Principle of dimensional homogeneity (8304)

, por F_y_Q

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What is the principle of dimensional homogeneity?

P.-S.

This principle states that equations relating physical quantities must be consistent, meaning that the same dimensions must appear on both sides of the equation. The best way to understand this is through an example.

The speed at which an object moves under the influence of acceleration is:

\color[RGB]{2,112,20}{\bm{v = v_0 + at}} (Ec. 1)

Speed is the ratio of distance to the time taken to cover it. In terms of dimensions, it is expressed as:

\color[RGB]{0,112,192}{\bm{[v] = \frac{[L]}{[t]}}}

Acceleration is the ratio of the change in speed to the time taken for that change, so it can be expressed as:

\color[RGB]{0,112,192}{\bm{[a] = \frac{[L]}{[t]^2}}}

If you apply this to equation (Eq. 1), you will have:

\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]^2}\cdot [t]\ \to\ \color[RGB]{192,0,0}{\bm{\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]}}}


As you can see, the dimensions are the same on both sides of the equation.

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