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S0.2 Units

[A] Units and standards

[B] Rules

Key Point 0.1

When two or more physical quantities are combined, the units combine in the same way.

Example

Example

With M a mass, v a speed, h a length
Mv2has unitskg(ms-1)2=kgm2s-2
Mghhas unitskgms-2m=kgm2s-2
$\frac{Mv^2}{Mgh}$is ‘unitless’(dimensionless)
 

Key Point 0.2

Two physical quantities that are equated, added or subtracted must have the same units.

Example

Example

With M a mass, v a speed and E an energy the equation

$ E =\frac{1}{2}Mv^2 \hspace*{1cm} \mbox{implies} \hspace*{1cm} \xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{\mbox{joule} = kg \cdot m^2 s^{-2}} $

 

Example

Example

Contrast the equations

$\frac{1}{2} Mv^2 = Mgh$ $\frac{1}{2} M v^2 = Mgh^2$
units matchunits do not match
…consistent…WRONG!

 
TConsistent Units

Learning Resources

Textbook: HRW Chapter 1
Self-Test Questions: