AMIE Section A Examination cheat sheet

SI base units: length metre (m), mass kilogram (kg), time second (s), electric current ampere (A), temperature kelvin (K), amount mole (mol), luminous intensity candela (cd).

Derived unit rules: force newton N = kg·m/s²; pressure pascal Pa = N/m²; energy joule J = N·m; power watt W = J/s; frequency hertz Hz = 1/s.

Prefix multipliers: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶, giga 10⁹; convert by shifting the decimal three places per step.

Ohm's law V = IR; series resistance R = R₁ + R₂; parallel resistance 1/R = 1/R₁ + 1/R₂; electrical power P = VI = I²R = V²/R.

Mechanical advantage of a lever: MA = effort arm ÷ load arm; for an ideal machine MA = load ÷ effort and efficiency = output work ÷ input work × 100%.

Stress σ = F/A, strain ε = ΔL/L, and Young's modulus E = σ/ε in the linear elastic region; units of E are pascals.

Density ρ = m/V; hydrostatic pressure p = ρgh; buoyant force equals the weight of displaced fluid (Archimedes' principle).

Thermal relations: Q = mcΔT for sensible heat, Q = mL for latent heat; absolute temperature T(K) = T(°C) + 273.15.

Engineering ethics decision rule: a design action is permissible only if it satisfies public safety, competence limits, legal codes, and full disclosure of conflicts of interest.

Factor of safety n = material strength ÷ working stress; design is acceptable when n exceeds the value specified by the governing code.

Beam bending: bending stress σ = My/I, with maximum stress at the greatest distance y from the neutral axis; second moment I depends on section geometry.

Truss analysis by method of joints: at any joint ΣFx = 0 and ΣFy = 0; a statically determinate truss satisfies m = 2j − 3.

First law of thermodynamics for a closed system: Q − W = ΔU; for a steady-flow open system Q − W = Δh + ΔKE + ΔPE.

Thermal efficiency of a heat engine η = W_net ÷ Q_in = 1 − Q_out/Q_in; Carnot limit η = 1 − T_cold/T_hot in kelvin.

Three-phase power P = √3 · V_L · I_L · cos φ, where cos φ is the power factor and V_L, I_L are line quantities.

Stress–strain interpretation: proportional limit marks the end of linearity, yield point marks permanent set, ultimate strength marks peak stress before necking.

Measurement rule: instrument resolution sets reading precision; uncertainty of a single reading is typically ±half the smallest division, and repeated readings reduce random error by 1/√n.

Material selection rule: compare strength-to-density ratio σ/ρ when weight is constrained and stiffness-to-density ratio E/ρ when deflection is constrained.