2.10: Measuring the World
- Page ID
- 472503
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Define mass, volume, and matter.
- Understand the relationship between mass, volume, and matter.
- Know the difference between base units and derived units.
The focus of this chapter is on movement, but sometimes knowledge of what is moving is important to completely understand the nature of the movement. Most movement that we will be studying in this course happens by objects we refer to as matter. There are several ways in which the movement of matter and the nature of that matter are related. We will investigate one of those in this chapter (force) and introduce others in later chapters. But to understand these relationships, we first must understand matter. Matter can be defined as anything that has a mass and takes up space.
Mass
The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. As we know from experience, some objects have more inertia than others. It is obviously more difficult to change the motion of a large boulder than that of a basketball, for example. The inertia of an object is measured by its mass. Roughly speaking, mass is a measure of the amount of “stuff” (or matter) in something. The mass concept will be explored in more detail when we consider Newton's Laws in the next chapter.
Volume
We have largely been ignoring the space taken up by objects so far. We have been considering the movement of objects as if they were particles. This simply means that we are not considering the size or shape of the object when we think about how it moves. There are obviously situations where this model will not work at all, but it is a good starting point to understanding motion. When we think about occupying space, we are thinking about something called volume.
We have already considered three measurements: distance, time, and mass. We have also discussed velocity, speed, and acceleration, which are all related to both distance and time. Volume is similar to these other measurements in that it is related to multiple other measurements. We can say that it is made up of other measurements. In this case, it is multiple measures of distance. Volume is a measure of the three dimensions which make up an object. These might be labeled length, width, and height in some cases. But objects have a volume whether it can be easily measured in this way or not.
Derived Units
Volume, velocity, and acceleration are all examples of what are called derived units. Derived units are things that we measure as they are related to other measurable properties, usually by the product or ratio of some other property. Derived units can be composed of other derived units. For example, acceleration is a derived unit of velocity and time. However, some properties of matter (and energy as we will later see) are not dependent upon other properties. The measure of these properties are called base units. So far we have encountered the base units of mass, length, and time. We will learn additional base units as we move through this text. We have also learned the derived units of acceleration, velocity, and volume. We will learn many, many more derived units as we move through this course. As we learn about new measurements of the world, consider what base units those measures are derived from and how they relate to other measures we have previously discussed.
Glossary
- Derived Units
- something measured about an object related to other measurable properties of that object.
- Inertia
- the property of an object to stay at rest or to remain in motion with a constant velocity.
- Mass
- a measure of the inertia of an object.
- Matter
- Any object that has mass and occupies space.
Contributors
Curated from resources found in Introduction to Physics published by OpenStax.
- Volume
- A measure of the space occupied by the three length dimensions which make up an object.