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Medicine: Physics: Units and dimensions

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### Units and dimensions

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

- Temperature: $\theta$

- 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.

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