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Kapittel 1 · Enheter, vektorer og kinematikk
Kapittel 2 · Rotasjonsmekanikk
Hoop vs Disk: Why a Disk Wins
Rolling without slipping — energy conservation gives v = √(2gh / (1 + I/MR²)); disk beats hoop because less inertia goes into rotation
Moment of Inertia
Moment of inertia — I = mr², quadratic radius scaling, disk integral I = ½MR²
Steiner's Theorem: The Cost of an Off-Centre Axis
Parallel-axis (Steiner's) theorem — I = I_cm + Md², the moment of inertia about any axis equals the inertia about a parallel axis through the centre of mass plus M times the squared offset
Torque: Why Leverage Beats Force
Torque (Dreiemoment) — τ = rF sin θ; only the perpendicular component of a force creates rotation, peaking at θ = 90° and vanishing when force is parallel to the lever arm
Kapittel 3 · Harmoniske svingninger
Damped Oscillation: Why Real Springs Stop
Damped harmonic oscillator — adding velocity-proportional drag turns Hooke's law into m·ẍ + b·ẋ + k·x = 0; underdamped solution x(t) = A·e^(-γt)·sin(ωt+φ); regimes: underdamped, critically damped, overdamped
Hooke's Law: Why a Spring Bobs
Simple harmonic motion of a spring — Hooke's law F = -kx leads to ω₀ = √(k/m) and period T = 2π√(m/k)
RLC and Pendulum: Same Math, Different Physics
RLC ↔ pendulum analogy — both obey the same second-order linear ODE, with q↔x, I↔v, L↔m, 1/C↔k, R↔b
The Simple Pendulum: Why Mass Doesn't Matter
Simple pendulum — for small swings, T = 2π√(L/g); the period depends on length and gravity, not mass