Fundamental Quantities and Dimensions in Research

We have mentioned three quantities—length, mass, and time— with some familiar units to express these. We may at this point note that the inch, the pound, and the second used in this discus­sion are simply circumstantial, in that, being located in the United States, I have used the units familiar to the general public in this country, almost all other countries have switched to the metric system, which is also the basis for the International System of Units (SI) more commonly followed by the scientific commu­nity. These three quantities are so fundamental that all quantita­tive relations in the physical world dealing with motion and the tendencies of objects to motion—the aspect of physics known as “mechanics”—can be adequately analyzed in terms of these. To deal with all other quantitative aspects of the physical world, only four additional quantities are required: (1) temperature difference (in degrees centigrade or Fahrenheit), (2) intensity of light source (in candles), (3) electric charge (in coulombs), and (4) amount of substance (in moles). As mentioned earlier, some of the other quantities that are thus far nonmeasurable may, in the future, be made measurable, hence quantified. Besides these seven funda­mental quantities, a considerable number of derived quantities are in use; we have cited speed and density.

The statement of the magnitude of a physical quantity con­sists of two parts: a number and a unit. The height of a person can be 6 foot, not just 6. Further, it is “foot,” not “feet,” because the height is six times 1 foot, or 6 x 1 ft. If we so choose, we can also state the height in inches: 6 ft. = 6 x (1 ft.) = 6 x (1 ft x 12 in.) = 72 in. Now let us consider a derived quantity: speed. An automobile requiring 4 hours to cover a distance of 240 miles obtains an average speed: length/time = 240 mi./4 hr. = 60 mph. Here we divided one number by another to obtain sixty. Further, we performed division between the two units to obtain the newly derived unit: mph. As in the case of fundamental units dealt with before, here again, a number combined with a unit expresses the magnitude of the physical quantity, speed. The magnitude, 60 mph, if we so choose, can be expressed in other units by using the required simple computation. While dealing with physical quan­tities, whether fundamental or derived, the units should be included throughout the computation. One may cancel, multi­ply, or divide units, as if they were numbers. Suppose we want to express the speed in feet per second. Knowing that 1 mi. = 5,280 ft. and 1 hr. = 3,600 sec., we proceed as follows:

1 mph = 1 mi. + 1 hr. = [1 mi. x (5,280 ft./1 mi.)] + [1 hr. x (3,600 sec./1 hr.)]

= 5280 ft./3,600 sec.

= 1.47 ft./s

Using this new unit, the average speed, 60 mph, may now be written as

Average speed = 60 x (1 mph)

= 60 x (1.47 ft./s)

= 88.2 ft./s

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.