IB Physics Formula Sheet

Topic 1: Measurements and Uncertainties

• Absolute uncertainty: Δx
• Fractional uncertainty: Δx / x
• Percentage uncertainty: (Δx / x) × 100%
• For sum/difference: add absolute uncertainties
• For product/quotient/powers: add percentage uncertainties
• For xⁿ: multiply percentage uncertainty by n

Topic 2: Mechanics

Kinematics (constant acceleration)

• v = u + at
• s = ut + ½at²
• v² = u² + 2as
• s = ½(u + v)t

Forces and Newton's Laws

• F = ma
• Weight: W = mg
• Friction: f ≤ μN

Work, Energy, Power

• W = Fs cos θ
• KE = ½mv²
• GPE = mgh
• Power: P = W/t = Fv
• Efficiency = useful output / total input

Momentum and Impulse

• p = mv
• Impulse: J = FΔt = Δp
• Conservation of momentum: Σp_before = Σp_after

Topic 3: Thermal Physics

• Q = mcΔT (heat for temperature change)
• Q = mL (latent heat)
• pV = nRT (ideal gas law)
• pV = NkT (where k = Boltzmann constant)
• Mean KE of molecule = (3/2)kT
• Internal energy: U = (3/2)nRT (monatomic ideal gas)

Topic 4: Waves

• v = fλ
• T = 1/f
• I = P/A (intensity)
• I ∝ A² (intensity proportional to amplitude squared)
• Snell's law: n₁ sin θ₁ = n₂ sin θ₂
• Critical angle: sin θ_c = n₂/n₁
• Double slit: s = λD/d (fringe spacing)
• Diffraction grating: dsinθ = nλ
• Stationary waves: nodes (zero displacement) and antinodes (max displacement)
• Fundamental frequency: f = v / 2L (string) or v / 4L (closed pipe)
• Doppler effect: f' = f · (v ± v_o)/(v ∓ v_s)

Topic 5: Electricity and Magnetism

Electric Fields

• F = kq₁q₂/r² (Coulomb's law)
• E = F/q = kQ/r²
• V = kQ/r (electric potential)
• E = V/d (uniform field)
• Work done: W = qV

Circuits

• V = IR (Ohm's law)
• P = VI = I²R = V²/R
• Series: R_total = R₁ + R₂ + …
• Parallel: 1/R_total = 1/R₁ + 1/R₂ + …
• EMF with internal resistance: ε = I(R + r)
• Terminal voltage: V = ε − Ir

Magnetic Fields and Forces

• F = qvB sin θ (force on moving charge)
• F = BIL sin θ (force on current-carrying conductor)
• Radius of circular path: r = mv / qB

Topic 6: Circular Motion and Gravitation

• Centripetal acceleration: a = v²/r = ω²r
• Centripetal force: F = mv²/r = mω²r
• Angular velocity: ω = 2π/T = 2πf
• Gravitational force: F = Gm₁m₂/r²
• Gravitational field strength: g = GM/r²
• Gravitational potential: V = −GM/r
• Orbital velocity: v = √(GM/r)
• Kepler's third law: T² ∝ r³ → T² = (4π²/GM)r³

Topic 7: Atomic, Nuclear and Particle Physics

• Photoelectric effect: E = hf = hc/λ
• Maximum KE of photoelectron: KE_max = hf − φ
• de Broglie wavelength: λ = h/mv = h/p
• Energy levels: E = hf for transition photon
• Radioactive decay: N = N₀ e^(−λt)
• Activity: A = λN
• Half-life: t₁/₂ = ln 2 / λ
• Mass-energy: E = mc²
• Binding energy = mass defect × c²

HL Extensions: Electromagnetic Induction

• Magnetic flux: Φ = BA cos θ
• Faraday's law: ε = −dΦ/dt = −N dΦ/dt (for N turns)
• Transformer: Vs/Vp = Ns/Np and Ip × Vp = Is × Vs (ideal)
• AC RMS: V_rms = V₀/√2; I_rms = I₀/√2
• Mean power in AC circuit: P = V_rms × I_rms (for resistors)