1.1. The Big Idea http://www.ck12.org
1.1 The Big Idea
Units identify what a specific number refers to. For instance, the number 42 can be used to represent 42 miles, 42
pounds, or 42 elephants! Numbers aremathematicalobjects, but units give themphysicalmeaning. Keeping track
of units can help you avoid mistakes when you work out problems.
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- Every answer to a physics problem must include units. Even if a problem explicitly asks for a speed in meters
per second (m/s), the answer is 5 m/s, not 5. - When you’re not sure how to approach a problem, you can often get insight by considering how to obtain
the units of the desired result by combining the units of the given variables. For instance, if you are given a
distance (in meters) and a time (in hours), the only way to obtain units of speed (meters/hour) is to divide the
distance by the time. This is a simple example of a method calleddimensional analysis, which can be used to
find equations that govern various physical situations without any knowledge of the phenomena themselves. - This textbook usesSI units(La Système International d’Unités), the most modern form of the metric system.
- When converting speeds from metric to American units, remember the following rule of thumb: a speed
measured in mi/hr is about double the value measured in m/s (i.e.,10 {m/s} is equal to about 20 MPH).
Remember that the speed itself hasn’t changed, just our representation of the speed in a certain set of units. - If a unit is named after a person, it is capitalized. So you write “10 Newtons,” or “10 N,” but “10 meters,” or
“10 m.” - Vectors are arrows that represent quantities with direction. In this textbook, vectors will be written in bold.
For instance, the force vector will be written asFin this textbook. Your teacher will likely use~Fto represent
vectors. Don’t let this confuse you:~Frepresents the same concept asF.
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