Schleswig-Holstein Abitur Physics cheat sheet

Kinematics: v = v₀ + a·t, s = v₀·t + ½a·t², v² = v₀² + 2a·s apply only for constant acceleration; in vector form each component is treated separately.

Newton's second law: F_res = m·a; the resultant force determines acceleration, not velocity - a body can move with constant speed while forces act if they cancel.

Friction: F_R = μ·F_N; static friction adjusts up to μ_H·F_N, kinetic friction is approximately constant and opposes relative sliding.

Circular motion: v = ω·r, a_z = v²/r = ω²·r, F_z = m·v²/r; the centripetal force is always directed toward the centre and is provided by a real force (tension, gravity, normal force).

Gravitation: F = G·m₁·m₂/r² with G ≈ 6.674·10⁻¹¹ N·m²/kg²; for circular orbits G·M/r² = v²/r gives v = √(G·M/r) and T² ∝ r³ (Kepler's third law).

Conservation of momentum: p = m·v is conserved in any system with no external net force; in elastic collisions kinetic energy is also conserved, in inelastic collisions it is not.

Energy: E_kin = ½m·v², E_pot = m·g·h near Earth, E_spann = ½D·s²; mechanical energy is conserved only when no friction or other dissipative force acts.

Work and power: W = F·s·cos(α), P = W/t = F·v·cos(α); work done perpendicular to motion is zero, e.g. centripetal force does no work.

Angular momentum L = J·ω = m·r²·ω is conserved when no external torque acts; a rotating skater pulling in the arms reduces J and increases ω.

Field concept: field strength is force per unit test quantity - E = F/q (N/C or V/m), B defined by F = q·v×B; field lines start on positive and end on negative charges and never cross.

Coulomb's law: F = (1/4πε₀)·q₁·q₂/r² with 1/4πε₀ ≈ 8.99·10⁹ N·m²/C²; the force is attractive for opposite and repulsive for like charges.

Uniform field of a plate capacitor: E = U/d; the force on a charge is F = q·E, and the work along the field is W = q·U.

Lorentz force: F = q·(E + v×B); the magnetic part is F = q·v·B·sin(α), is perpendicular to v and B, and therefore does no work and changes only the direction of motion.

Charged particle in a uniform magnetic field moves on a circle with r = m·v/(q·B); the period T = 2π·m/(q·B) is independent of speed (basis of the cyclotron).

Magnetic flux Φ = B·A·cos(α); induction law: U_ind = −N·dΦ/dt - the minus sign (Lenz's law) means the induced current opposes the change that causes it.

Self-induction: U_ind = −L·dI/dt, energy stored in an inductor E = ½L·I²; a coil opposes changes in current, giving an exponential rise or decay with time constant τ = L/R.

Motion of a conductor rod in a magnetic field: U_ind = B·l·v when B, rod and v are mutually perpendicular; the induced current produces a force that brakes the motion.

Harmonic oscillator: restoring force F = −D·s gives s(t) = s_max·sin(ω·t + φ₀) with ω = √(D/m) and T = 2π·√(m/D); the period is independent of amplitude.

Pendulum: for small angles T = 2π·√(l/g); energy oscillates between potential ½D·s² and kinetic ½m·v², the total stays constant without damping.

Wave equation: c = λ·f = λ/T; the phase velocity depends on the medium, the frequency is set by the source and does not change at a boundary.

Superposition: displacements add; two waves of equal frequency and amplitude give constructive interference at a path difference Δs = n·λ and destructive at Δs = (n + ½)·λ.

Double slit: maxima at sin(θ_n) = n·λ/d; for small angles the fringe spacing on a screen at distance a is Δy = a·λ/d.

Single slit and grating: single-slit minima at sin(θ_n) = n·λ/b; a grating with N slits sharpens the principal maxima to sin(θ_n) = n·λ/d and increases resolution.

Refraction and total internal reflection: Snell's law sin(α₁)/sin(α₂) = c₁/c₂ = n₂/n₁; total internal reflection occurs above the critical angle sin(α_c) = n₂/n₁ for n₁ > n₂.

Standing waves: nodes at fixed positions, distance between adjacent nodes is λ/2; a string of length l fixed at both ends supports λ_n = 2l/n and f_n = n·f₁.

Doppler effect: f_beob = f_quelle·(c ± v_beob)/(c ∓ v_quelle); a receding source produces a lower observed frequency, an approaching one a higher frequency.

Photon: E = h·f = h·c/λ with h ≈ 6.626·10⁻³⁴ J·s; intensity is photon number per time, colour is photon energy.

Photoelectric effect: E_kin,max = h·f − W_A; below the threshold frequency f_G = W_A/h no electrons are emitted regardless of intensity, and the stopping voltage U_G satisfies e·U_G = E_kin,max.

Wave-particle duality: light shows interference and diffraction (wave) and the photoelectric effect or Compton scattering (particle); matter shows diffraction with λ = h/p (de Broglie).

Bohr model of hydrogen: E_n = −13.6 eV/n², orbit radius r_n = n²·r₁ with r₁ ≈ 5.29·10⁻¹¹ m; transitions emit or absorb photons with h·f = E_n − E_m.

Spectral lines: the Lyman series ends at n = 1 (ultraviolet), Balmer at n = 2 (visible), Paschen at n = 3 (infrared); the series limit is the shortest wavelength of the series.

Heisenberg uncertainty: Δx·Δp ≥ h/(4π) (or order h); localisation in space implies spread in momentum, which limits classical trajectories.

Quantum phenomena: energy levels are discrete and bound states are quantised; the double-slit experiment with single particles builds up an interference pattern statistically, one detection at a time.

Atom: nucleus of protons (Z) and neutrons (N) with mass number A = Z + N, surrounded by electrons; isotopes share Z but differ in N, nuclide notation ᴬZX.

Radioactive decay law: N(t) = N₀·e^(−λ·t), activity A = λ·N with unit becquerel (1 Bq = 1 decay/s); half-life T₁/₂ = ln2/λ ≈ 0.693/λ.

Decay types: alpha (A − 4, Z − 2), beta-minus (n → p + e⁻ + ν̄, Z + 1), beta-plus (p → n + e⁺ + ν, Z − 1), gamma (no change in A or Z, photon emission).

Penetration and shielding: alpha is stopped by paper, beta by a few millimetres of aluminium, gamma is attenuated by thick lead; ionising power is largest for alpha.

Mass-energy: E = m·c², 1 u ≈ 1.6605·10⁻²⁷ kg corresponds to about 931.5 MeV; mass defect Δm = Z·m_p + N·m_n − m_K gives the binding energy.

Binding energy per nucleon peaks near A ≈ 56 (iron); fusion of light nuclei and fission of heavy nuclei both release energy because the product is more tightly bound.

Nuclear reactions obey conservation of charge Z, mass number A and energy; Q value = (m_before − m_after)·c², positive for exothermic reactions.

Radiation dose: absorbed dose in gray (1 Gy = 1 J/kg), equivalent dose in sievert (H = D·w_R); background radiation and half-life determine handling and storage requirements.

Postulates: physical laws are identical in all inertial frames, and the speed of light in vacuum c ≈ 3.00·10⁸ m/s is the same for every observer regardless of source or observer motion.

Lorentz factor γ = 1/√(1 − v²/c²) ≥ 1; for v < 0.1·c, γ ≈ 1 and classical mechanics is a good approximation.

Time dilation: Δt = γ·Δt₀, where Δt₀ is the proper time measured by a clock at rest relative to the events (same place).

Length contraction: l = l₀/γ, where l₀ is the proper length measured in the rest frame of the object; contraction occurs only along the direction of motion.

Relativistic momentum p = γ·m·v; total energy E = γ·m·c², rest energy E₀ = m·c², kinetic energy E_kin = (γ − 1)·m·c².

Energy-momentum relation: E² = (p·c)² + (m·c²)²; for photons m = 0, so E = p·c and p = h/λ.

Relativity principle: no experiment inside a closed inertial frame can reveal absolute motion; simultaneity is relative - events simultaneous in one frame need not be in another.

Addition of velocities: u = (u′ + v)/(1 + u′·v/c²); the result never exceeds c, which resolves the light-speed postulate.

Variable control: an experiment needs a manipulated variable, a measured dependent variable and controlled constants; repeat measurements reduce random error.

Systematic vs random error: random errors scatter symmetrically and are reduced by averaging; systematic errors shift all values in one direction and require calibration or correction.

Uncertainty propagation: for sums and differences absolute uncertainties add, for products and quotients relative uncertainties add; for a power x^n the relative uncertainty is |n| times that of x.

Graphical analysis: linearisation (e.g. plotting T² against l for a pendulum) allows the slope to give the physical constant; error bars and a best-fit line make the evaluation transparent.

Significant figures: the result carries no more significant figures than the least precise input; uncertainties are usually given to one significant figure.

Modelling: a model simplifies reality (point mass, ideal spring, no air resistance); its validity must be checked against measured deviations, and limits of the model stated.

Evaluation criteria: accuracy (closeness to the true value), precision (spread of repeats), reproducibility, and identification of the dominant error source with a concrete improvement.

Data analysis: mean x̄ = (Σx_i)/n, standard deviation of the mean s_x̄ = s/√n; outliers are only removed with a documented, physical justification.

Energy supply: efficiency η = E_useful/E_input; comparing power plants or engines requires stating the full chain from primary energy to useful energy.

Technical applications link to the curriculum: induction in generators and transformers, Lorentz force in mass spectrometers and particle accelerators, semiconductors in LEDs and solar cells.

Radiation protection: justification, dose limitation and optimisation (ALARA); handling rules follow from half-life, radiation type and activity.

Data presentation: a diagram needs labelled axes with units, a clear scale and a caption; a physical statement needs quantity, value and unit.

Argumentation: a physics claim is supported by a measured value with uncertainty or by a cited law; a plausible everyday explanation must be checked against the model.

Model limits in context: ray optics fails at slit widths near the wavelength, classical mechanics fails near c, and the Bohr model fails for multi-electron atoms.

Risk communication: absolute and relative risks must be distinguished, and a measured effect needs a stated reference (per year, per dose, per person).