Measurement and Uncertainties establishes the foundation of physics — SI units, error analysis, and the distinction between scalars and vectors that runs through the entire course.
SI base quantities: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol), luminous intensity (cd). Derived units built from base units: e.g., N = kg m s⁻², Pa = kg m⁻¹ s⁻², J = kg m² s⁻². Homogeneity: both sides of an equation must have the same units. Estimation: ability to estimate orders of magnitude (e.g., mass of car ≈ 10³ kg).
Scalars: magnitude only (mass, temperature, energy, speed). Vectors: magnitude and direction (force, velocity, acceleration, displacement, momentum). Adding vectors: triangle/parallelogram rule, or resolve into components. Resolving: Fx = F cosθ, Fy = F sinθ. Equilibrium: resolved components sum to zero in each direction.
Systematic errors: shift all readings in one direction (e.g., zero error). Random errors: scatter readings above and below true value. Precision: how close repeated readings are to each other. Accuracy: how close to the true value. Absolute uncertainty: ±Δx. Percentage uncertainty: (Δx/x) × 100%. Combining: addition/subtraction → add absolute uncertainties. Multiplication/division → add percentage uncertainties. Powers: multiply percentage uncertainty by the power.
Systematic errors affect all measurements in the same way — they shift results consistently above or below the true value. Examples: zero error on a balance, parallax from reading at the wrong angle, a clock running fast. They affect accuracy but not precision. Random errors cause scatter in readings — some above, some below. They arise from unpredictable fluctuations in conditions or human judgement. They affect precision. Random errors can be reduced by repeating and averaging; systematic errors cannot be reduced by repeating — you must identify and correct the source.
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