# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [Dimensional analysis: checking ½mv²=mgh with exponent vectors and ruling out v=2gh](/en/derivations/derivation-mko-dimensional-analysis-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-dimensional-analysis)

With integer exponent vectors d(Q)=(a,b,c) over the base dimensions L, M, T: compute the dimensions of speed, acceleration and two energy expressions; decide that ½mv²=mgh is dimensionally consistent, that v=2gh is not and cannot be repaired by a pure-number constant, and that v²=4gh is consistent but wrong in the constant-acceleration model; decide that m+v cannot be added; solve E=C·m^α v^β for α=1 and β=2; and explain that equal dimensions do not mean equal unit conversion factors.

Dimensional analysis

derivation-mko-dimensional-analysis-01





1 1 results · Page 1 of 1