AP Physics C: Mechanics Free Response Questions2019 to 2026 FRQ Archive

What do AP Physics C: Mechanics FRQs test?

The ability to set up and execute calculus based solutions to mechanics problems, not just recall formulas or substitute numbers.

Each of the three free response questions on AP Physics C: Mechanics is multi part and multi skill. A single question routinely requires drawing a free body diagram, writing Newton's second law, integrating a force function to find velocity or displacement, applying conservation of energy or momentum, and providing a written justification. The calculus requirement is non-negotiable: parts that call for integration or differentiation award credit only when those steps are explicitly shown. According to the AP Physics C: Mechanics Chief Reader Reports, students who write the correct final answer without showing the calculus work receive zero credit for those parts, because the rubric awards the setup and execution of calculus, not just the numerical result.

How are the three AP Physics C: Mechanics FRQs structured?

Three questions of comparable depth, each multi part, each requiring a sequence of physics and calculus steps.

Unlike AP Physics 1, which has named question types (Experimental Design, Quantitative Qualitative Translation), the three AP Physics C: Mechanics FRQs do not follow a rigid named structure. Each question covers a different unit cluster and tests a different set of physics principles, but all three share the same expectation: students must move through a sequence of connected parts that build on each other, applying both physics reasoning and calculus execution.

How are AP Physics C: Mechanics FRQs scored?

Each part of each question earns points on a rubric. Showing the calculus work is the primary way to earn those points.

The three free response questions together make up 50% of the composite score. Each question is scored on a point rubric specifying exactly what work must appear for each part to earn credit. Key rubric principles: correct free body diagrams earn diagram points; written equations earn setup points; correct integration or differentiation with limits shown earns calculus points; and a correct numerical answer with no work earns zero for the calculus parts. College Board trains readers to award credit for correct physics reasoning even when the final answer is numerically wrong due to a downstream arithmetic error, so showing complete work always dominates omitting it.

Worked example: how a real AP Physics C: Mechanics FRQ part is scored

A rotation question asking for the angular velocity of a disk using conservation of angular momentum, from a released AP Physics C: Mechanics exam.

This example walks through a representative FRQ part from the rotation unit, showing exactly what the rubric requires, what a response earning full credit looks like, and what a response that reaches the same numerical answer without showing the required physics earns instead. Rotation questions represent 20 to 25% of the exam and are the most frequently cited source of point loss in Chief Reader Reports.

1. A disk of moment of inertia I sub disk rotates at initial angular velocity omega sub 0. A small mass m is dropped onto the rim of the disk at radius R and sticks. Find the final angular velocity of the disk plus mass system.

   Rubric: Apply conservation of angular momentum with correct identification of initial and final angular momenta, including the moment of inertia of the added mass as m times R squared, and solve algebraically for the final angular velocity.

   Earns the point: Initial angular momentum: L sub i equals I sub disk times omega sub 0. Final angular momentum: L sub f equals (I sub disk plus m R squared) times omega sub f. Setting L sub i equal to L sub f and solving: omega sub f equals I sub disk times omega sub 0 divided by (I sub disk plus m R squared). This response shows the conservation principle, the correct moment of inertia for the point mass at the rim, the algebra, and the final expression.

   Loses the point: Writing omega sub f equals omega sub 0 times I sub disk divided by (I sub disk plus m) misses the factor of R squared for the added mass moment of inertia. This earns the point for applying conservation of angular momentum but loses the point for the correct expression for the added moment of inertia. The error costs half the available credit for this part.

2. Is kinetic energy conserved in this process? Justify your answer.

   Rubric: State that kinetic energy is not conserved, and justify by citing the inelastic collision (mass sticks to disk) or by computing initial and final kinetic energies and showing the final is smaller.

   Earns the point: Kinetic energy is not conserved. The mass sticking to the disk is a perfectly inelastic collision; internal deformation converts kinetic energy to thermal and internal energy. The initial rotational kinetic energy is (1/2) times I sub disk times omega sub 0 squared. The final is (1/2) times (I sub disk plus m R squared) times omega sub f squared, which is less than the initial. The loss is the difference.

   Loses the point: Writing 'No, because angular momentum is conserved instead' earns no credit. Angular momentum and kinetic energy are independent quantities; conservation of angular momentum does not imply non conservation of kinetic energy. The correct reason is that the collision is inelastic, and the justification must reference the collision type or explicitly compare initial and final kinetic energies.

The two most common errors in rotation FRQ parts are omitting R squared when computing the moment of inertia of a point mass at a given radius, and confusing conservation of angular momentum with conservation of kinetic energy. Both errors appear in Chief Reader Reports across multiple years. The rubric awards the physics reasoning explicitly: naming 'conservation of angular momentum' earns a justification point that cannot be earned by substituting numbers alone.

Common AP Physics C: Mechanics FRQ mistakes

1. 01

   Using algebra instead of calculus when calculus is required

   Students who know that velocity is distance divided by time frequently apply v equals d divided by t to situations where acceleration is non-constant, where that equation does not hold. The correct approach is to integrate the acceleration function over time. This error is identified across multiple Chief Reader Reports as the single most costly category of FRQ loss: it produces the wrong numerical answer AND loses the calculus execution point. Students who have internalized the kinematic equations as universal formulas, rather than as special cases valid only for constant acceleration, consistently underperform on Unit 1 and Unit 2 FRQ parts.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

2. 02

   Incomplete or misdirected free body diagrams

   Free body diagrams that omit a force (commonly friction on an inclined surface, or the normal force from a surface below a rotating object), show the net force as an arrow on the diagram instead of only contact and field forces, or misplace the point of application for torque analysis cost diagram points that cannot be recovered in subsequent parts. Chief Reader Reports note that students frequently draw the correct forces but assign incorrect directions, particularly for friction in rolling without slipping scenarios where friction direction depends on whether the object is accelerating or decelerating.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

3. 03

   Omitting R squared when computing the moment of inertia of a point mass

   The moment of inertia of a point mass at distance R from the rotation axis is m times R squared. Students who write m times R (missing the squared) or simply add m to the existing moment of inertia of the extended body without the R squared factor produce incorrect final angular velocities or kinetic energies. This error appears in nearly every administration's Chief Reader Report for problems involving objects dropped onto rotating disks or platforms.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

4. 04

   Failing to show the definite integral setup for work by a variable force

   Work done by a variable force is the definite integral of force regarding displacement from the initial to the final position. Students who write W equals F times d using the initial or average force value lose the calculus setup point entirely, even if their numerical estimate happens to be approximately correct. The rubric requires seeing the integral sign, the force function (for x or r), d x or d r, and the limits of integration. Chief Reader Reports identify this as the most common error on energy unit FRQ parts.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

5. 05

   Confusing when to apply conservation of energy versus Newton's second law

   Conservation of energy cannot be applied directly when a non conservative force (friction, drag) does work on the system, because mechanical energy is not conserved. Students who apply the work energy theorem without accounting for work done by friction, or who use energy conservation in situations where a torque is doing angular work over a changing angle, reach incorrect results and lose the conservation law application point. Chief Reader Reports note that students often identify the principle correctly but misidentify whether the conditions for applying it are met.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

6. 06

   Providing conclusions without naming the physics principle in justification parts

   FRQ parts that ask students to 'justify' or 'explain' a result require explicitly naming the physics principle used. A response that writes 'omega increases because moment of inertia decreases' earns no justification credit without adding 'by conservation of angular momentum, since there is no net external torque on the system.' Chief Reader Reports consistently flag that students who understand the physics intuitively nevertheless lose justification points for omitting the named principle. The rubric awards the articulation of the principle, not just the correct conclusion.

   AP Physics C: Mechanics Chief Reader Reports, multiple administrations

How do you practice AP Physics C: Mechanics FRQs effectively?

Work released FRQs under timed conditions, then score your response against the official rubric part by part.

The most effective FRQ practice starts with released questions from College Board's AP Central archive. Set a timer for 45 minutes for all three questions together. After completing them, compare your response part by part against the official scoring guidelines. For each part: did you draw the diagram correctly? Did you write and evaluate the required integral? Did you name the physics principle in the justification? Identify which error types you commit most frequently (calculus setup, free body diagrams, justification language) and target those specifically. Repeating this cycle with 5 to 7 released years before the exam builds the procedural fluency the rubric rewards.

1. 1

   Read all three FRQ questions during the 15 minute reading period before writing anything. Identify which question covers kinematics, which covers rotation, and plan your time at 12 to 15 minutes per question.

2. 2

   Draw the free body diagram before writing any equations. The diagram is both a graded deliverable and your own analytical tool for identifying all forces correctly.

3. 3

   When the problem involves a non-constant force or acceleration, ask immediately: do I need to integrate or differentiate? The answer is almost always yes, and showing the integral is how you earn the calculus point.

4. 4

   For rotation parts, write the rotational analog of Newton's second law (net torque equals I times alpha) explicitly before solving. Do not proceed from the translational version without converting.

5. 5

   For SHM parts, identify the restoring force, write the differential equation (d squared x divided by d t squared equals negative omega squared times x), and state what omega equals for given quantities before solving for period.

6. 6

   Justification parts require the named physics principle. Write 'by conservation of angular momentum, since no net external torque acts on the system' rather than just stating the numerical result.

7. 7

   Show all calculus work: write the integral or derivative, include the limits of integration, show the evaluation. A correct numerical answer with no calculus work shown earns zero for the calculus part.

AP Physics C: Mechanics FRQ FAQ

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