Dimensional Analysis (AQA A-Level Further Maths): Flashcards

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Dimensional Analysis
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Dimensional analysis

Technique examining relationships between physical quantities

Three fundamental dimensions

M (Mass), L (Length), T (Time)

Notation for dimensions

Square brackets: [quantity][quantity] in terms of M, L, T

Dimensions of speed

LT1LT^{-1}

Dimensionless quantities

Pure numbers and angles (in radians)

Dimensions of energy

ML2T2ML^2T^{-2}

Dimensional consistency

All added/subtracted terms have identical dimensions

Dimensions of acceleration

LT2LT^{-2}

Limitation of dimensional consistency

Can't prove formula correct, only show if it's wrong

Building formulas strategy

Assume form with unknown powers, equate & solve dimensions

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