Describes dimensional analysis and explains a method for converting physical units
UnitsAlthough the MKS (Meters, Kilograms & Seconds) system is slowly becoming universal, there are actually two different systems and each is split into two variations. Happily nearly ever body uses seconds but decimal minutes are in use for specialist applications.
|MKS||Metre (m)||Kilo (K)||Second (s)||Newton|
|CGS||Centi metre (cm)||Gram (s)||Dyne|
|FPS||Foot (ft)||Pound (lb)||Second (s)||Poundal|
|F Slug S||Foot (ft)||Slug||Pound|
NOTES For those who are not used to the Imperial system.
- A Force of one pound is that force which will produce an acceleration of one foot per second squared when acting on a mass of one Slug.
- There is considerable variation in how the unit of pressure is shown, so that:
Dimensional AnalysisIn Applied Mathematics, based on Newton's three laws of motion, there are three dimensions; Mass; Length; and Time and all physical quantities can be expressed in terms of these. It is important to note that all equations must balance dimensionally and each term within the equation must have the same dimensional value.
therefore strain is dimensionless
Physical EquationsAs all terms in an equation must have the same nature. i.e.When expressed in terms of the fundamental units they must be the same. For example, in the following elementary dynamic equations, the dimensions are shown in brackets.
Conversion Between Units Of Different SystemsThe system described here is based on the idea of "Unity Brackets". For example 25.4 mm is the same length as 1 inch so we consider the following bracket as having a value of unity.
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