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Physical Measures & Unit Systems


Last Update: February 24, 2005

shameless self-promotion: DWIII

Contents:
Introduction
Mechanical Units of Measurement
Unit Systems
Numeric Relations
JavaScript Tools
Links
Other Stuff
Disclaimers

Introduction:
The number of measurement units that have been devised and utilized throughout history is, quite frankly, enormous. The purpose of this page is to attempt to bring a bit of order to chaos, by providing basic information and techniques for comparing and inter-converting physical quantities from unit to unit, and from system to system.

Before the development of theoretical physics, virtually all measurement units concerned only the quantities of length, mass (given as "weight"), time, area, and volume (a.k.a. capacity, liquid or dry). For each of these quantities (which were usually considered basic), a sort of hierarchy congealed, in which units were conceived as "chunk-ed"... that is, built out of multiples of smaller units, and with each size of unit often specialized for some specific use. And, of course, many countries had developed their own unit systems independently.

The introduction of the Metric System in the late 18th century was a step in the right direction: a uniform system of clearly defined units of measurement that were not a priori tailored to any specific culture or application, and would thus be universally applicable. However, in the following century, what with the rise of theoretical physics (thermodynamics, electromagnetism, etc.), new units were continually invented to express other such quantities as the need arose, regardless of whether or not those units were reasonably compatible with the older (traditional) units or the newer (metric) units, or even with each other.

Well, to make an exceedingly long story short, the concept of "intra-system unit coherency" eventually caught on. Thus arose the MKS system (meter, kilogram, second), the CGS system (centimeter, gram, second), and the USCS system (foot, pound_force, second). The MKS system (as modified by additional base units) was officially adopted by SI (System International) and is currently the international standard in scientific work. CGS, although popular with astronomers of the past century or so, appears to be on the decline. As for USCS (not to be confused with the hodge-podge of English units that is still used by us stubborn Americans in our everyday lives, for some reason), it is sort of a contrivancy, and often introduced in physics text as an example of a coherent system with an alternate set of base quantities (length, force, time).

(to be continued...)



Mechanical Units of Measurement:

Note: Each physical quantity is accompanied by a vector (x,y,z), which is a representation of its dimensional breakdown in terms of length, mass, and time. In SI, this corresponds to mxkgysz. Click an entry in the following tables for a list of units for that quantity, sorted by size.



Density
(-3,1,0)










Mass
(0,1,0)





Rotational
inertia
(2,1,0)





Sound
impedance
(-2,1,-1)


Viscosity
(-1,1,-1)






Momentum
(1,1,-1)

Angular
momentum
(2,1,-1)





"Weight"
density
(-2,1,-2)


Pressure
(-1,1,-2)

Surface
tension
(0,1,-2)


Force
(1,1,-2)


Energy
(2,1,-2)









Spectral
Radiancy
(-1,1,-3)


Irradiance
(0,1,-3)


Yank
(1,1,-3)


Power
(2,1,-3)













Time
(0,0,1)













Fuel
Efficiency
(-2,0,0)

Wave
number
(-1,0,0)

Pure
numbers
(0,0,0)


Length
(1,0,0)


Area
(2,0,0)


Volume
(3,0,0)










Frequency
(0,0,-1)


Velocity
(1,0,-1)

Kinematic
viscosity
(2,0,-1)

Volumetric
flow
(3,0,-1)














Acceleration
(1,0,-2)

Specific
energy
(2,0,-2)


















Jerk
(1,0,-3)












Unit Systems:
SI Units & Dimensions:
Base units: Length (meter), Mass (kilogram), Time (second), Current (ampere), Temperature (kelvin), Amount of substance (mole), Luminous intensity (candela).
CGS Units & Dimensions:
Base units: Length (centimeter), Mass (gram), Time (second).
USCS Units & Dimensions:
Base units: Length (foot), Force (pound_f), Time (second).
Planck Units & Dimensions:
Base units: Speed of light (c), Gravitational constant (G), Planck constant (hbar).

Numeric Relations:
Definitions of Units
Metric Prefixes
Conversion Factors

JavaScript Tools:
Determinant of a Matrix
Matrix Inverter
Factorization Machine

Links:

International System of Units from NIST
An explanation of all the official units of SI, including the history of their development.
The International System of Units, by Robert A. Nelson
A detailed history of the formulation & adoption of SI.
Fundamental Physical Constants from NIST
Probably the best source for the most recently established values of the universal physical constants (as of 2002).
Units of Measurement
An alphabetical listing of virtually all units ever used in physics, plus many obscure ones from around the world, compiled by Russ Rowlett (University of NC). Not for the faint of heart...
ConvertIt.com
(?)


Other stuff:

UNDER CONSTRUCTION...


Disclaimers:
The information presented here is, to the best of my knowledge, reasonably accurate. If you happen to spot any specific errors or malfunctions, please feel free to e-mail me at dwiiiandspam@aol.com. Any material on this site may be used for public or private purposes, but it sure would be nice if you could credit the author, who worked his @$$ off doing the necessary research. Use only as directed. Do not exceed recommended dosage. Keep this product away from small pets and open flames. If a strange, inexplicable rash develops, discontinue use and consult your doctor. Do not read this while operating heavy equipment. Machine wash warm, tumble dry only. Do not take these disclaimers seriously. Slippery when wet. Caution: small print may cause eye strain. Close cover before striking. Do not taunt Happy Fun Ball. Void where prohibited. May not be kosher in your state of residence; check with local bylaws and zoning restrictions.