Quantity Equation in Coherent Units

Q

How should a physical quantity equation be expressed?

✍: FYIcenter.com

A

A physical quantity equation should be expressed with quantities in coherent units to avoid conversion factors.

The following equation assumes that v, v and v are in SI coherent units:

     v = d 
      /
      t 
where
    v is the velocity in m/s
    d is the distance in m
    t is the time in s

The following equation has coherent units specified explicitly:

<math> <msub><mrow> <mo>{</mo> <mi>v</mi> <mo>}</mo>
  </mrow> <mrow> <mi mathvariant="normal">m</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">s</mi>
  </mrow> </msub> <mo>=</mo> 
  <msub><mrow> <mo>{</mo> <mi>d</mi> <mo>}</mo>
  </mrow> <mi mathvariant="normal">m</mi></msub>
  <mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
  <msub><mrow> <mo>{</mo> <mi>t</mi> <mo>}</mo>
  </mrow> <mi mathvariant="normal">s</mi></msub> </math>
      { v }
        m
      /
      s
        = 
       { d }
       m
      /
       { t }
       s 

If we change the velocity unit to km/h, the same equation will have a conversion factor:

<math> <msub><mrow> <mo>{</mo> <mi>v</mi> <mo>}</mo>
  </mrow> <mrow> <mi mathvariant="normal">km</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">h</mi>
  </mrow> </msub> <mo>=</mo> <mn>3.6</mn> <mo>×</mo>
  <msub><mrow> <mo>{</mo> <mi>d</mi> <mo>}</mo>
  </mrow> <mi mathvariant="normal">m</mi></msub>
  <mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
  <msub><mrow> <mo>{</mo> <mi>t</mi> <mo>}</mo>
  </mrow> <mi mathvariant="normal">s</mi></msub> </math>
      { v }
        km
      /
      h
        = 3.6 ×
       { d }
       m
      /
       { t }
       s 

 

⇒ Numerical Value Expression

⇐ Quantity Expressed with Value and Unit

⇑ ISO/IEC 80000 - Quantities and units

⇑⇑ MathML (Mathematical Markup Language)

2026-10-28, ∼1937🔥, 0💬