Units of measurement

Chapter 4 Units of measurement



Chapter contents



4.1 Aim 21


4.2 Units of measurement 21


4.3 SI base units 21


4.3.1 Derived SI units 22

4.3.2 Speed and velocity 23

4.3.3 Acceleration 23

4.3.4 Force 23

4.3.5 Pressure 23

4.3.6 Weight and mass 23

4.3.7 Work and energy 24

4.3.7.1 Kinetic energy 24

4.3.7.2 Potential energy 24

4.3.8 Power 24

4.3.9 Momentum 25

4.4 Units used in radiography 25


4.4.1 mA and mAs 25

4.4.2 keV 26

Further reading 26



4.1 Aim


This chapter introduces the reader to the main units that are used in measurement in radiographic science.



4.2 Units of measurement


Science has three fundamental tools that are used in its attempts to understand the external world:



1. theory


2. logic


3. experimental measurements.


Problems arise when making experimental measurements as to what quantities to measure and how to measure them. In particular, the units in which these quantities are expressed must be defined so that when two people make the same measurement they get the same results. Also, there are obvious advantages if one set of units is universally adopted as the basis for all measurements.


Each of the base units discussed in the next section relies on the appropriate standard to which each measurement is compared. Thus, there are units of standard length, standard mass, standard time interval and so on. Without such standards, no accurate measurements can be made. This in turn retards the development of adequate theories, or models, of the world.



4.3 SI base units


There are a plethora of units of measurement used throughout the world. The International System of Units (SI) attempts to replace this with seven standard units. These standards are termed SI units (see Table 4.1) and represent the fundamental measurements that we might wish to make of a body:



• What is its size? (unit of length–metre)


• How massive is it? (unit of mass–kilogram)


• How bright is it? (unit of luminous intensity–candela)


• How much electrical current flows through it? (unit of electrical current–ampere)


• How many elementary particles does it contain? (unit of amount of substance–mole)


• How hot is it? (unit of temperature–Kelvin)


• How do all the quantities vary with time? (unit of time–second)


Table 4.1 SI base units



































QUANTITY UNIT OF MEASUREMENT SYMBOL
Length Metre m
Mass Kilogram kg
Luminous intensity Candela cd
Electric current Ampere A
Amount of a substance Mole mol
Temperature Kelvin K
Time Second s

The very precise definitions of the units are not required for the rest of this text, but if you wish to see them, they are given in Appendix C.


The base units of mass, length and time are termed fundamental or base units since one or more of them is always involved in the measurement of any other quantity.


These seven SI base units may be combined to give derived units, as described in the next section.



4.3.1 Derived SI units


A number of derived SI units can be formed by the combination of the seven base units. Some of these are sufficiently important to be given their own names and they are listed in Table 4.2 and discussed in the rest of this chapter.


Table 4.2 Derived SI units and their definitions





























































Quantity DEFINITION SI UNIT SCALAR/VECTOR
Speed Distance travelled in unit time Metre per second (m.s−1) Scalar
Velocity Distance travelled in unit time in a given direction Metre per second (m.s−1) Vector
Acceleration Change of velocity in unit time Metre per second (m.s−2) Vector
Force The application of unit force to unit mass produces unit acceleration Newton (N) (kg.m.s−2) Vector
Pressure Force applied per unit area Pascal (Pa) (N.m−2) Vector
Weight Force acting on a body due to gravity Newton (N) (kg.m.s−2) Scalar
Work Product of the force acting on a body times the distance the body moves Joule (J) (n.m) Scalar
Energy Kinetic energy: work which can be done by a system because of its velocity Joule (J) Scalar
Potential energy: work which can be performed because of the position or state of a system Joule (J)
Power Rate of doing work Watt (W) (J.s−1) Scalar
Momentum Product of mass and the velocity of the body (kg.m.s−1) Vector

Further derived units are of a more specialized nature (e.g. absorbed radiation dose) and will be discussed in the specific chapters which require such measurement.



Insight


For some quantities, we can consider a body moving between two points. For certain measurements, it is important to know how far the body has travelled between the two points. In other cases, we wish to know not only how far it has travelled but also the direction it has travelled. Measurements where the direction is important are termed vector quantities whereas those where the direction is not important are known as scalar quantities.




4.3.2 Speed and velocity


The speedometer in a car is calibrated in terms of kilometres per hour (kph) or miles per hour (mph). Either of these shows that speed means distance travelled in unit time.


In SI units, speed (S), distance (d) and time (t) are related by the equation:

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Mar 6, 2016 | Posted by in GENERAL RADIOLOGY | Comments Off on Units of measurement

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