Basic Units and Dimensions

 

Science (from the Latin scientia) has evolved over the last 4000 years in two stages. The first serious attempt to understand the physical world and the different interactions of matter was by the Greeks, in particular the philosopher Aristotle. Aristotelian science, however, involved little or no experimentation but was developed by argument, conjecture and observation of natural behavior. Everything could be understood if enough thought was given to it. With the rising of Christianity, however, accompanied by the concept that physical phenomena need not always be what they might appear to be, experimentation was introduced and attempts were made to verify conjecture by experimental evidence. Thus, the concept of measurement was introduced and as a consequence the units by which measurements could be made had to be considered. 

 

To define any physical quantity it is necessary to express the unit in which the quantity is measured and also the number of times the quantity contains that unit. The unit selected will depend on the magnitude of the quantity. For example if length is being considered the unit may be 1 meter, which will be the same as 100 centimeter, 1000 millimeters or kilometer. There are many units that have been defined and used but three basic units of mass, length and time are, in general, considered fundamental. Physicists generally and engineers in Europe often employ the kilogram, meter, second (KMS) system, the engineers in the USA, to some extent in Australia and partly in the UK employ the pound, foot, second (FPS) system whereas chemists and biologists tend to us the centimeter, gram, second (CGS) system. There is no particular advantage to any of the three systems; each is chosen as the most convenient for the magnitude of the quantities being measured.  In fact, any measurement can be taken as fundamental such as, for example force or velocity but a standard is necessary and whereas it is easy to obtain a standard for mass, length and time (the weight of a particular platinum bar, the distance between two points on a scale or a particular fraction of the time taken for the earth to rotate) it is not so easy to set a standard for force or velocity.

 

The value of any unit depends on the value of the fundamental unit from which it is derived. Thus, taking the centimeter as the standard length, the unit of area will be the square centimeter (cm²) and the unit of volume taken as the cubic centimeter (cm³). If the inch is taken as the standard length, the unit of area will be the square inch (in²) and the unit of volume taken as the cubic inch (in³). The area and volume are, thus, said to be of 2 and 3 dimensions respectively in length.

 

If any derived unit is dependent on the (r^th) power of a fundamental unit, it is said to be of (r) dimensions in the fundamental.

Velocity is the rate of change of distance with time (i.e.) and, thus, has dimensions of +1 in length and –1 in time. In addition, acceleration is the rate of change of velocity with time (i.e. ) and, thus, has dimensions of +1 in length and –2 in time. Force, as defined by Newton’s second law, is the rate of change of momentum with time (i.e. F = ), thus, force has dimensions of +1 in mass, +1 in length and –2 in time.