PAU Physics (Aragón) cheat sheet

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).

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).

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

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

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