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In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.
A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol. Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit, defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as rad = m/m. Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.
The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, a quantity proportional to the number of elementary entities of a substance. One mole contains exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) expressed in mol-1. The value was chosen on the basis of the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of 12C, which made the mass of a mole of a compound expressed in grams, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 revision of the SI, the numerical equivalence is now only approximate but may be assumed for all practical purposes.
The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI), but is accepted for use alongside the SI.
The dalton or unified atomic mass unit is a unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.
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 Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann.
A base unit of measurement is a unit of measurement adopted for a base quantity. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. The SI base units, or Systéme International d'unités, consists of the metre, kilogram, second, ampere, kelvin, mole and candela.
The becquerel is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as an activity of one decay per second. For applications relating to human health this is a small quantity, and SI multiples of the unit are commonly used.
In physics, angular frequency, also called angular speed and angular rate, is a scalar measure of the angle rate or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function . Angular frequency is the magnitude of the pseudovector quantity angular velocity.
Relative atomic mass, also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant is defined as being 1/12 of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 revision of the SI.
IEC 60027 is a technical international standard for letter symbols published by the International Electrotechnical Commission (IEC), comprising the following parts:
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.
A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants.
The joule-second is the unit of action and of angular momentum in the International System of Units (SI) equal to the product of an SI derived unit, the joule (J), and an SI base unit, the second (s). The joule-second is a unit of action or of angular momentum. The joule-second also appears in quantum mechanics within the definition of the Planck constant. Angular momentum is the product of an object's moment of inertia, in units of kg⋅m2 and its angular velocity in units of rad⋅s−1. This product of moment of inertia and angular velocity yields kg⋅m2⋅s−1 or the joule-second. The Planck constant represents the energy of a wave, in units of joule, divided by the frequency of that wave, in units of s−1. This quotient of energy and frequency also yields the joule-second (J⋅s).
In mathematics and physics, vector is a term that refers to quantities that cannot be expressed by a single number, or to elements of some vector spaces. They have to be expressed by both magnitude and direction.
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.
The Joint Committee for Guides in Metrology (JCGM) is an organization in Sèvres that prepared the Guide to the Expression of Uncertainty in Measurement (GUM) and the International Vocabulary of Metrology (VIM). The JCGM assumed responsibility for these two documents from the ISO Technical Advisory Group 4 (TAG4).
References
- 1 2 de Boer, J. (1995), "On the History of Quantity Calculus and the International System", Metrologia , 31 (6): 405–429, Bibcode:1995Metro..31..405D, doi:10.1088/0026-1394/31/6/001
- ↑ Fourier, Joseph (1822), Théorie analytique de la chaleur
- ↑ Maxwell, J. C. (1873), A Treatise on Electricity and Magnetism, Oxford: Oxford University Press, hdl: 2027/uc1.l0065867749
- ↑ A. Majhi (2022). "A logico-linguistic inquiry into the foundations of physics: Part 1". Axiomathes. 32: 153–198. arXiv: 2110.03514 . doi:10.1007/s10516-021-09593-0.
- ↑ Emerson, W.H. (2008), "On quantity calculus and units of measurement", Metrologia , 45 (2): 134–138, Bibcode:2008Metro..45..134E, doi:10.1088/0026-1394/45/2/002
- ↑ Johansson, I. (2010), "Metrological thinking needs the notions of parametric quantities, units and dimensions", Metrologia , 47 (3): 219–230, Bibcode:2010Metro..47..219J, doi:10.1088/0026-1394/47/3/012