차원의 동차성
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정의
물리적으로 유효한 방정식의 모든 항이 동일한 차원을 가져야 하며, 서로 다른 종류의 양이 더해지거나 등치될 수 없다는 요건.
설명
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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