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Unit symbols & use

Using units in your math

It is highly important that you attach symbols to numerical answers in Physics problems because the units change the meaning of your value significantly.

For example, let's say you get in trouble with your parents and they say you are restricted form using your phone. You ask "How long?" and they respond "5." This answer does not satisfy you, because there is a big difference between 5 minutes, 5 hours, 5 days and 5 weeks, all of which are units of time.

You should also understand that these units get altered when we perform functions like multiplication, division, and power functions (like squaring and finding the square root).

For example, we all know that when finding the area of a room 10 feet wide and 14 feet long we and up with an area of 140 square feet. The reason is because when we multiplied the number values we also multiplied the units and the result of ft x ft = ft2.

When units do not match we end up with a derived unit, which is simply a unit expressed by combining other units. You are already used to using some of these already, like miles per hour, which is a derived unit because it is a combination of 2 other units.

For example, we all know that when finding the speed of a car that travels 300 miles in 5 hours we divide 300 miles by 5 hours and we get the answer of 60 miles per hour. When we write this algebraically it will look like this:
Pro tip: Derived units will be easier to process when performing math functions if you write them in fractional form as the example answer has the mi on top and the h of the bottom of a fraction instead of writing an abbreviation like mph or using a slash notation like mi/h.

Identical units can also cancel out or be reduced through division or multiplication of fractions.

For example, when finding the amount of distance a car will travel in 5 hours if moving at an average speed of 60 mi/h we perform the following operations:

You can see that the hours in the bottom of the derived unit fraction cancel the hours in the time being multiplied and leave an approriate unit of miles for the distance.

In complex processes we will perform several operations at once and may end up with some very long-winded derived units. Can you see how the units in the end result were determined by the process shown to its left?

Unit Symbols

The following is a list of symbols for common units we may use throughout the year. There are many more units possible, but these should cover pretty much everything we need. I do not bother with common prefixes or variations (ex. I will not list feet, yards, inches or centimeters).

The following are additional units just for AP Physics 2

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