A Bit About Units

For the most part in science we use the metric system. The cool thing about the metric system is that it is based on the number 10. Why is it cool you ask (it is like I can hear you)? Well, if you think about it we are base 10 beings (10 fingers. 10 toes). The thing about the metric system is that we have all of the prefixes that are associated with the powers of 10. So how does this relate to physics…

In Physics we build all of our metric system based units off of some fundamental quantities. All other units will result in the mathematical combination of our units for time, length, and mass. The base units we use for these are seconds, meters, and kilograms. There are other fundamental quantities (http://physics.suite101.com/article.cfm physical_fundamental_quantities).

As we move throughout the course we will always need to be conscious of the units our values have. The reason for this is that when we add or subtract values they need to have the same units, not just same type of quantity (you cannot subtract 25m and 150cm). When we multiply or divide units, we will end up with derived units. You need to be conscious of making sure all lengths are in m, times are in s, masses are in kg.

If you do not “mind your units” you will end up with answers that are going to be off by factors of 10 or worse.

So what are we to do if we are given values that do not have the appropriate units? We use the factor label method for unit conversions. This method will work for fundamental quantities as well as derive quantities (http://en.wikipedia.org/wiki/Units_conversion_by_factor-label).

Example:

Convert 15 miles/hr into m/s

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You will notice in the use of conversion factors above, we do not use decimals. I always ask myself which quantity is larger. Then how many of the smaller ones make up one of the big ones. You also need to notice how the units cancel out. Units will obey the same mathematical operations that numbers do. So, to get rid of something in the numerator of the units, it must be in the denominator of the conversion factor.

It is also worth pointing out in my example that I went right from hours to seconds. You can go from hours to minutes, and then minutes to seconds. As we move on throughout the year, it will be important for you to memorize some of the more common conversion factors.

The factor label method can also be used to convert from cm to m or from grams to kg. However, it takes more time that moving the decimal left or right.