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AP Physics C: Mechanics practice questions and exam guide

150 multiple-choice questions and 212 flashcards, written to the College Board AP Physics C: Mechanics Course and Exam Description blueprint. Every question carries a full rationale.

Written and maintained by Nick Burton · last updated 2026-08-22 · how we write and review questions

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About the AP Physics C: Mechanics exam

College Board AP Physics C: Mechanics Course and Exam Description — 7 CED units (calculus-based): 1) Kinematics, 2) Newton's Laws of Motion, 3) Work, Energy, and Power, 4) Systems of Particles and Linear Momentum, 5) Rotation, 6) Oscillations, 7) Gravitation. MCQs are original items requiring calculus/physics reasoning per public CED skill descriptions.

CoStudy's AP Physics C: Mechanics bank holds 362 items. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.

Free AP Physics C: Mechanics practice questions

A sample of 12 multiple-choice questions from the bank, with the full rationale shown.

A solid cylinder rolls without slipping down an incline angle θ. Acceleration?

  1. g sin θ
  2. g sin θ / 2
  3. (2/3) g sin θ
  4. (1/2) g sin θ

Answer: C — (2/3) g sin θ

C) a = g sin θ /(1 + I/(MR²)) = g sin θ /(1 + 1/2) = (2/3) g sin θ. A) Frictionless slide. B/D) Wrong fraction.

The center of mass of a system moves as if:

  1. All mass is at the geometric center
  2. ALL mass is concentrated at the center of mass, and net external force acts there; internal forces don't move the CoM
  3. CoM is fixed
  4. CoM rotates
  5. CoM has no momentum

Answer: B — ALL mass is concentrated at the center of mass, and net external force acts there; internal forces don't move the CoM

F⃗_ext = M·a⃗_CoM (Newton's 2nd law for systems). Even a complex tumbling system has a CoM moving in a simple trajectory (e.g., dropped wrench: CoM falls in straight line). Foundation for AP Physics C rigid body chapters.

A 2 kg block experiences F(x) = 3x² N. Acceleration at x = 2 m?

  1. 12 m/s²
  2. 24 m/s²
  3. 3 m/s²
  4. 6 m/s²

Answer: D — 6 m/s²

D) a = F/m = 3(2)²/2 = 12/2 = 6 m/s². A) Forgot dividing by mass. B) Wrong. C) Coefficient only.

A 0.05 kg bullet at 400 m/s embeds in a 2 kg block at rest on frictionless surface. Speed after embedding?

  1. 9.76 m/s
  2. 8 m/s
  3. 10 m/s
  4. 400 m/s

Answer: A — 9.76 m/s

A) v = (0.05·400)/(2.05) ≈ 9.76 m/s. B) Used wrong total mass. C) Wrong. D) No collision.

The center of mass of a system of particles is:

  1. r_cm = (Σ m_i · r_i) / Σ m_i
  2. The position of the heaviest particle
  3. The midpoint of the system's extent
  4. The point with the highest potential energy

Answer: A — r_cm = (Σ m_i · r_i) / Σ m_i

A) Standard formula. B/C/D) Each contradicts the definition.

Velocity is defined as:

  1. The derivative of position with respect to time, v = dx/dt
  2. The product of mass and acceleration
  3. The integral of force with respect to position
  4. The same as speed

Answer: A — The derivative of position with respect to time, v = dx/dt

A) Standard calculus-based definition. B) That's net force (Newton's second). C) Work. D) Speed is the scalar magnitude.

In an elastic 1D collision of equal masses where m₂ is at rest, after collision:

  1. Both move with v₁/2
  2. Both reverse direction
  3. m₁ stops; m₂ moves off with v₁
  4. Both stop

Answer: C — m₁ stops; m₂ moves off with v₁

C) Standard result for elastic equal-mass collision. A) That's perfectly inelastic. B) Sign error. D) Violates momentum.

Kepler's third law for planetary motion states:

  1. Force is proportional to distance
  2. Velocity is constant
  3. The square of the orbital period is proportional to the cube of the semi-major axis (T² ∝ a³)
  4. Acceleration is zero in orbit

Answer: C — The square of the orbital period is proportional to the cube of the semi-major axis (T² ∝ a³)

C) Kepler's third law. A/B/D) Each is incorrect.

Conservative force F satisfies:

  1. It depends on path
  2. Path-independent work: F = −dU/dx (1D) or F⃗ = −∇U (3D) — has a potential energy function; mechanical energy conserved
  3. F is constant
  4. F is friction-like
  5. F can do negative work only

Answer: B — Path-independent work: F = −dU/dx (1D) or F⃗ = −∇U (3D) — has a potential energy function; mechanical energy conserved

Conservative forces (gravity, springs, electrostatic): path-independent work, mechanical energy conserved. Non-conservative (friction, drag): path-dependent. Relationship F = −dU/dx is essential. AP Physics C-defining.

A particle moves under F = (3x²)x̂ + (2y)ŷ. Work along path from (0,0) to (1,1) along x-axis then y-axis?

  1. 0
  2. 5
  3. 3
  4. ∫₀¹ 3x² dx + ∫₀¹ 2y dy = 1 + 1 = 2 J

Answer: D — ∫₀¹ 3x² dx + ∫₀¹ 2y dy = 1 + 1 = 2 J

D) Path integral splits cleanly along axes. Other choices ignore vector components.

Two blocks (3 kg, 5 kg) connected by string over frictionless pulley. Acceleration of system (g = 10):

  1. g/8 = 1.25 m/s²
  2. g = 10 m/s²
  3. 5 m/s²
  4. a = (5 − 3)g/(5 + 3) = 2.5 m/s²

Answer: D — a = (5 − 3)g/(5 + 3) = 2.5 m/s²

D) Atwood machine: a = (Δm)g/Σm. A) Wrong fraction. B) Ignores constraint. C) Bad denominator.

A force F(x) = 6x² N moves an object from x = 1 to x = 3 m. Work done?

  1. 12 J
  2. 26 J
  3. 52 J
  4. 54 J

Answer: C — 52 J

C) W = ∫₁³ 6x² dx = [2x³]₁³ = 54 − 2 = 52 J. A) Wrong. B) Off by 26. D) Used 0 lower bound.

AP Physics C: Mechanics flashcards

6 sample cards from the 212 in the bank.

Difference between Physics 1 and Physics C: Mechanics?

Physics 1: algebra-based, broader topics. Physics C: calculus-based, deeper into mechanics only.

Resonance?

Driving force at natural frequency → large amplitude oscillation.

Friction's role in rolling without slipping?

Static friction provides torque for angular acceleration. Often does no work.

Moment of inertia (point masses)?

I = Σm_i r_i².

If x(t) = t³ - 6t² + 9t, find v(t).

v(t) = 3t² - 12t + 9.

Newton's 2nd Law (rigorous)?

F_net = ma. For systems with changing mass: F = dp/dt.

Practise the full AP Physics C: Mechanics bank

These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.

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AP Physics C: Mechanics — frequently asked

How many AP Physics C: Mechanics practice questions does CoStudy have?

The AP Physics C: Mechanics bank holds 362 items: 150 multiple-choice questions, 212 flashcards. 18 of them are on this page to read free, with no signup.

Do the AP Physics C: Mechanics questions come with explanations?

Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.

What is on the AP Physics C: Mechanics exam?

College Board AP Physics C: Mechanics Course and Exam Description — 7 CED units (calculus-based): 1) Kinematics, 2) Newton's Laws of Motion, 3) Work, Energy, and Power, 4) Systems of Particles and Linear Momentum, 5) Rotation, 6) Oscillations, 7) Gravitation. MCQs are original items requiring calculus/physics reasoning per public CED skill descriptions.

Are the AP Physics C: Mechanics practice questions free?

The samples on this page are free to read in full, rationales included, with no account. The complete 362-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.

How current is the AP Physics C: Mechanics content?

Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.

Primary source

This bank is written against the College Board's published exam material. Check the AP Course and Exam Descriptions for the current outline, fees and eligibility rules — those change, and the certifying body is the only authority on them. CoStudy is not affiliated with the College Board.

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