AP Physics C

Calculus-based mechanics and electricity & magnetism — derivatives, integrals, and differential equations applied to physics.

10
Core Units
60+
Key Formulas
6
Quiz Sets
AI
Graded FRQs

AP Physics C Exam Structure

Mechanics — 90 min
35 MC (45 min) + 3 FRQs (45 min)
Calculator allowed on FRQs
E&M — 90 min
35 MC (45 min) + 3 FRQs (45 min)
Calculator allowed on FRQs
Core Topics
Mechanics: Kinematics · Forces · Energy · Momentum · Rotation
E&M: Electrostatics · Circuits · Magnetism · Induction

Flashcards

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Formula Sheets

Every key equation for AP Physics C, organized by unit. Rendered with KaTeX.

Comparison Tables

High-yield side-by-side comparisons for exam-day clarity.

Linear Motion vs. Rotational Motion (Analogies)

Linear Quantity Symbol Rotational Analog Symbol
Displacement x (m) Angular displacement θ (rad)
Velocity v (m/s) Angular velocity ω (rad/s)
Acceleration a (m/s²) Angular acceleration α (rad/s²)
Force F (N) Torque τ (N·m)
Mass m (kg) Moment of inertia I (kg·m²)
Newton's 2nd: F = ma — Rotational 2nd: τ = Iα —
Momentum: p = mv — Angular momentum: L = Iω —
KE = ½mv² — Rotational KE = ½Iω² —

Elastic vs. Inelastic Collisions

Feature Perfectly Elastic Perfectly Inelastic Inelastic (partial)
Momentum conserved? ✓ Always ✓ Always ✓ Always
KE conserved? ✓ Yes — KE before = KE after ✗ No — maximum KE lost ✗ No — some KE lost
Objects after collision Bounce apart separately Stick together (one mass) Separate, but deformed
Example Billiard balls, atomic collisions Car crash, ballistic pendulum Most real-world collisions

Types of Forces

Force Symbol Formula / Notes Direction
Weight / Gravity F_g or W F_g = mg Always downward toward Earth's center
Normal Force F_N or N Perpendicular to surface; ≠ mg on incline Perpendicular to contact surface, away from it
Friction (kinetic) F_k F_k = μ_k · N Opposite to direction of motion
Friction (static) F_s F_s ≤ μ_s · N (max) Opposite to tendency of motion
Tension T Force through a rope/string; same magnitude throughout ideal rope Along rope, toward center
Spring Force F_sp F_sp = −kx (Hooke's Law) Opposite to displacement from equilibrium
Centripetal Force F_c F_c = mv²/r = mω²r Always toward center of circular path

Energy Types & Conservation

Energy Type Formula Notes
Kinetic (translational) KE = ½mv² Energy of linear motion
Kinetic (rotational) KE_rot = ½Iω² Rolling objects have both KE and KE_rot
Gravitational PE PE_g = mgh h measured from reference point; choose wisely
Elastic PE (spring) PE_sp = ½kx² x = displacement from equilibrium
Work W = Fd·cosθ θ = angle between F and displacement; W by friction is negative
Power P = W/t = Fv Rate of energy transfer; unit: Watt (W)
Conservation of Energy: E_total = KE + PE + thermal = constant (isolated system)

Series vs. Parallel Circuits

Feature Series Parallel
Current (I) Same through all components: I_total = I₁ = I₂ Splits at junction: I_total = I₁ + I₂
Voltage (V) Divides: V_total = V₁ + V₂ Same across all branches: V_total = V₁ = V₂
Resistance (R) Adds: R_eq = R₁ + R₂ + ... (R_eq > any R) 1/R_eq = 1/R₁ + 1/R₂ (R_eq < any R)
If one branch breaks All components stop — circuit is open Other branches continue — independent
Brightness of identical bulbs Dimmer than parallel (shared voltage) Brighter (full voltage across each)

Electric vs. Gravitational Fields

Property Gravitational Electric
Source Mass (m) Charge (q)
Force law F = Gm₁m₂/r² F = kq₁q₂/r²
Field g = GM/r² (always attractive) E = kQ/r² (attractive or repulsive)
Potential energy U = −GMm/r U = kq₁q₂/r
Potential V_g = −GM/r V = kQ/r
Direction Always attractive Like charges repel, opposite attract

Capacitors: Series vs. Parallel

Property Series Parallel
Charge (Q) Same on each: Q₁ = Q₂ = Q_total Splits: Q_total = Q₁ + Q₂
Voltage (V) Divides: V_total = V₁ + V₂ Same across each: V₁ = V₂
Capacitance 1/C_eq = 1/C₁ + 1/C₂ (C_eq < smallest) C_eq = C₁ + C₂ (C_eq > largest)

Practice Quiz

Scenario-based multiple choice questions by unit. Select a set to begin.

Full AP Physics C Practice Test

20 MC questions (randomized from a large pool) + 3 FRQs covering Mechanics and E&M — graded by Gemini AI with calculus-specific feedback.

Section I — Multiple Choice (20 Questions)

Section II — Free Response Questions

FRQ 1 — Mechanics (Calculus-Based)

A particle moves along the x-axis with velocity v(t) = 3t² − 12t + 9 (m/s). At t = 0, the particle is at x = 2 m.
Find the acceleration a(t) as a function of time. At what time(s) is the acceleration zero?
Find the position x(t) by integrating v(t). Use the initial condition x(0) = 2.
Find the total distance traveled by the particle from t = 0 to t = 3 s. (Hint: the particle may change direction.)

FRQ 2 — Rotation & Energy

A uniform solid cylinder (mass M = 4 kg, radius R = 0.2 m) rolls without slipping down a ramp of height h = 3 m. I_cylinder = ½MR².
Using energy conservation (include both translational and rotational KE), derive the speed at the bottom of the ramp.
Compare the speed to that of a frictionless sliding block. Why is the rolling cylinder slower?
If the cylinder starts from rest and the ramp is inclined at 30°, find the linear acceleration using τ = Iα and Newton's 2nd Law.

FRQ 3 — Electrostatics & Circuits

A parallel-plate capacitor has plate area A = 0.02 m² and separation d = 0.005 m. It is connected to a 12 V battery, fully charged, then disconnected. ε₀ = 8.85 × 10⁻¹² F/m.
Calculate the capacitance, the charge on each plate, and the energy stored in the capacitor.
After disconnecting from the battery, the plate separation is doubled to 0.01 m. What happens to C, Q, V, and U? Justify each.
Now the capacitor (at its new separation) is connected in series with a resistor R = 1000 Ω. Write the differential equation for discharge and solve for Q(t).

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