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Engineering
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Base SI units used in engineering Prefixes and powers of ten in calculations Derived units used in mechanical and electrical engineering Converting between units correctly Standard form and engineering notation Significant figures and rounding in engineering answers Rearranging engineering formulae safely (with units) Checking answers using dimensional consistency Solving linear equations in engineering contexts Solving simultaneous equations for unknowns Solving quadratic equations in engineering problems Proportion, ratios and scaling for designs Using trigonometry to find missing sides and angles Resolving forces into horizontal and vertical components Sine rule and cosine rule in engineering triangles Degrees and radians conversion Arc length and sector area calculations Using vectors and components in 2D problems Understanding gradient as rate of change Differentiating basic functions for engineering rates Using differentiation to find turning points (optimisation) Integrating basic functions to find totals/areas Using integration with motion graphs (area under curve) Density, mass and volume in mechanical contexts Pressure and force relationships in engineering systems Moments and equilibrium in static systems Stress and strain: what they mean physically Young’s modulus: interpreting and using the formula Shear stress and shear strain in components Modulus of rigidity and what it tells you Factors of safety and allowable stress Linear motion with uniform acceleration (SUVAT) Newton’s laws in engineering motion problems Momentum and impulse in collisions Conservation of momentum in engineering scenarios Angular velocity and angular acceleration Centripetal acceleration and circular motion Torque, rotational power and efficiency Rotational kinetic energy and moment of inertia ideas Density and buoyancy: upthrust calculations Charge, current and time relationships Coulomb’s law and electrostatic force Electric field strength (two definitions) and use Resistance vs resistivity (what’s different) Temperature coefficient of resistance in practice Series and parallel resistor networks Ohm’s law and non-ohmic behaviour (recognising it) Electrical power equations (P=VI, I²R, V²/R) Electrical efficiency calculations Kirchhoff’s laws for circuit analysis Magnetism: fields and field lines Magnetic flux and flux density (B) Force on a current-carrying conductor (motor effect) Electromagnets: factors affecting strength Electromagnetic induction: what causes an emf Lenz’s law and direction of induced effects Alternating current waveforms and key features Peak, period, frequency and angular frequency RMS values and why they’re used Impedance and phase (conceptually) Capacitive and inductive reactance (what changes them) AC power and power factor (what it means) Resonance in RLC systems (what it looks like) Transformers: stepping voltage up/down and efficiency
