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Measurements

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Interested in more information on measurements? You can also read A Brief History of Measurements, practice conversions with The Conversions Page, or learn more about the metric system and the U.S. congress in Go Metric! Think Metric!.

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Previously Asked Questions

Q:   "In SI system there is a clear distinction between units of mass (1 kg) and unit of force (1 N=1 kg x m/s2).  In "English" system of units there is only one unit (lb) for both.  If basic Newton's formula is F= m x a in SI system we say 1 N=1 kg x m/s2, but if we claim the same to be valid for English system 1 lb=1 lb x 1, which means acceleration is dimensionless unit (a = 1), then there is something wrong.  How is this possible?  I suppose this has something to do with definition of this (lb) unit.

A:  The pound is a very old measurement unit.  Its name derives from the Roman phrase "libra pondo" (hence the abbreviation "lb" and the name "pound") meaning a "pound of weight".  The Saxon pound was the oldest standard in England until it was replaced by Henry VIII with the Troy pound in 1527.  (Incidentally, the new pound, on which the minting process was based, was 6.25% heavier than the Saxon pound, meaning that Henry could collect more taxes.)  Before the advent of the metric system, all the countries in western Europe used similar pound units, divided into either 12 or 16 ounces.  The unit currently used in the United States is the avoirdupois pound, from the French phrase "avoir du poids" meaning "goods of weight".  This phrase indicates that the goods being sold were sold by weight and not by item (mass) or volume.  By international agreement, one avoirdupois pound is equal 453.59237 grams. 

The pound was around long before Galileo Galilei (1564 - 1642), Isaac Newton (1642 - 1727) or Johannes Kepler (1571 - 1630).  Therefore, it predates the discovery of the gravitational force.  So, traditional measurements of a "pound" had no clear distinction between a unit of force and a unit of mass.  (Weight and mass were not yet divorced from each other.)  This is why there is confusion between "pound mass" (a unit of mass) and "pound force" (a unit of force or weight).  Ideally the "pound mass" should be abbreviated lbm and the "pound force" lbf to reduce confusion.  The U.S. pound has officially been defined as a fraction of a kilogram (the SI-metric standard for mass) since 1889; it is therefore a mass.

The "pound force" is simply the gravitational force experienced at Earth's surface by a mass of one pound.  To compute this force, we use Newton's Second Law which states: "The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."  This law leads to the equations:

a = Fnet / m      or    Fnet = m a

A one pound mass = 1 lbm.  The average acceleration of gravity on Earth's surface expressed in "English" units is 32.2 feet/second2.  The "pound force" is thus 32.2 lbm X ft / sec2.   (1 lbf = 32.2 lbm X ft / sec2).

For the SI metric units, one pound mass is 0.45 kilogram and the acceleration of gravity averages 9.8 meters/second2 at Earth's surface.  This means 1 lbf =  (1 lbf X 9.8 m/s2) = (0.45 kg X 9.8 m/s2) = 4.41 N.  (The "Newton", symbol "N", is the metric unit for force: 1 N = 1 kg m/s2.)

Q:      What is a unit?

A:      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.

Example: The meter is exactly 1.0 units of length, whereas a millimeter is 10-3 units of length.

Q:      What is a standard?

A:     A standard is reference to which all other quantities of the same type are compared. 

Example: The meter is the SI Systems standard for length.   When we talk about a kilometer, a centimeter, or any other SI unit of length we are referencing these to the standard meter.

Q:     What is a conversion factor?

A:     A conversion factor is a ration of one unit to another.  It is used to convert between units.  It is always equal to 1. 
(Note: because it is equal to 1 the numerator and denominator can be flipped and it will still be 1.  This is helpful in canceling units.)

Example:  The conversion factor for feet to meters is equ1.gif (1095 bytes).  So to convert 12 feet to meters you would multiply 12 feet by the conversion factor and cross out the feet.  This leaves meters.  Like this:

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Try the Conversions Page to practice converting between SI and non standard units

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References

Prefixes for SI Units

Factor Prefix Symbol
1024 yotta- Y
1021 zetta- Z
1018 exa- E
1015 peta- P
1012 tera- T
109 giga- G
106 mega- M
103 kilo- k
102 hecto- h
101 deka- da
Factor Prefix Symbol
10-24 yocto- y
10-21 zepto- z
10-18 atto- a
10-15 femto- f
10-12 pico- p
10-9 nano- n
10-6 micro- µ
10-3 milli- m
10-2 centi- c
10-1 deci d

 

The Basic SI Units

Quantity Unit Symbol Definition
Length meter m The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.
Mass kilogram kg The kilogram is equal to the mass of the international prototype of the kilogram.
Time second s The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
Electric current ampere A The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per meter of length.
Thermodynamic temperature kelvin K The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Amount of substance mole mol The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.
Luminous intensity candela cd The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian

 

Derived SI Units

Quantity

SI derived unit

Name in terms of other units... Expression in terms of SI base units
plane angle radian (a) rad   m·m-1 = 1 (b)
solid angle steradian (a) sr (c)   m2·m-2 = 1 (b)
frequency hertz Hz   s-1
force newton N J/m m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C   s·A
electric potential difference, electromotive force volt V W/A m2·kg·s-3·A-1 = J/(A·s)
capacitance farad F C/V m-2·kg-1·s4·A2
electric resistance ohm W V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2 = 1/W
magnetic flux weber Wb V·s m2· kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2· kg·s-2·A-2
Celsius temperature degree Celsius(d) °C   K - 273.15
luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
activity (referred to a radionuclide) becquerel Bq   s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2
dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent, organ equivalent dose sievert Sv J/kg m2·s-2
(a) The radian and steradian may be used with advantage in expressions for derived units to distinguish between quantities of different nature but the same dimension.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the name steradian and the symbol sr are usually retained in expressions for units.
(d) This unit may be used in combination with SI prefixes, e.g. millidegree Celsius, m°C.

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Mechanics List of Topics

Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of
Rigid Bodies
Elasticity
Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical
Oscillations
Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves
Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy
and Work
Circular Motion of Point-Mass Objects Equilibrium Sound

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