Unitless in the context of "Bound vector"

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⭐ Core Definition: Unitless

Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL).

The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference.

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👉 Unitless in the context of Bound vector

In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity.It is typically formulated as the product of a unit of measurement and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction.For example, a position vector in physical space may be expressed as three Cartesian coordinates with SI unit of meters.

In physics and engineering, particularly in mechanics, a physical vector may be endowed with additional structure compared to a geometrical vector.A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. Bound vector quantities are formulated as a directed line segment, with a definite initial point besides the magnitude and direction of the main vector.For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons (describing the magnitude and direction of the force) and an accompanying two-dimensional position vector in meters (describing the point of application of the force), for a total of four numbers on the plane (and six in space).A simpler example of a bound vector is the translation vector from an initial point to an end point; in this case, the bound vector is an ordered pair of points in the same position space, with all coordinates having the same quantity dimension and unit (length and meters).A sliding vector is the combination of an ordinary vector quantity and a line of application or line of action, over which the vector quantity can be translated (without rotations).A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector.

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Unitless in the context of Relative change

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably.

Relative change is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change (relative change expressed as a percentage) called percent error occurs in measuring situations where the reference value is the accepted or actual value (perhaps theoretically determined) and the value being compared to it is experimentally determined (by measurement).

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Unitless in the context of Molecular mass

The molecular mass (m) is the mass of a given molecule, often expressed in units of daltons (Da). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The derived quantity relative molecular mass is the unitless ratio of the mass of a molecule to the atomic mass constant (which is equal to one dalton).

The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of the substance, and is expressed in grams per mole (g/mol). That makes the molar mass an average of many particles or molecules (weighted by abundance of the isotopes), and the molecular mass the mass of one specific particle or molecule. The molar mass is usually the more appropriate quantity when dealing with macroscopic (weigh-able) quantities of a substance.

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Unitless in the context of Capacity factor

The net capacity factor is the unitless ratio of actual electrical energy output over a given period of time to the theoretical maximum electrical energy output over that period. The theoretical maximum energy output of a given installation is defined as that due to its continuous operation at full nameplate capacity over the relevant period. The capacity factor can be calculated for any electricity producing installation, such as a fuel-consuming power plant or one using renewable energy, such as wind, the sun or hydro-electric installations. The average capacity factor can also be defined for any class of such installations and can be used to compare different types of electricity production.

The actual energy output during that period and the capacity factor vary greatly depending on a range of factors. The capacity factor can never exceed the availability factor, or uptime during the period. Uptime can be reduced due to, for example, reliability issues and maintenance, scheduled or unscheduled. Other factors include the design of the installation, its location, the type of electricity production and with it either the fuel being used or, for renewable energy, the local weather conditions. Additionally, the capacity factor can be subject to regulatory constraints and market forces, potentially affecting both its fuel purchase and its electricity sale.

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LINKED FROM (PARENTS)
← Relative change ← Molecular mass ← Bound vector ← Free vector ← Vector quantity ← Capacity factor
LINKS TO (CHILDREN)
Implicitly defined → Unit of measurement → Ratio → Alcohol by volume → Volumetric ratio → Unit of volume → Milliliter → 1 → Base unit of measurement → Radian → Angle → Radius →