Dimensional Homogeneity
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Definition
The requirement that all terms in a physically valid equation must have identical dimensions, so that quantities of different kinds are never added or equated.
Explanation
In the kinematic equation v² = u² + 2as, every term has dimensions of [length]²[time]⁻² (m²/s²): v² is (m/s)², u² is (m/s)², and 2as is (m/s²)(m) = m²/s². Adding a term in meters would violate dimensional homogeneity and expose a derivation error. This principle, formalized by Fourier in 1822, is the basis of dimensional analysis and a powerful error-checking tool.
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