Measurement

Dimension A qualitative description of a physical quantity in terms of fundamental base quantities (mass, length, time, etc.). Dimensions are not numbers or units; they represent the nature of the quantity. For example, velocity has dimensions of length per time, regardless of whether it is measured in m/s or km/h. Dimensional Formula An expression showing how a physical quantity relates to the base dimensions. Written as [Mᵃ Lᵇ Tᶜ Iᵈ Θᵉ Nᶠ Jᵍ], where exponents are integers or fractions. For example, force has [M L T⁻²] because it depends on mass, length, and time (acceleration). This formula is unique for each quantity. Dimensional Analysis A technique to check the consistency of equations, derive relationships, and convert units using dimensions. The principle of dimensional homogeneity states that every term in a physically valid equation must have the same dimensions. For example, in s = ut + (1)/(2)at² , both sides have dimension [L] (length). If dimensions mismatch, the equation is wrong.