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AP Physics C: Mechanics AI Tutor Playbook 2026

Audience: US-high-school-juniors + US-high-school-seniors preparing for the May 2027 AP Physics C Mechanics exam — typically the cohort in AP-Physics-C-Mechanics + Calculus-AB + Calculus-BC + AP-Chemistry + AP-Biology + AP-Computer-Science-A + AP-Computer-Science-Principles, often paired with AP Physics C Electricity-and-Magnetism for physics-major-bound candidates targeting MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM admissions. Covers AP Physics C Mechanics teachers who want an AI workflow for grading FRQs + free-body-diagrams + energy-bar-charts + orbital-mechanics-calculations, parents paying for AP-Physics-C-prep courses ($200-$2000 for prep-books + $500-$3000 for prep-courses + $1500-$5000 for private-tutors), homeschool families using AP-Physics-C-Mechanics for transcript strength in Engineering-Physics + Classical-Mechanics college-credit + STEM-Admissions, and overseas students applying to MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM.

Hook: AP Physics C Mechanics is the most-respected AP STEM exam for Pre-Engineering-bound US-high-school-juniors + US-high-school-seniors — calculus-based mechanics that integrates derivatives + integrals + differential-equations throughout every unit. The 2025 score distribution is selective but high (due to self-selection by strong physics students): score-5 rate of approximately 35-40 percent, score-4 rate of approximately 25 percent, score-3 rate of approximately 18 percent (the score-3+ "passing-rate" 78 percent benchmark for Engineering-Physics + Classical-Mechanics college-credit), score-2 rate of approximately 14 percent, score-1 rate of approximately 8 percent. The score-4+ cumulative rate (60-65 percent) is the AP Physics C Mechanics benchmark for Year-12-Physics + first-year-undergraduate-Mechanics + MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM admissions readiness. The 8-units-of-AP-Physics-C-Mechanics map onto Year-12-Physics + first-year-undergraduate-Physics at MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM:

• Unit 1 — Kinematics (14-18%): position + velocity + acceleration + derivatives (dx/dt) + 1D-motion + 2D-motion + projectile-motion + relative-velocity + circular-motion + integrals (∫a·dt).
• Unit 2 — Newton's Laws of Motion (14-18%): force + mass + acceleration + F=ma + free-body-diagrams + static-equilibrium + dynamic-equilibrium + friction + drag + tension + spring-force.
• Unit 3 — Work-Energy-and-Power (14-18%): work + kinetic-energy + potential-energy (gravitational + elastic) + work-energy-theorem + conservation-of-energy + power + conservative-vs-non-conservative-forces.
• Unit 4 — Linear Momentum (10-14%): momentum + impulse + impulse-momentum-theorem + conservation-of-momentum + elastic-collisions + inelastic-collisions + center-of-mass + 2D-momentum.
• Unit 5 — Rotational Motion (10-14%): angular-position + angular-velocity + angular-acceleration + torque + moment-of-inertia + rotational-kinetic-energy + angular-momentum + conservation-of-angular-momentum + rolling-motion.
• Unit 6 — Energy + Oscillations (10-14%): simple-harmonic-motion + spring-mass-system + simple-pendulum + physical-pendulum + period + frequency + angular-frequency + energy-of-SHO + damped-oscillations.
• Unit 7 — Gravitation (10-14%): Newton's-law-of-universal-gravitation + gravitational-potential-energy + Kepler-laws + orbital-mechanics + circular-orbits + elliptical-orbits + escape-velocity + gravitational-binding-energy.
• Unit 8 — Advanced Topics (10-14%): rotational-kinematics + rolling-motion + moment-of-inertia-calculus + non-inertial-frames + fictitious-forces (centrifugal + Coriolis).

The calculus-required framework means: every kinematics problem involves derivatives (d²x/dt²) + integrals (∫v·dt); every work-energy problem uses line-integrals; every Newton-law problem can be solved via Lagrangian-formalism or Newtonian-method. The AI tutor must hold all 8-units + 200+-course-content-specifications + calculus-derivatives + calculus-integrals + differential-equations + free-body-diagram + energy-bar-chart + momentum-vector + rotational-kinematics + orbital-mechanics + simple-pendulum + spring-mass-system.

Tone: Quantitative, rigorous, calculus-based, dimensional-analysis-aware, free-body-diagram-fluent, energy-bar-chart-fluent, Lagrangian-aware, conservation-law-fluent, MIT-style-problem-solving, TI-83/84/TI-Nspire/Desmos-strategy-aware, dimensional-analysis-aware.

Word count target: 4,800-5,200

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Section 1 — Why AP Physics C Mechanics is the most-respected AP STEM exam + the MIT + Stanford + Caltech + Ivy-Plus + Top-Ranked-STEM + Engineering-Physics + Classical-Mechanics college-credit + STEM-Admissions-ready subject

AP Physics C Mechanics is the most-respected AP STEM exam for Pre-Engineering-bound US-high-school-juniors + US-high-school-seniors and is the de-facto Engineering-Physics + Classical-Mechanics college-credit + first-year-undergraduate-Mechanics readiness subject at MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM admissions. MIT + Caltech + Stanford + Harvey-Mudd admittees who score 5 on AP Physics C Mechanics have approximately 85-90% acceptance odds into Pre-Engineering-track + Mechanical-Engineering-track + Aerospace-Engineering-track + Civil-Engineering-track + Chemical-Engineering-track + Electrical-Engineering-track + Materials-Science-track + Applied-Physics-track + Physics-track + Engineering-Physics-track + Computer-Science-track + Engineering-Science-track programs at MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard-Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM. Mechanical-Engineering candidates who score 5 on AP Physics C Mechanics have an edge at MIT-Mechanical + Stanford-Mechanical + Berkeley-Mechanical + Caltech-Mechanical + CMU-Mechanical + Georgia-Tech-Mechanical + Michigan-Mechanical + Purdue-Mechanical + UIUC-Mechanical + UT-Austin-Mechanical + Cornell-Mechanical + Top-50-Mechanical-Engineering schools. Aerospace-Engineering candidates who score 5 on AP Physics C Mechanics have an edge at MIT-Aerospace + Stanford-Aerospace + Caltech-Aerospace + Georgia-Tech-Aerospace + Michigan-Aerospace + Purdue-Aerospace + Virginia-Tech-Aerospace + Cornell-Aerospace + Illinois-Aerospace + Maryland-Aerospace + Top-15-Aerospace schools.

The 8-units-of-AP-Physics-C-Mechanics map onto first-year-undergraduate-Physics at MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM:

• Unit 1 — Kinematics (14-18%): position-vectors + velocity-vectors + acceleration-vectors + derivatives (dx/dt + dv/dt + dv/dx) + 1D-motion + 2D-motion + projectile-motion + relative-velocity + uniform-circular-motion + non-uniform-circular-motion + integrals-of-acceleration.
• Unit 2 — Newton's Laws of Motion (14-18%): F=ma + F=dp/dt + free-body-diagrams + static-equilibrium + dynamic-equilibrium + kinetic-friction + static-friction + drag-forces (linear + quadratic) + tension + spring-force (Hooke's-law) + constraint-forces.
• Unit 3 — Work-Energy-and-Power (14-18%): W = ∫F·dr + KE = ½mv² + PE_grav = mgh + PE_spring = ½kx² + work-energy-theorem + conservation-of-energy + non-conservative-forces (friction-work) + power (P = dW/dt = F·v).
• Unit 4 — Linear Momentum (10-14%): p = mv + J = ∫F·dt + impulse-momentum-theorem + conservation-of-momentum (elastic + inelastic-collisions + perfectly-inelastic + 2D-momentum) + center-of-mass + center-of-mass-frame.
• Unit 5 — Rotational Motion (10-14%): τ = r × F + I = ∫r²dm + L = Iω + rotational-KE = ½Iω² + angular-momentum-conservation + rolling-without-slipping.
• Unit 6 — Energy + Oscillations (10-14%): simple-harmonic-motion + ω² = k/m + simple-pendulum + period-of-pendulum + physical-pendulum + energy-of-SHO + damped-oscillations + driven-oscillations.
• Unit 7 — Gravitation (10-14%): F = GMm/r² + U = -GMm/r + Kepler-laws (elliptical-orbits + equal-areas + T² ∝ a³) + circular-orbits + escape-velocity + gravitational-binding-energy.
• Unit 8 — Advanced Topics (10-14%): rotational-kinematics + rolling-motion + non-inertial-frames + fictitious-forces + Coriolis-force + centrifugal-force.

Each unit carries ~10-18% of the exam, but the AI tutor weighting should reflect the candidate's score-gap. A candidate stuck at 3 who consistently drops points in rotational-motion + oscillations needs 4-5x more drill on Units 5 + 6 than a candidate stuck on kinematics. The AI tutor diagnostic must measure all 8-units + 3-FRQ-types + free-body-diagrams + energy-bar-charts + orbital-mechanics + calculus-derivatives + calculus-integrals separately.

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Section 2 — The 22-week AP Physics C Mechanics AI tutor study plan: weeks 1-4 = foundations + diagnostic, weeks 5-13 = core unit mastery, weeks 14-18 = FRQ + free-body-diagram mastery, weeks 19-22 = mock exams + polish

The 22-week AP Physics C Mechanics playbook (May 2027 exam = April 2026 start) runs in four phases. Phase 1 — Foundations + Diagnostic (weeks 1-4) establishes the calculus framework + 8-unit-diagnostic. The AI tutor gives a 50-question diagnostic covering all 8-units + 3-FRQ-types + free-body-diagrams + energy-bar-charts + orbital-mechanics + calculus-derivatives + calculus-integrals, scores the candidate on each unit separately, and routes them into Phase 2 with a per-unit weighting that reflects their actual score-gap. The diagnostic must be timed (90-minutes for the MCQ-only portion + 45-minutes for the FRQ-only portion) so the candidate experiences the actual exam pacing. Phase 2 — Core Unit Mastery (weeks 5-13) runs 1-week per unit across Units 2-9 (skipping Unit 1, which is taught in Phase 1). Each week: 3 hours of AI-tutor-led concept instruction + 3 hours of practice problems (MCQ-set + FRQ-set + free-body-diagram + energy-bar-chart) + 1 hour of error-analysis. Phase 3 — FRQ + Free-Body-Diagram Mastery (weeks 14-18) runs 1-week per FRQ-type (FRQ-1 mechanics + FRQ-2 rotation + FRQ-3 gravitation + review + cumulative). Each FRQ week: 2 hours of FRQ-rubric-training + 4 hours of practice FRQs + 1 hour of error-analysis. Phase 4 — Mock Exams + Polish (weeks 19-22) is 4 full-length mock exams (1 per week) + 1-week-of-error-analysis-on-weakest-2-units for the final polish. The total: 22 weeks × 7 hours/week = 154 hours of focused prep. Candidates who extend to 30-32 weeks (September start) increase their score-5 odds by ~30%.

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Section 3 — Unit 1 — Kinematics: position + velocity + acceleration + derivatives + 1D + 2D + projectile + circular motion

Kinematics is the foundation of all mechanics — the candidate must demonstrate fluency with derivatives (dx/dt + dv/dt) + integrals (∫v·dt = Δx + ∫a·dt = Δv). The MCQ traps: confusing instantaneous-velocity with average-velocity; confusing velocity with acceleration; misreading 2D-projectile-motion as 1D; miscomputing tangential-vs-centripetal-acceleration; misapplying uniform-circular-motion (v²/r is centripetal-acceleration); confusing angular-velocity (ω) with angular-frequency (also ω but in radians/second); miscomputing relative-velocity. The FRQ traps: not drawing the trajectory-equation-with-correct-sign-convention; failing-to-identify-acceleration-component-tangential-vs-centripetal; missing the time-of-flight-derivation; miscomputing range; miscomputing maximum-height. The AI tutor must walk the candidate through every AP-Central-practice-kinematics problem + every 2014-2024-released-exam-kinematics problem + every released-FRQ-kinematics problem.

Section 4 — Unit 2 — Newton's Laws of Motion: F=ma + free-body-diagrams + friction + drag + tension + spring force

Newton's Laws are the second-most-tested unit (14-18% of exam). The AI tutor must score free-body-diagrams rigorously: identify all forces + correct direction + correct magnitude + correct point-of-application + correct angle-of-application. Friction: kinetic-friction-vs-static-friction; coefficient-table; dependence-on-normal-force; independence-from-contact-area. Drag: linear-drag (F=-bv) + quadratic-drag (F=-cv²) + terminal-velocity. Tension: atwood-machines + pulley-systems. Spring-force: Hooke's-law + elastic-potential-energy. The MCQ traps: missing a force on the free-body-diagram; miscomputing net-force (sign-errors); applying F=ma when the system is in equilibrium; ignoring tension-changes-in-pulley-systems; misapplying Newton's-third-law (action-reaction pairs on different objects).

Section 5 — Unit 3 — Work-Energy-and-Power: W = ∫F·dr + work-energy-theorem + conservation-of-energy + power

Work-energy-theorem (W_net = ΔKE) is the cleanest way to solve many mechanics problems. The AI tutor must walk the candidate through: identifying conservative-vs-non-conservative-forces; computing work-along-a-path (line-integrals); applying conservation-of-energy for closed-systems; computing power (instantaneous-power + average-power); handling dissipative-forces (friction-work = -μ_k·N·d). The FRQ traps: forgetting that friction-work is path-dependent; confusing work with potential-energy-change; miscomputing elastic-PE (½kx² not kx²); misapplying conservation-of-energy when external-forces-are-present; failing-to-show-every-step-of-the-line-integral.

Section 6 — Unit 4 — Linear Momentum: impulse + conservation + elastic + inelastic + 2D + center-of-mass

Linear-momentum is the second-tier-tested unit (10-14% of exam). The AI tutor must walk the candidate through: impulse-calculations (J = ∫F·dt = Δp) + collision-analysis (1D + 2D) + perfectly-elastic-collisions (kinetic-energy-conserved) + perfectly-inelastic-collisions (objects-stick-together + KE-not-conserved) + partially-elastic-collisions (coefficient-of-restitution). The MCQ traps: confusing momentum-conservation with kinetic-energy-conservation (only elastic-collisions conserve KE); missing that momentum-is-a-vector-and-2D-collisions-need-vector-analysis; miscomputing center-of-mass-position. The FRQ traps: failing-to-set-up-the-correct-momentum-component-equations; missing the kinetic-energy-component-when-comparing-collision-types; miscomputing the impulse-on-each-object.

Section 7 — Unit 5 — Rotational Motion: torque + moment-of-inertia + angular-momentum + rolling-without-slipping

Rotational-motion is the second-tier-tested unit (10-14% of exam). The AI tutor must walk the candidate through: torque (τ = r × F) + moment-of-inertia (I = ∫r²dm + parallel-axis-theorem) + angular-momentum (L = Iω + conservation) + rotational-KE (½Iω²) + rolling-without-slipping (v = Rω). The MCQ traps: miscomputing torque-magnitude-vs-direction (cross-product-not-commutative); misapplying parallel-axis-theorem; confusing rotational-KE with translational-KE; miscomputing angular-momentum-conservation-when-the-moment-of-inertia-changes. The FRQ traps: failing-to-set-up-the-correct-rolling-without-slipping-constraint-equation; miscomputing the moment-of-inertia-of-composite-objects; misapplying conservation-of-angular-momentum-in-multi-body-systems; forgetting that gravity-creates-torque-on-unbalanced-objects.

Section 8 — Unit 6 — Energy + Oscillations: simple-harmonic-motion + spring-mass + simple-pendulum + physical-pendulum + damped-oscillations

Oscillations is the second-tier-tested unit (10-14% of exam). The AI tutor must walk the candidate through: simple-harmonic-motion (x = A·cos(ωt + φ)) + period-formulas (spring-mass T = 2π√(m/k) + simple-pendulum T = 2π√(L/g)) + energy-of-SHO (½kx² + ½mv² = constant) + physical-pendulum (I-around-pivot + period-formula) + damped-oscillations (exponential-decay-envelope) + driven-oscillations + resonance. The MCQ traps: miscomputing period-of-spring-mass (T = 2π√(m/k) not T = 2π√(k/m)); miscomputing period-of-simple-pendulum for small-angle-approximation (T = 2π√(L/g), independent of amplitude); misapplying small-angle-approximation-for-large-amplitudes; miscomputing energy-of-SHO at-extreme-positions (only PE) + at-equilibrium (only KE).

Section 9 — Unit 7 — Gravitation: Newton's-law-of-universal-gravitation + gravitational-PE + Kepler-laws + orbital-mechanics + escape-velocity

Gravitation is the second-tier-tested unit (10-14% of exam). The AI tutor must walk the candidate through: F = GMm/r² + U = -GMm/r + circular-orbits (v² = GM/r for orbital-speed + T² ∝ r³ from Newton's-third-law + Kepler) + elliptical-orbits (a = semi-major-axis) + escape-velocity (v_esc = √(2GM/r)) + gravitational-binding-energy + gravitational-potential-energy-of-multiple-masses. The MCQ traps: confusing gravitational-force with gravitational-PE; miscomputing orbital-speed (v = √(GM/r) not v = GM/r); misapplying Kepler's-third-law (T²/a³ = constant for all-orbits-around-the-same-central-mass). The FRQ traps: failing-to-set-up-the-correct-energy-conservation-equation-for-escape-velocity; miscomputing orbital-period-from-semi-major-axis; miscomputing the gravitational-PE-difference-between-two-orbits; miscomputing the energy-of-a-binary-system.

Section 10 — Unit 8 — Advanced Topics: rotational-kinematics + rolling-with-non-slipping + non-inertial-frames + fictitious-forces

Advanced-topics round out the 22-week prep. The AI tutor must walk the candidate through: rolling-with-non-slipping (kinetic-friction-provides-torque) + rotating-reference-frames + fictitious-forces (centrifugal-force-in-rotating-frame + Coriolis-force-on-moving-objects-in-rotating-frame) + Euler's-equations-for-rigid-body-rotation. The MCQ traps: confusing fictitious-forces-with-real-forces; miscomputing Coriolis-deflection-direction (right-in-Northern-Hemisphere). The FRQ traps: failing-to-identify-the-correct-rotating-frame; missing the constraint-that-fictitious-forces-only-appear-in-non-inertial-frames; miscomputing Coriolis-deflection-magnitude.

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Section 11 — The 7 calculus-integration competencies for AP Physics C Mechanics

AP Physics C Mechanics is calculus-based — every problem-solving-step integrates calculus. The AI tutor must score the candidate on all 7 calculus competencies separately:

1. Derivatives-of-vector-quantities — Computing d²x/dt² (acceleration-from-position) + dv/dt (acceleration-from-velocity) + dr/dt (velocity-from-position).
2. Integrals-of-acceleration — Computing ∫a·dt (velocity-from-acceleration) + ∫a·dt (position-from-acceleration-given-initial-conditions).
3. Line-integrals-for-work — Computing W = ∫F·dr for non-constant-forces + work-along-curved-paths (gravitational-work along inclined-planes + spring-work over multiple distances).
4. Differential-equations-for-SHO — Setting-up + solving d²x/dt² + (k/m)x = 0 for simple-harmonic-motion + applying-initial-conditions.
5. Taylor-expansion-for-small-angles — sin θ ≈ θ + cos θ ≈ 1 - θ²/2 + tan θ ≈ θ (radians) for small-angle-approximation-in-pendulum-problems.
6. Integrals-for-moment-of-inertia — Computing I = ∫r²dm for continuous-mass-distributions (uniform-rods + disks + spheres + cylinders).
7. Implicit-differentiation-for-related-rates — Computing related-rates-in-mechanics (e.g., how-orbital-period-changes-with-orbital-radius via Kepler's-third-law).

Section 12 — The 5 free-body-diagram competencies for AP Physics C Mechanics

Every AP Physics C Mechanics FRQ involves a free-body-diagram (FBD). The AI tutor must walk the candidate through all 5 FBD-competencies:

1. FBD of point-masses — Identify all forces (gravity + normal + tension + friction + spring + drag) + correct directions + correct magnitudes + correct angles + correct point-of-application.
2. FBD of extended-bodies — Identify all forces + correct applications-on-the-body + correct torque-arms for rotational-equilibrium.
3. FBD of systems-of-bodies — Identify internal-forces (Newton's-third-law-pairs) + external-forces + correct free-body-diagrams-for-each-body.
4. FBD with constraint-forces — Identify pulleys + strings + rods + hinges + correct tension-and-constraint-forces.
5. FBD in non-inertial-frames — Identify pseudo-forces (centrifugal + Coriolis) + correct applications + correct directions.

Section 13 — The 4 energy-bar-chart competencies for AP Physics C Mechanics

Every conservation-of-energy problem involves an energy-bar-chart. The AI tutor must walk the candidate through all 4 EBC-competencies:

1. EBC for falling-objects — Plot gravitational-PE + KE at every instant + label-energy-axis + identify-initial-and-final-energies.
2. EBC for spring-mass-systems — Plot elastic-PE + KE at every instant + identify-maximum-compression-or-extension + identify-turning-points.
3. EBC for pendulums — Plot gravitational-PE + KE through-cycle + identify-minimum-PE + identify-maximum-PE.
4. EBC with dissipative-forces — Plot KE + PE + thermal-energy-due-to-friction + verify-energy-conservation.

Section 14 — The 4 orbital-mechanics competencies for AP Physics C Mechanics

AP Physics C Mechanics tests orbital-mechanics rigorously. The AI tutor must walk the candidate through all 4 orbital-competencies:

1. Circular-orbits — Compute orbital-speed (v² = GM/r) + orbital-period (T² ∝ r³) + orbital-energy (E = -GMm/2r).
2. Elliptical-orbits — Compute semi-major-axis-from-perihelion-and-aphelion + apply-Kepler's-second-law-equal-areas + apply-Kepler's-third-law-T²/a³.
3. Escape-velocity — Compute v_esc = √(2GM/r) + verify-energy-balance-for-escape-orbit.
4. Binary-systems — Compute center-of-mass-velocity + reduced-mass + orbital-period + binding-energy.

Section 15 — The 6 MCQ-strategy competencies for AP Physics C Mechanics

AP Physics C Mechanics has 35 MCQs in 45 minutes (~1.3 minutes per MCQ). The AI tutor must train the candidate on all 6 MCQ-strategies:

1. Time-budgeting — Spend ~75-seconds on each MCQ; flag difficult-MCQs + revisit; never-spend-more-than-2-minutes.
2. Free-body-diagram-first — Always draw the FBD before solving; identifies hidden forces + correct direction-of-applied-forces.
3. Energy-method-as-alternative — Use work-energy-theorem as a faster-alternative-to-Newton's-second-law for many problems.
4. Dimensional-analysis — Always-verify-units-of-final-answer; catches algebraic-errors.
5. Limiting-case-analysis — Test-extreme-cases (zero-friction + zero-mass + infinite-distance + zero-velocity) to verify-formulas.
6. Calculator-strategy — Pre-program constants (G + M_earth + R_earth + k_B) into the calculator + use-scientific-notation.

Section 16 — The 3 FRQ-strategy competencies for AP Physics C Mechanics

AP Physics C Mechanics has 3 FRQs in 45 minutes (~15 minutes per FRQ). The AI tutor must train the candidate on all 3 FRQ-strategies:

1. Rubric-fluency — Every AP-Physics-C-Mechanics-FRQ has a 12-15-point-rubric; the AI tutor must score every step (setup + diagram + equation + derivation + final-answer + units) and identify the specific-step-costing-marks.
2. Calculus-showing-work — Every derivation requires calculus-integration (derivatives + integrals) + differential-equations; the AI tutor must score the candidate on whether they wrote-∫-or-d/dt-correctly + applied-initial-conditions.
3. Free-body-diagram-and-energy-bar-chart — 90% of FRQs require FBD-and-EBC; the AI tutor must score the candidate on whether they drew-correct-FBD + correct-EBC with labels.

Section 17 — The AI tutor prompt library for AP Physics C Mechanics

The AI tutor holds a library of ~150-prompts covering all 8-units + 7-calculus-competencies + 5-free-body-diagram-competencies + 4-energy-bar-chart-competencies + 4-orbital-mechanics-competencies + 6-MCQ-strategies + 3-FRQ-strategies. Each prompt: (1) gives a practice-problem; (2) scores the candidate's-response against the official-College-Board-AP-Physics-C-Mechanics-scoring-rubric; (3) identifies the specific-step-that-cost-marks; (4) generates-a-follow-up-problem-targeting-that-gap. The prompts are organized by unit + competency + strategy + difficulty-level. The AI tutor rotates through these prompts throughout the 22-week-prep, focusing more time on the units + competencies + strategies where the candidate has the biggest-score-gap.

Section 18 — The AP Physics C Mechanics score-5 rubric: 4 dimensions + 8-units + 3-FRQ-types + calculus-integration mastery + free-body-diagram fluency + energy-bar-chart fluency

The AP Physics C Mechanics score-5 candidate demonstrates mastery on 4 dimensions:

1. Conceptual mastery (30%) — Understands 8-units + 200+-course-content-specifications + Newton-laws + conservation-laws + oscillations + gravitation at the level of MIT + Stanford + Caltech + Ivy-Plus + Top-Ranked-STEM first-year-undergraduate-Physics.

2. Quantitative mastery (30%) — Solves kinematics-with-differential-calculus + work-energy-with-line-integrals + momentum-with-impulse-integrals + rotational-with-moment-of-inertia-integrals + oscillations-with-SHO-differential-equation + gravitation-with-orbital-mechanics-calculations with correct units + significant-figures + calculator-output.

3. FRQ + free-body-diagram + energy-bar-chart mastery (25%) — Draws-correct-FBDs + EBCs + shows-all-calculus-steps-on-quantitative-FRQs + writes-clear-justifications-on-experimental-FRQs.

4. MCQ strategic mastery (15%) — Manages time-on-35-MCQs-in-45-minutes (~1.3-min-per-MCQ) + draws-FBD-first + uses-energy-method-as-alternative + applies-dimensional-analysis + verifies-limiting-cases.

The AI tutor should score the candidate on all 4 dimensions separately and provide targeted practice for the weakest dimension.

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Section 19 — Closing: the 22-week AP Physics C Mechanics AI tutor playbook

The 22-week AP Physics C Mechanics AI tutor playbook gives MIT + Stanford + Caltech + Harvey-Mudd + Princeton + Harvard + Yale + Columbia + Penn + Cornell + Dartmouth + Brown + Berkeley + UCLA + Michigan + Georgia-Tech + UT-Austin + CMU + Rice + Duke + Northwestern + Johns-Hopkins + Ivy-Plus + Ivy-League + Top-Ranked-STEM-bound US-high-school-juniors + US-high-school-seniors the 8-units + 200+-course-content-specifications + 35-MCQ + 3-FRQ + free-body-diagram + energy-bar-chart + calculus-derivatives + calculus-integrals + differential-equations + orbital-mechanics + simple-pendulum + spring-mass-system + line-integrals + moment-of-inertia-integrals mastery required to score 5. The framework: Phase 1 (weeks 1-4) = diagnostic + foundations on Unit 1 + Unit 2; Phase 2 (weeks 5-13) = 1-week per remaining unit (Units 3-8); Phase 3 (weeks 14-18) = FRQ + free-body-diagram + energy-bar-chart mastery on 3-FRQ-types; Phase 4 (weeks 19-22) = 4 full-length mock exams + polish on weakest 2-units. The AI tutor holds the 8-units + 200+-course-content-specifications + calculus-derivatives + calculus-integrals + differential-equations + free-body-diagrams + energy-bar-charts + line-integrals + moment-of-inertia-integrals + orbital-mechanics + simple-pendulum + spring-mass-system + TI-83/84/TI-Nspire/Desmos + dimensional-analysis + limiting-case-analysis, scores every response against the AP-CED-scoring-guidelines, and surfaces the specific AP Physics C Mechanics gap (kinematics-vs-Newton-laws-vs-work-energy-vs-momentum-vs-rotational-vs-oscillations-vs-gravitation-vs-calculus-integration-vs-free-body-diagram-vs-energy-bar-chart-vs-orbit-mechanics-calculation) that is costing marks toward the score 5. The difference between a 3 and a 5 is 22 weeks of focused prep with an AI tutor that holds all 8-units + 200+-course-content-specifications + calculus-derivatives + calculus-integrals + differential-equations + free-body-diagrams + energy-bar-charts + orbital-mechanics + simple-pendulum + spring-mass-system + line-integrals. This playbook is that workflow.

Pairs with IB Physics HL (post-157)

The IB Physics HL playbook (post-157) + [this playbook] form the IB Diploma + IB Physics Higher Level + IBO-mastery + Year-13-physics + first-year-undergraduate-Physics + Engineering + Medicine + Architecture + Astrophysics pair for the IB-Diploma-Programme Year-12 + Year-13 candidates + IB-Bilingual + IB-Course-Companion + Pre-Engineering + Pre-Medicine + Pre-Architecture + Pre-Physics + Pre-Astrophysics cohorts at IB-World-Schools in Switzerland + Singapore + Hong-Kong + UAE + UK + US + Canada + Australia + New-Zealand + Japan + Korea + China + India + Pakistan + Bangladesh + Indonesia + Malaysia + Thailand + Vietnam + Philippines + Egypt + South-Africa + Kenya + Nigeria + Ghana + Saudi + Qatar + Bahrain + Kuwait + Oman + Jordan + Lebanon + Brazil + Mexico + Argentina + Chile + Colombia + Peru + Russia + Turkey + Iran + Iraq + Israel targeting MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc + UCL + LSE + Warwick + Edinburgh + Manchester + Bristol + Durham + KCL admissions. The IB Physics HL 8-core-topics (Topic 1 Measurements + Uncertainties + Topic 2 Mechanics + Topic 3 Thermal Physics + Topic 4 Waves + Topic 5 Electricity + Magnetism + Topic 6 Circular Motion + Gravitation + Topic 7 Atomic + Nuclear + Topic 8 Energy Production) + 4-additional-higher-level-topics (Topic 9 Wave Phenomena-HL + Topic 10 Fields-HL + Topic 11 Electromagnetic Induction-HL + Topic 12 Quantum + Nuclear Physics-HL) + 12-practical-lab-groups + Internal-Assessment-Individual-Investigation + Paper-1A-MCQ + Paper-1B-data-based + Paper-2-extended-response + Paper-3-Optional-Topic + calculus-based + critical-thinking-driven + extended-response-required + IA-scientific-writing-assessed + 7-IA-Individual-Investigation-competencies + 4-Paper-1A-MCQ-competencies + 4-Paper-1B-data-based-competencies + 4-Paper-2-extended-response-competencies + 4-Paper-3-Optional-Topic-competencies + 8-Topic-mastery-competencies + AI-tutor-prompt-library + score-7-rubric covers everything the IB-World-School-cohort needs to bridge Year-12 + Year-13-physics + IB-Diploma + IBO-mastery-track + first-year-undergraduate-Physics + Engineering + Medicine + Architecture + Astrophysics-university-credit + STEM-Admissions-readiness at MIT + Imperial + Cambridge + Oxford + ETH-Zurich + EPFL + NUS + NTU + HKUST + KAIST + IIT + IISc + UCL + LSE + Warwick + Edinburgh + Manchester + Bristol + Durham + KCL. See post-157 for the IB-Physics-HL-specific exam, score-distribution, and 30-week score-7 master schedule.