physical quantity

The angular velocity of a point particle or rigid body describes the rate at which its orientation changes. It is analogous to translational velocity, and is defined in terms of the derivative of orientation with respect to time, just as translational velocity is the derivative of displacement with respect to time. It is customary to introduce the concept of velocity by first defining average velocity as displacement divided by time. There the analogy with angular velocity is less useful: for example, if a body is rotating at a ...

Including:

• Angular velocity - Vector angular velocity.
• Angular velocity - The non-circular motion case
• Angular velocity - Derivation

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The Weber–Fechner law attempts to describe the relationship between the physical magnitudes of stimuli and the perceived intensity of the stimuli. Ernst Heinrich Weber (1795–1878) was one of the first people to approach the study of the human response to a physical stimulus in a quantitative fashion. Gustav Theodor Fechner (1801–1887) later offered an elaborate theoretical interpretation of Weber's findings, which he called simply Weber's law, though his admirers made the law's name a hyphenate. Weber-Fechner law - ...

Including:

• Weber-Fechner law - Background
• Weber-Fechner law - The case of weight
• Weber-Fechner law - The case of vision
• Weber-Fechner law - The case of sound
• Weber-Fechner law - Economics
• Weber-Fechner law - A non-Fechnerian interpretation of Weber's results

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See Cartesian coordinate system or Coordinates (mathematics) for a more elementary introduction to this topic. In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. "Numbers" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other field. If the space or manifold is curved, it may not be possible to provide one consistent coordinate system for the entire space. In this case, a set of coordinate systems, called charts, are ...

Including:

• Coordinate system - Examples
• Coordinate system - Transformations
• Coordinate system - Singularities
• Coordinate system - Systems commonly used
• Coordinate system - Astronomical systems

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The term displacement can have one of several meanings, depending on context: Displacement (distance), a physical quantity in kinematics another term for a congruent transformation in geometry Electric displacement field, a physical quantity in electrodynamics Engine displacement, a property of an internal combustion engine Displacement (fencing) Displacement (fluid), a different physical quantity, used in fluid mechanics and navigation; used

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Let there be a system or piece of substance a of amount ma and another piece of substance b of amount mb. Let V be an intensive variable. The value of variable V corresponding to the first substance is Va, and the value of V corresponding to the second substance is Vb. If the two pieces a and b are put together, forming a piece of substance "a+b" of amount ma+b = ma+mb, then the value of their ...

See also:

Intensive quantity, Intensive quantity - Combined intensive quantities, Intensive quantity - Joining systems, Intensive quantity - Examples of intensive quantities

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The SI unit of luminous energy is the lumen second, which is unofficially known as the Talbot in honor of William Henry Fox Talbot. In other systems of units, luminous energy may be expressed in basic units of energy. ...

See also:

Luminous energy, Luminous energy - Units

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The word "symmetry" in the previous paragraph really means the covariance of the form that a physical law takes with respect to a one-dimensional Lie group of transformations which satisfies certain technical criteria. The conservation law of a physical quantity is usually expressed as a continuity equation. The most important examples of the theorem are the following: the energy is conserved if and only if the physical laws are invariant under time translations (if their form does not depend on time) the momentu ...

See also:

Noether's theorem, Noether's theorem - Explanation, Noether's theorem - Mathematical statement of the theorem, Noether's theorem - Applications, Noether's theorem - Proof, Noether's theorem - A more general and elegant proof, Noether's theorem - Example 1, Noether's theorem - Example 2, Noether's theorem - Example 3

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In one of his classic experiments, Weber gradually increased the weight that a blindfolded man was holding and asked him to respond when he first felt the increase. Weber found that the response was proportional to a relative increase in the weight. That is to say, if the weight is 1 kg, an increase of a few grams will not be noticed. Rather, when the mass is increased by a certain factor, an increase in weight is perceived. If the mass is doubled, the threshold is also doubled. This kind of relationship can be descr ...

See also:

Weber-Fechner law, Weber-Fechner law - Background, Weber-Fechner law - The case of weight, Weber-Fechner law - The case of vision, Weber-Fechner law - The case of sound, Weber-Fechner law - Economics, Weber-Fechner law - A non-Fechnerian interpretation of Weber's results

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In physics, a pseudoscalar denotes a physical quantity analogous to scalar. Both are physical quantities which assume a single value which is invariant under proper rotations. However, under the parity transformation, pseudoscalars flip their signs while scalars do not. Pseudoscalar - Examples. the scalar triple product the magnetic charge (as it is mathematically defined, ...

See also:

Pseudoscalar, Pseudoscalar - Scalar in physics, Pseudoscalar - Examples, Pseudoscalar - Scalar in abstract algebra

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Scientific notation is a very convenient way to write large or small numbers. It also quickly conveys two properties of a measurement that are useful to scientists—significant figures and order of magnitude. Scientific notation - Examples. An electron's mass is 0.00000000000000000000000000000091093826 kg. In scientific notation, it is written 9.1093826×10−31 kg. The Earth's mass is 5,973,600,000,000,000,000,000,000 kg. In scientific notation, it is written 5.9736×1024 kg. See also:

Scientific notation, Scientific notation - Description, Scientific notation - Engineering notation, Scientific notation - Exponential notation, Scientific notation - Motivation, Scientific notation - Examples, Scientific notation - Significant digits, Scientific notation - Order of magnitude, Scientific notation - Using scientific notation, Scientific notation - Converting, Scientific notation - Basic operations

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Heat capacity - Gas phase. According to the equipartition theorem from classical statistical mechanics, for a system made up of independent and quadratic degrees of freedom, any input of energy into a closed system composed of N molecules is evenly divided among the degrees of freedom available to each molecule. It can be shown that, in the classical limit of statistical mechanics, for each independent and quadratic degree of freedom, that where Ei is the mean energy (measured in ...

See also:

Heat capacity, Heat capacity - Definition, Heat capacity - Heat capacity at absolute zero, Heat capacity - Heat capacity of compressible bodies, Heat capacity - Specific heat capacity, Heat capacity - Dimensionless heat capacity, Heat capacity - Theoretical models, Heat capacity - Gas phase, Heat capacity - Solid phase

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In the common case of isotropic media, D and E are parallel vectors and is a scalar, but in general anisotropic media this is not the case and is a rank-2 tensor (causing birefringence). The permittivity and magnetic permeability μ of a medium together determine the phase velocity v of electromagnetic radiation through that medium: When an electric field is applied to a medium, a current flows. The total current flowing in a real medium is in general mad ...

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Permittivity, Permittivity - Explanation, Permittivity - Vacuum permittivity, Permittivity - Permittivity in media, Permittivity - Complex permittivity, Permittivity - Classification of materials, Permittivity - Dielectric absorption processes, Permittivity - Quantum-mechanical interpretation, Permittivity - Permittivity measurements, Permittivity - Suggested readings

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A logarithmic scale is also a graphic scale on one or both sides of a graph where a number x is printed at a distance c·log(x) from the point marked with the number 1. A slide rule has logarithmic scales, and nomograms often employ logarithmic scales. On a logarithmic scale an equal difference in order of magnitude is represented by an equal distance. The geometric mean of two numbers is midway between the numbers. Logarithmic graph paper, before the advent of computer graphics, was a basic scientific tool. Plots on paper with one log scale can show up exponenti ...

See also:

Logarithmic scale, Logarithmic scale - Graphic representation

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In the Euclidean space there is a strong relationship between the dot product and lengths and angles. For a vector a, a·a is the square of its length, and if b is another vector where a and b denote the length of a and b, and θ is the angle between them. Since a·cos(θ) is the projection of a onto b, the dot product can be understood geometrically as the ...

See also:

Dot product, Dot product - Geometric interpretation, Dot product - The dot product in physics, Dot product - Properties, Dot product - Generalization, Dot product - Proof of the geometric interpretation

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A coordinate transformation is a conversion from one system to another, to describe the same space. With every bijection from the space to itself two coordinate transformations can be associated: such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the formulas for the mapping are the inverse of those for the coordinate transformation) such that the old coordinates of the image of each point are the same as the new coordinates of the original point (the formulas for the mapping are the sa ...

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Coordinate system, Coordinate system - Examples, Coordinate system - Transformations, Coordinate system - Singularities, Coordinate system - Systems commonly used, Coordinate system - Astronomical systems

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If a set of parameters {ai} are intensive quantities and another set {Aj} are extensive quantities, then the function F({ai},{Aj}) is an extensive quantity if for all α, F({ai},{αAj}) = αF({aSee also:

Extensive quantity, Extensive quantity - Combined extensive quantities, Extensive quantity - Examples of extensive quantities

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Angular velocity is the vector physical quantity that represents the process of rotation (change of orientation) that occurs at an instant of time. For a rigid body it supplements translational velocity of the center of mass to describe the full motion. It is usually represented by the symbol omega (Ω or ω). The magnitude of the angular velocity is the angular speed (or angular frequency) and is denoted by ω. The line of direction of the angular velocity is given by the axis of rotation, and the r ...

See also:

Angular velocity, Angular velocity - Vector angular velocity., Angular velocity - The non-circular motion case, Angular velocity - Derivation

Read more here: » Angular velocity: Encyclopedia II - Angular velocity - Vector angular velocity.

An example of a coordinate system is to describe a point P in the Euclidean space Rn by an n-tuple P = (r1, ..., rn) of real numbers r1, ..., rn. These numbers r1, ..., rn are called the coordinates of the point P. If a subset S of a Euclidean space is mapped continuously onto another topological space, this defines coordinates in ...

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Coordinate system, Coordinate system - Examples, Coordinate system - Transformations, Coordinate system - Singularities, Coordinate system - Systems commonly used, Coordinate system - Astronomical systems

Read more here: » Coordinate system: Encyclopedia II - Coordinate system - Examples

In physics, for a vector a, a·a is the square of its magnitude, and if b is another vector where a and b denote the magnitude of a and b, and θ is the angle between them. In physics, magnitude is a scalar in the physical sense, i.e. a physical quantity independent of the coordinate system, expressed as the product of a numerical value and a physical unit, not just a number. The dot product is also a scalar in this sense, given by the formula, indepen ...

See also:

Dot product, Dot product - Geometric interpretation, Dot product - The dot product in physics, Dot product - Properties, Dot product - Generalization, Dot product - Proof of the geometric interpretation

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Stevens' power law is generally considered to provide a more accurate and/or general description, although both the Weber–Fechner law and Stevens' power law entail implicit assumptions regarding the measurement of perceived intensity of stimuli. In the case of the Weber–Fechner law, the implicit assumption is that just noticeable differences are additive; i.e. that they can be added in an analogous manner to the addition of units of a physical quantity. Of relevance, L. L. Thurstone made explicit this assumption in terms of the concept of discriminal dispersion ...

See also:

Weber-Fechner law, Weber-Fechner law - Background, Weber-Fechner law - The case of weight, Weber-Fechner law - The case of vision, Weber-Fechner law - The case of sound, Weber-Fechner law - Economics, Weber-Fechner law - A non-Fechnerian interpretation of Weber's results

Read more here: » Weber-Fechner law: Encyclopedia II - Weber-Fechner law - Background