Units as dimensions
Any value of a physical quantity Informally, a physical quantity is a physical property that can be quantified. This means it can be measured and/or calculated and expressed in numbers. For example, "weight" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pounds or newton, while "beauty" is a property is expressed as a comparison to a unit of that quantity. For example, a physical quantity Z is expressed as the product of a unit [Z] and a numerical factor:
The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. The conventions used to express quantities is referred to as quantity calculus Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. Despite the name, it is more analogous to a system of algebra than calculus in the mathemtaical sense of the term. However, units refer to actual quantities, such as the cm, and are not algebraic symbols. In formulas the unit [Z] can be treated as if it were a specific magnitude of a kind of physical dimension In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two: see dimensional analysis Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving certain physical quantities. It is routinely used by mathematicians, statisticians, physical scientists and engineers to check the plausibility of derived equations and computations. It is also used to form for more on this treatment.
A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be one metre long only at a certain temperature.
<<Table of Contents The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System of units, the modern form of the metric system. The SI has been or is in the process of | Next>> | Show All>>
