Dimensions & Dimensional Analysis — A/L Physics

What must I remember about Dimensions & Dimensional Analysis?

• Dimensions of Fundamental Quantities: Mass [M], Length [L], Time [T], Current [I], Temperature [θ].
• Principle of Dimensional Homogeneity: An equation is physically meaningful and dimensionally correct only if every additive term on both sides has identical dimensions.
• Applications of Dimensional Analysis: 1) Checking correctness of equations; 2) Deriving relationships between physical quantities up to dimensionless constants; 3) Converting units between systems.
• Limitations of Dimensional Analysis: Cannot determine numerical dimensionless proportionality constants; cannot handle trigonometric, logarithmic, or exponential arguments which must be dimensionless.

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1. Core Dimensions to memorize

   Force = [M L T⁻²], Work/Energy = [M L² T⁻²], Power = [M L² T⁻³], Pressure = [M L⁻¹ T⁻²], Viscosity η = [M L⁻¹ T⁻¹], Surface Tension γ = [M T⁻²].

2. Dimensionless quantities

   Strain (ΔL/L), Refractive index, Relative density, Reynolds number, Angle (rad = arc/radius) all have dimension [M⁰ L⁰ T⁰] = 1.

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Must know

• Dimensional correctness is a necessary but INSUFFICIENT condition for physical truth (e.g., s = ut + at² is dimensionally homogeneous but physically wrong by a factor of 1/2).

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 1: Measurement

What should I study first?

What comes next?

Next in the syllabus

Where does Dimensions & Dimensional Analysis fit in the syllabus?

Unit 1.3 · Year 1 · Term 1