Dynamics — Newton's Laws
The most heavily tested unit. Free body diagrams, net force, friction, and Newton's three laws.
Dynamics is the study of what causes motion. Nearly every AP Physics 1 FRQ involves drawing a free body diagram and applying Newton's second law.
Newton's Three Laws
- Inertia: An object at rest stays at rest; an object in motion stays in motion — unless acted on by a net external force.
- F = ma: The net force on an object equals its mass times acceleration. Direction matters: always define a positive direction first.
- Action-Reaction: For every force, there is an equal and opposite reaction force. These act on different objects — they never cancel each other.
Free Body Diagrams
Draw one dot representing the object. Draw arrows for every force acting on it: gravity (down), normal force (perpendicular to surface), tension (along string), friction (opposing motion), applied force. Sum forces in each direction and set equal to ma.
Friction
Kinetic friction acts when surfaces slide. Static friction prevents sliding and can take any value up to its maximum μₛN. The normal force N is not always mg — on an incline or in an elevator it differs.
Kinematics (1D and 2D)
The "Big Four" kinematic equations (constant acceleration only):
Kinematics — Position, Velocity & Acceleration
Drag the a (acceleration), v₀ (initial velocity), and x₀ (initial position) sliders. The blue curve shows position x(t) and the red curve shows velocity v(t). Notice how the slope of x(t) equals v(t) at every point — that's calculus-level insight the AP exam tests conceptually.
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Forces and Motion Basics
Apply forces to objects with friction and observe how net force, mass, and acceleration relate. Build intuition for free body diagrams.
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Exam tip: Newton's 3rd Law action-reaction pairs act on DIFFERENT objects — they can never cancel. The most common exam trap: a book sits on a table. The normal force on the book (from the table) and gravity on the book are NOT a Newton's 3rd Law pair — they're both on the same object. The true 3rd Law pair of gravity on the book is the book pulling Earth upward.
Common mistake: Never write F = ma without first identifying what 'F' means. It must be the NET force — the vector sum of all forces on the object. Writing just one force (like tension) equal to ma is wrong if other forces are also present.
Key Concepts
Exam prediction: This topic frequently appears on the AP Physics 1 exam. See our full AP Physics 1 predictions →
Energy & Work
Work-energy theorem, kinetic and potential energy, conservation of energy, and power.
Energy is one of the most powerful tools in physics — it lets you solve problems without knowing forces at every instant. When forces are complicated, energy often isn't.
Work and the Work-Energy Theorem
Work is done on an object when a force has a component in the direction of displacement. Only the parallel component counts.
Types of Energy
Conservation of Energy
In a closed system with no non-conservative forces (no friction, no air resistance), total mechanical energy is constant:
When friction is present, mechanical energy is lost to thermal energy: ΔE_thermal = fₖd.
Power
Energy Conservation — KE vs PE
Drag the h slider (height) to move an object up and down. Watch KE and PE trade off while their sum E stays constant — this is conservation of mechanical energy. Drag E to change the total energy.
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Energy Skate Park
Watch KE and PE bars update in real time as a skater moves along a track. Add friction and watch mechanical energy decrease. Drag the skater to any height and release.
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Exam tip: Use energy when you don't know (or don't need) the time or the forces during motion — only the start and end states matter. Use F = ma when you need acceleration, force, or time. The AP FRQ frequently requires you to justify which approach you're using.
Key Concepts
Momentum & Collisions
Impulse, conservation of momentum, elastic and inelastic collisions, and center of mass.
Momentum is always conserved in a closed system — no matter what forces act internally. It's the go-to tool for collisions and explosions where forces are unknown.
Momentum and Impulse
Impulse equals the area under an F vs t graph — a frequent AP graph-reading question.
Conservation of Momentum
Collision Types
| Type | Momentum | KE | Example |
|---|---|---|---|
| Elastic | Conserved | Conserved | Billiard balls, ideal springs |
| Inelastic | Conserved | Not conserved | Most real collisions |
| Perfectly inelastic | Conserved | Maximum KE lost | Objects stick together |
For perfectly inelastic collisions: m₁v₁ + m₂v₂ = (m₁ + m₂)vf
Collision Lab
Set masses and initial velocities for elastic or inelastic collisions. Watch momentum arrows and KE readouts before and after — perfect for verifying conservation laws.
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Exam tip: Momentum is a vector — direction signs matter. Always define a positive direction before writing conservation equations. In 2D collisions, write separate conservation equations for x and y. The AP exam frequently gives you a graph of force vs. time and asks for the impulse (area under the curve).
Common mistake: Kinetic energy is NOT conserved in inelastic collisions — only momentum is. Never use energy conservation in a collision problem unless told it's elastic. The missing KE goes to heat, sound, and deformation.
Key Concepts
Exam prediction: This topic frequently appears on the AP Physics 1 exam. See our full AP Physics 1 predictions →
Waves & Sound
Transverse and longitudinal waves, wave speed, standing waves, harmonics, and resonance.
Waves transfer energy without transferring matter. AP Physics 1 focuses on mechanical waves — you don't need EM waves here.
Wave Properties
Every wave has amplitude (A), wavelength (λ), frequency (f), and period (T). These relate through:
Wave speed depends on the medium, not the frequency. Doubling frequency halves wavelength at the same speed.
Standing Waves and Harmonics
When a wave reflects and interferes with itself, standing waves form at specific resonant frequencies. For a string fixed at both ends (or open pipe open at both ends):
Nodes are points of zero displacement. Antinodes are points of maximum displacement. The fundamental (n = 1) has one antinode; each harmonic adds one more.
Wave Superposition
When two waves overlap, their displacements add. Constructive interference occurs when crests align; destructive when a crest meets a trough.
Wave Superposition — Constructive & Destructive Interference
The blue and red curves are two individual waves. The green sum shows their superposition. Set f₁ = f₂ for pure constructive or destructive interference. Make f₁ slightly different from f₂ to see beating — a low-frequency amplitude oscillation caused by interference.
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Wave on a String
Set the string to 'Oscillate' mode and adjust frequency and tension. Switch to 'Resonance' to see standing wave harmonics form. Observe node and antinode positions.
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Exam tip: Standing wave problems almost always require drawing the harmonic pattern first. For a string fixed at both ends: n = 1 is half a wavelength, n = 2 is one full wavelength, n = 3 is one-and-a-half wavelengths. Use λₙ = 2L/n then v = fλ to find the nth harmonic frequency.
Key Concepts
Rotational Motion & Torque
Torque, rotational inertia, angular momentum, and rolling without slipping.
Rotational motion is the direct analog of linear motion. Every linear quantity has a rotational counterpart — once you see the pattern, the formulas write themselves.
Linear → Rotational Analogs
| Linear | Rotational |
|---|---|
| Displacement x | Angle θ (radians) |
| Velocity v | Angular velocity ω (rad/s) |
| Acceleration a | Angular acceleration α (rad/s²) |
| Force F | Torque τ (N·m) |
| Mass m | Rotational inertia I (kg·m²) |
| Momentum p = mv | Angular momentum L = Iω |
| F = ma | τ = Iα |
Torque
Torque is the rotational effect of a force. It depends on how far from the pivot the force is applied and the angle between the force and the lever arm.
For rotational equilibrium (no angular acceleration): Στ = 0. Sum torques about any point — choose the pivot to eliminate unknown forces from the equation.
Rolling Without Slipping
When an object rolls without slipping, its translational and rotational motion are linked:
Conservation of Angular Momentum
In a closed system with no external torque, angular momentum is conserved. This explains why a spinning figure skater spins faster when they pull their arms in — I decreases, so ω increases to keep L = Iω constant.
Exam tip: When calculating torque for a static equilibrium problem (e.g., a beam balanced on a fulcrum), always choose your pivot point to be where an unknown force acts. That torque then drops out of the equation, leaving you to solve for fewer unknowns.
Common mistake: Rotational inertia I depends on both mass and how that mass is distributed. A hollow cylinder has more rotational inertia than a solid cylinder of the same mass and radius — the mass is farther from the axis. Don't confuse I with mass alone.
Key Concepts
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