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Kind Of Quantity
A physical quantity (or simply 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 (for kilogram). Quantities that are vectors have, besides numerical value and unit, direction or orientation in space. Components Following ISO 80000-1, any value or magnitude of a physical quantity is expressed as a comparison to a unit of that quantity. The ''value'' of a physical quantity ''Z'' is expressed as the product of a ''numerical value'' (a pure number) and a unit 'Z'' :Z = \ \times /math> For example, let Z be "2 metres"; then, \ = 2 is the numerical value and = \mathrm is the unit. Conversely, the numerical value expressed in an arbitrary unit can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar (physics)
Scalar quantities or simply scalars are physical quantities that can be described by a single pure number (a ''scalar'', typically a real number), accompanied by a unit of measurement, as in "10cm" (ten centimeters). Examples of scalar are length, mass, charge, volume, and time. Scalars may represent the magnitude of physical quantities, such as speed is to velocity. Scalars do not represent a direction. Scalars are unaffected by changes to a vector space basis (i.e., a coordinate rotation) but may be affected by translations (as in relative speed). A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change. In classical physics, like Newtonian mechanics, rotations and reflections preserve scalars, while in relativity, Lorentz transformations or space-time translations preserve scalars. The term "scalar" has origin in the multiplication o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dalton (unit)
The dalton or unified atomic mass unit (symbols: Da or u, respectively) is a unit of mass defined as of the mass of an Bound state, unbound neutral atom of carbon-12 in its nuclear and electronic ground state and invariant mass, at rest. It is a Non-SI units mentioned in the SI, non-SI unit accepted for use with SI. The word "unified" emphasizes that the definition was accepted by both IUPAP and IUPAC. The atomic mass constant, denoted , is defined identically. Expressed in terms of , the atomic mass of carbon-12: . Its value in International System of Units, SI units is an experimentally determined quantity. The 2022 CODATA recommended value of the atomic mass constant expressed in the SI base unit kilogram is:This value serves as a Conversion of units, conversion factor of mass from daltons to kilograms, which can easily be converted to Gram, grams and other metric units of mass. The 2019 revision of the SI redefined the kilogram by fixing the value of the Planck constant (), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pound (mass)
The pound or pound-mass is a unit of mass used in both the British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defined as exactly , and which is divided into 16 avoirdupois ounces. The international standard symbol for the avoirdupois pound is lb; an alternative symbol (when there might otherwise be a risk of confusion with the pound-force) is lbm (for most pound definitions), # ( chiefly in the U.S.), and or ̶ (specifically for the apothecaries' pound). The unit is descended from the Roman (hence the symbol ''lb'', descended from the scribal abbreviation, '). The English word ''pound'' comes from the Roman ('the weight measured in '), and is cognate with, among others, German , Dutch , and Swedish . These units are now designated as historical and are no longer in common usage, being replaced by the metric system. Usage of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Units Of Measurement
A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually meant is 10 times the definite predetermined length called "metre". The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of System of measurement, systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system. In trade, weights and measures are often a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Théorie Analytique De La Chaleur
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre, Burgundy and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect. Biography Fourier was born in Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at the age of nine. Fourier was recommended to the Bishop of Auxerre and, through this introduction, he was educated by the Benedictine Order of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent part in his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Stress Tensor
In continuum mechanics, the Cauchy stress tensor (symbol \boldsymbol\sigma, named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration. The second order tensor consists of nine components \sigma_ and relates a unit-length direction vector e to the ''traction vector'' T(e) across an imaginary surface perpendicular to e: :\mathbf^ = \mathbf e \cdot\boldsymbol\quad \text \quad T_^= \sum_\sigma_e_i. The SI base units of both stress tensor and traction vector are newton per square metre (N/m2) or pascal (Pa), corresponding to the stress scalar. The unit vector is dimensionless. The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle for stress. The Cauchy stress tensor is used for stress analysis of mater ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics ( stress, elasticity, quantum mechanics, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called scalar (mathematics), ''scalars''. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field (mathematics), field. Vector spaces generalize Euclidean vectors, which allow modeling of Physical quantity, physical quantities (such as forces and velocity) that have not only a Magnitude (mathematics), magnitude, but also a Orientation (geometry), direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix (mathematics), matrices, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axioms
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a "logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. Non- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
