Units and dimension
What is a physical dimension?
"What is a dimension? It is simply a tag we attach to a quantity in an equation expressing some physical law, no more." McNish, 1957. The only way to define a dimension is in terms of some physical law:" One view held at present is that the definition of a physical quantity has been given when the procedures for measuring that quantity have been given. This view is called the operational view because the definition is, at root, a set of laboratory operations leading ultimately to a number with a unit." (Halliday and Resnick, 1963)
The 7 primary dimensions of the International
System of Units (SI) and their symbols
(Thompson and Taylor, 2008):
- Length: L
- Mass: M
- Time: T
- Electric current: I
- Luminous intensity: J
- Amount of substance: N
Units and physical dimensions are different!
A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value. The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed. There is a special relationship between dimensions and units. A unit belongs to one and only one dimension. While the dimension of a unit is unique.