== AP PHYSICS 1 UNIT 1: KINEMATICS ==
Scalars vs vectors: magnitude only vs magnitude+direction
1D motion: track position, velocity, acceleration separately
Slope of position-time = velocity
Slope of velocity-time = acceleration
Area under velocity-time = displacement
Average velocity = total displacement / total time
Constant acceleration: use kinematic equations
Instantaneous velocity = slope of position-time at point
Reference frames: relative velocity
Vectors in 2D: add/subtract components, resolve angles
Projectile: horizontal = constant velocity, vertical = constant acceleration
Range = v_x*t, max height = v_y^2/(2g)
Symmetry: time up = time down (launch/land same height)
Acceleration always points down = g
Equal time intervals: equal vertical displacement increments

== AP PHYSICS 1 UNIT 2: FORCE AND TRANSLATIONAL DYNAMICS ==
System: choose boundaries, internal forces cancel
External forces cause system acceleration
ΣF = ma (net force = mass x acceleration)
Free-body diagram: ONLY external forces on chosen object
Weight = mg (field force)
Normal force: contact perpendicular, NOT always equal to weight
Friction: kinetic = μ_k*F_N, static ≤ μ_s*F_N
Friction opposes motion, direction opposite velocity
Incline: resolve gravity into parallel (mg sin θ) and perpendicular (mg cos θ)
Tension: pulls along string/rope, same throughout ideal rope
Pulley: massless frictionless pulley transmits force unchanged
Newton's 3rd Law: action-reaction pairs equal opposite different objects
Mass vs weight: mass constant, weight depends on location
Equilibrium: ΣF = 0, not necessarily zero velocity
Terminal velocity: when drag = weight, a = 0, v constant

== AP PHYSICS 1 UNIT 3: WORK, ENERGY, AND POWER ==
Work done: W = F*d*cos(θ) where θ is angle between force and displacement
Only force component parallel to displacement does work
Negative work: force opposes motion (friction, air resistance)
Work-energy theorem: net work = change in kinetic energy
Kinetic energy: KE = 0.5*m*v^2
Conservative force: work path independent (gravity, spring)
Non-conservative force: work path dependent (friction)
Gravitational PE: PE_g = m*g*Δh (only height change matters)
Spring PE: PE_s = 0.5*k*x^2 where x is displacement from equilibrium
Mechanical energy: E = KE + PE
Conservation of energy: E_initial = E_final (if only conservative forces)
Non-conservative work: W_nc = ΔKE + ΔPE
Power: P = W/t (average) or P = F*v (instantaneous)
Energy transfer via work
Energy transfers between forms, never created/destroyed

== AP PHYSICS 1 UNIT 4: LINEAR MOMENTUM AND COLLISIONS ==
Momentum: p = m*v (vector quantity)
Impulse: J = F_avg*Δt = Δp (change in momentum)
Impulse-momentum theorem: impulse = momentum change
Force-time graph area = impulse
Center of mass: x_cm = Σ(m_i*x_i) / Σm_i
v_cm = Σ(m_i*v_i) / Σm_i
Conservation of momentum: Σp_initial = Σp_final (isolated system)
External force = rate of change of momentum
Elastic collision: KE conserved AND momentum conserved
Inelastic collision: momentum conserved, KE NOT conserved
Perfectly inelastic: objects stick together, max KE loss
1D vs 2D: use components for 2D collisions
Explosions: reverse of inelastic collision, momentum conserved
Internal forces don't change center of mass motion

== AP PHYSICS 1 UNIT 5: TORQUE AND ROTATIONAL DYNAMICS ==
Torque: τ = r*F*sin(θ) = F_perp*r
r is distance from pivot to force application point
Lever arm: perpendicular distance from pivot to force line
τ = I*α (rotational analog of F = ma)
Moment of inertia: I = Σ(m_i*r_i^2)
Parallel axis theorem: I = I_cm + M*d^2
Rotational KE: KE_rot = 0.5*I*ω^2
Angular momentum: L = I*ω
Angular momentum conserved if no external torque
Rotational work: W = τ*Δθ
Rotational power: P = τ*ω
Rolling without slipping: v = r*ω, a = r*α
Static friction enables rolling
Angular acceleration same for all points
Angular velocity same for all points
Angular momentum: L = m*v*r*sin(θ) for point mass
Rotational inertia depends on mass distribution

== AP PHYSICS 1 UNIT 6: ENERGY AND MOMENTUM OF ROTATING SYSTEMS ==
Rotational systems: combine translational + rotational energy
Rolling objects: total KE = KE_trans + KE_rot
Solid sphere: I = 0.5*M*R^2
Hollow sphere: I = 2/3*M*R^2
Disk/cylinder: I = 0.5*M*R^2
Hoop: I = M*R^2
Angular impulse: J_ang = τ*Δt = ΔL
Angular momentum conserved if Στ_ext = 0
Collisions of rotating systems
Rolling friction vs static friction (no slip = static)
Angular momentum conservation in collisions
Energy conservation includes rotational terms
Angular momentum transfer between objects
Rotational energy transfer via work

== AP PHYSICS 1 UNIT 7: OSCILLATIONS ==
Simple harmonic motion (SHM): restoring force F = -k*x
Equilibrium position: net force = 0
Amplitude: maximum displacement from equilibrium
Period: time for one complete cycle
Frequency: f = 1/T cycles per second
Angular frequency: ω = 2πf
Spring oscillator period: T_s = 2π*sqrt(m/k)
Pendulum period: T_p = 2π*sqrt(L/g)
Simple pendulum: small angles only (<15°)
Period independent of mass (spring) or amplitude (small angles)
Energy in SHM: E = 0.5*k*A^2 = 0.5*m*v_max^2
PE_max = KE_max at equilibrium
At extremes: v = 0, a = max, PE = max, KE = 0
At center: a = 0, v = max, PE = min, KE = max
Damped oscillation: energy loss to friction
Forced oscillation: driving frequency
Resonance: driving freq = natural freq
Period vs frequency inverse relationship

== AP PHYSICS 1 UNIT 8: FLUIDS ==
Density: ρ = m/V (constant for incompressible)
Pressure: P = F/A (force perpendicular to surface)
Pressure increases with depth: P = P_0 + ρ*g*h
Gauge pressure: P_gauge = ρ*g*h
Atmospheric pressure: ~1 atm = 1.0E5 Pa = 101 kPa
Pascal's principle: pressure change transmits equally
Buoyant force: F_b = ρ_fluid*V_displaced*g
Archimedes: buoyant force = weight of displaced fluid
Object floats if ρ_object < ρ_fluid
Floats submerged if ρ_object = ρ_fluid (neutral buoyancy)
Sink if ρ_object > ρ_fluid
Continuity equation: A_1*v_1 = A_2*v_2 (incompressible flow)
Bernoulli: P_1 + 0.5*ρ*v_1^2 + ρ*g*h_1 = P_2 + 0.5*ρ*v_2^2 + ρ*g*h_2
High velocity = low pressure
Torricelli: exit speed = sqrt(2*g*h)
Ideal fluid: incompressible, non-viscous, laminar
Streamline flow
Viscosity: internal friction between fluid layers