# 2.3: Untitled Page 15

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## Chapter 2

necessarily used in the creation of alternate units, and this leads to complications which in turn lead to errors.

Table 2‐2. Alternate Units of Length

1 *kilo* meter (km) = 103 meter (m)

1 *deci* meter (dm) = 10‐1 m

1 *centi* meter (cm) = 10‐2 m

1 *milli* meter (mm) = 10‐3 m

1 *micro* meter (μm) = 10‐6 m

1 *nano* meter (nm) = 10‐9 m

*2.1.2 Systems of units*

If we focus our attention on the *fundamental standards* and ignore the electric charge, we can think of the SI (Système International) system as dealing with *length*, *mass* and *time* in terms of *meters*, *kilograms* and *seconds*. At one time this was known as the MKS‐system to distinguish it from the CGS‐system in which the fundamental units were expressed as *centimeters*, *grams* and *seconds*. Another well‐known system of units is referred to as the British (or English) system in which the fundamental units are expressed in terms of *feet*, *pounds‐mass*, and *seconds*. Even though there was general agreement in 1960 that the SI system was preferred, and is now required in most scientific and technological applications, one must be prepared to work with the CGS and the British system, in addition to other systems of units that are associated with specific technologies.

**2.2 Derived Units **

In addition to using some alternative units for length, time, mass and electric charge, we make use of many *derived units* in the SI system and a *few* are listed in Table 2‐3. Some derived units are sufficiently notorious so that they are named after famous scientists and represented by specific symbols. For example, the unit of kinematic viscosity is the stokes (St), named after the British mathematician Sir George G. Stokes (Rouse and Ince, 1957), while the equally important molecular and thermal diffusivities are known only by their generic names and represented by a variety of symbols. The key point to remember concerning units is that the *basic units * represented in Table 2‐1 are sufficient to describe all physical phenomena, while the *alternate units* illustrated Table 2‐2

and the *derived units* listed in Table 2‐3 are used as a matter of convenience.

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Table 2‐3. Derived SI Units

*Physical Quantity *

*Unit *( *Symbol*)

*Definition *

force

newton (N)

kg m/s2

energy

joule (J)

kg m2/s2

power

watt (W)

J/s

electrical potential

volt (V)

J/(A s)

electric resistance

ohm ()

V/A

frequency

hertz (Hz)

cycle/second

pressure

pascal (Pa)

N/m2

kinematic

stokes (St)

cm2/s

viscosity

thermal

square meter/second

m2/s

diffusivity

molecular

square meter/second

m2/s

diffusivity

While the existence of derived units is simply a matter of convenience, this *convenience* can lead to *confusion*. As an example, we consider the case of Newton’s second law which can be stated as

time rate of change

force acting

of linear momentum

(2‐5)

on a body

of the body

In terms of mathematical symbols, we express this axiom as

*d*

**f**

*m***v**

(2‐6)

*dt*

Here we adopt a nomenclature in which a lower case, boldface Roman font is used to represent *vectors* such as the force and the velocity. Force and velocity are quantities that have both *magnitude and direction* and we need a special notation to remind us of these characteristics.

Let us now think about the use of Eq. 2‐6 to calculate the force required to accelerate a mass of 7 kg at a rate of 13 m/s2. From Eq. 2‐6 we determine the magnitude of this force to be

2

2

*f*

(7 kg)(13m/s ) 91 kg m/s

(2‐7)