## Units Conversion

We will

typicallymeasure distance inmeters, time inseconds, and mass inkilograms. But not always.In the lab, we might measure the speed of a cart as

v = 12.3 ^{m}/_{s}But how fast is that? Really? I think of speed in miles per hour (mi/h or mph) or, at least in kilometers per hour (km/h). Quick, what's the "conversion factor" from meters per second to kilometers per hour?

Don't memorize conversion factors!Just multiply by one.

2 = ?

2 = 2 [ ^{4}/_{4}] =^{8}/_{4}[

^{4}/_{4}]_{ }is just one; that is [^{4}/_{4}] = 1. Likewise [^{km}/_{1000 m}] is one or [^{km}/_{1000 m}] = 1 and [^{60 s}/_{min}] is one or [^{60 s}/_{min}] = 1 and [^{60 min}/_{h}] is one or [^{60 min}/_{h}] = 1 . We can use these to change our velocity of v = 12.3^{m}/_{s}to a velocity with units of^{km}/_{h}.

v = 12.3 ^{m}/_{s}

v = 12.3 ^{m}/_{s}[^{km}/_{1000 m}] [^{60 s}/_{min}] [^{60 min}/_{h}]Notice that all the units "cancel" and we are left with

^{km}in the numerator and_{h}in the denominator for^{km}/_{h},

v = 44.3 ^{km}/_{h}We can go ahead and even change this to a velocity in miles per hour,

^{mi}/_{h}. We know that

1 mi = 1.61 km so that means

[ ^{mi}/_{1.61 km}] = 1so we can can again "multiply by 'one'",

v = 44.3 ^{km}/_{h }[^{mi}/_{1.61 km}]

v = 27.5 ^{mi}/_{h}

Don't memorize conversion factors!Just multiply by "one".

Dimensional Analysis Order of Magnitude Return to Table of Contents, Ch 1 Introduction(c) Doug Davis, 2001; all rights reserved