AP Calculus AB units with published exam weightings, from limits through applications of integration. ## Independence and trademark notice AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. Arcade Academy is an independent educational resource. Confirm current exam format, dates, and policies with College Board directly. AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. Arcade Academy is an independent educational resource.