Extremadura PAU Physics cheat sheet
Extremadura PAU Physics · Keep the key ideas within reach.
Campo gravitatorio: campo, potencial y órbitas
F = G·M·m/r² y g = G·M/r²; el campo apunta hacia la masa que lo crea.
V = −G·M/r y E_p = −G·M·m/r, con referencia cero en el infinito.
Órbita circular: v = √(G·M/r) y T² = 4π²·r³/(G·M).
Energía mecánica de una órbita circular: E = −G·M·m/(2r).
La velocidad de escape cumple v_e = √(2G·M/R).
Campo electromagnético: electrostática, magnetismo e inducción
F = k·q₁·q₂/r²; E = F/q y V = k·q/r.
E_p = q·V; las líneas de campo son perpendiculares a las equipotenciales.
F = q·v×B no realiza trabajo; con v perpendicular a B y modelo no relativista, r = m·v/(|q|B) y T = 2πm/(|q|B).
Φ = B·S·cos θ y ε = −N·dΦ/dt (Ley de Faraday-Lenz).
1 T = 1 Wb/m² = 1 N/(A·m).
Waves and Optics
Phase difference = 2π × path difference/λ
Stationary waves: node spacing λ/2, node–antinode λ/4, no energy transfer
Grating equation d sinθ = nλ with d = 1/N in metres
Young's slits: x = λD/a for small angles
Snell: n₁ sinθ₁ = n₂ sinθ₂; critical angle sinθc = n₂/n₁ requires n₁ > n₂
Keep one lens sign convention throughout and state it
Relatividad: tiempo, longitud y energía
γ = 1/√(1 − v²/c²) ≥ 1.
Dilatación temporal: Δt = γ·Δt₀; contracción: L = L₀/γ.
p = γmv y E = γmc²; E_k = (γ − 1)mc².
E² = p²c² + m²c⁴; para el fotón E = pc.
El tiempo propio se mide en el sistema donde los sucesos ocurren en el mismo lugar.
Modern Physics
hf = φ + KEmax; intensity affects rate, not maximum energy
Threshold frequency f₀ = φ/h in the ordinary single-photon model; below it that model predicts no photoemission
hf = E₂ − E₁ explains line spectra
λ = h/p generally; p = mv for a nonrelativistic massive particle
α: A−4, Z−2; β⁻: Z+1; γ: no change in A or Z
N = N₀e^(−λt) with t½ = ln2/λ; 1 u c² is approximately 931.5 MeV
Practical and Experimental Skills
State resolution and uncertainty convention for each instrument
Random errors → repeats and means; systematic errors → correction
For first-order worst-case bounds, add relative contributions; independent standard uncertainties use quadrature
Gradient from two points on the best-fit line, with units
Average repeated timings and time many oscillations to cut reaction error
Never quote more significant figures than the data justify