== 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