H1 Physics 8867 · objective lesson
SI units, prefixes and homogeneity
Convert prefixes explicitly and use base dimensions to reject inhomogeneous equations; homogeneity alone cannot prove a model.
Repair the common break
Common misconception: Matching dimensions proves a physical equation is correct.
Correct model: Convert prefixes explicitly and use base dimensions to reject inhomogeneous equations; homogeneity alone cannot prove a model.
Worked transfer
For P = kρAv³, [ρAv³] = (M L⁻³)(L²)(L³ T⁻³) = M L² T⁻³, the dimensions of power. Therefore k is dimensionless; this consistency check supports, but does not prove, the model.
Guided practice
Explain why “Matching dimensions proves a physical equation is correct.” fails. Then construct one example that correctly applies si units, prefixes and homogeneity.
Independent practice
A proposed drag-power model is P = CρAr²v³. Determine the dimensions of C and decide whether the expression can represent power.
Return to the recorded repair plan when the explanation and application are secure enough to re-test.