S0.2 Units
- Physics restricts itself to what is measurable in principle.
- Measurement is comparison with established unit.
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Examples
meter, second, kilogram, joule
- Units are interdependent.
Example


Example
joule=kilogram⋅meter2/second2
- Units are defined through practical standards.
- Interdependence of units limits number of necessary standards.
Example


Example
We don’t need a standard for ‘joule’
- Accepted system of units and standards:
Systeme Internationale
- Failure to abide by the rules can be
very expensive
- Precision of standards evolves with and for science.
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
Mv2 | has units | kg⋅(m⋅s-1)2=kg⋅m2s-2 |
| | |
Mgh | has units | kg⋅m⋅s-2⋅m=kg⋅m2s-2 |
| | |
 | is ‘unitless’ | (dimensionless) |
| | |
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}} $](mastermathpng-1.png)
Example


Example
Contrast the equations
 | |  |
units match | | units do not match |
…consistent | | …WRONG! |
Learning Resources
Textbook:
| HRW Chapter 1 |
Self-Test Questions: | |