Linear density
Encyclopedia
Linear density, linear mass density or linear mass is a measure of mass
per unit of length
, and it is a characteristic of strings or other one-dimensional objects. The SI
unit of linear density is the kilogram
per metre
(kg/m). The linear density,
(sometimes denoted by λ), of an object is defined as:
where m is the mass, and x is a coordinate along the (one dimensional) object.
For the common case of a homogeneous substance of length L and total mass m, this simplifies to:
In drawing or printing, the term linear density also refers to how densely or heavily a line is drawn.
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
per unit of length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...
, and it is a characteristic of strings or other one-dimensional objects. The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
unit of linear density is the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...
per metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
(kg/m). The linear density,
(sometimes denoted by λ), of an object is defined as:where m is the mass, and x is a coordinate along the (one dimensional) object.
For the common case of a homogeneous substance of length L and total mass m, this simplifies to:
In drawing or printing, the term linear density also refers to how densely or heavily a line is drawn.
Units
Common units include:- kilogram per meter
- ounce (mass) per foot
- ounce (mass) per inch
- pound (mass) per yard: used in the North American railway industry for the linear density of railRail tracksThe track on a railway or railroad, also known as the permanent way, is the structure consisting of the rails, fasteners, sleepers and ballast , plus the underlying subgrade...
s - pound (mass) per foot
- pound (mass) per inch
- denier, a unit of measure for the linear density of fiberFiberFiber is a class of materials that are continuous filaments or are in discrete elongated pieces, similar to lengths of thread.They are very important in the biology of both plants and animals, for holding tissues together....
s, defined as the mass in grams per 9,000 meters. - decitex (dtex), the SIInternational System of UnitsThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
unit for the linear density of fiberFiberFiber is a class of materials that are continuous filaments or are in discrete elongated pieces, similar to lengths of thread.They are very important in the biology of both plants and animals, for holding tissues together....
s, defined as the mass in grams per 10,000 meters