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Angular Velocity: Encyclopedia - Angular Velocity
The angular velocity of a point particle or rigid body describes the rate at which its orientation changes. It is analogous to translatio...
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Weber-fechner Law: Encyclopedia - Weber-fechner Law
The Weber–Fechner law attempts to describe the relationship between the physical magnitudes of stimuli and the perceived intensity of t...
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Coordinate System: Encyclopedia - Coordinate System
See Cartesian coordinate system or Coordinates (mathematics) for a more elementary introduction to this topic.
In mathematics as applied ...
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Displacement: Encyclopedia - Displacement
The term displacement can have one of several meanings, depending on context:
Displacement (distance), a physical quantity in kinematics...
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Intensive Quantity: Encyclopedia Ii - Intensive Quantity - Joining Systems
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....
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Luminous Energy: Encyclopedia Ii - Luminous Energy - Units
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 ot...
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Noether's Theorem: Encyclopedia Ii - Noether's Theorem - Explanation
The word "symmetry" in the previous paragraph really means the covariance of the form that a physical law takes with respect to a one-dim...
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Weber-fechner Law: Encyclopedia Ii - Weber-fechner Law - The Case Of Weight
In one of his classic experiments, Weber gradually increased the weight that a blindfolded man was holding and asked him to respond when ...
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Pseudoscalar: Encyclopedia Ii - Pseudoscalar - Scalar In Physics
In physics, a pseudoscalar denotes a physical quantity analogous to scalar. Both are physical quantities which assume a single value whic...
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Scientific Notation: Encyclopedia Ii - Scientific Notation - Motivation
Scientific notation is a very convenient way to write large or small numbers. It also quickly conveys two properties of a measurement tha...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Theoretical Models
Heat capacity - Gas phase.
According to the equipartition theorem from classical statistical mechanics, for a system made up of indepen...
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Permittivity: Encyclopedia Ii - Permittivity - Permittivity In Media
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 ca...
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Logarithmic Scale: Encyclopedia Ii - Logarithmic Scale - Graphic Representation
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 ...
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Dot Product: Encyclopedia Ii - Dot Product - Geometric Interpretation
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 ...
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Coordinate System: Encyclopedia Ii - Coordinate System - Transformations
A coordinate transformation is a conversion from one system to another, to describe the same space.
With every bijection from the space t...
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Extensive Quantity: Encyclopedia Ii - Extensive Quantity - Combined Extensive Quantities
If a set of parameters {ai} are intensive quantities and another set {Aj} are extensive quantities, then the function F({ai},{Aj}) is an ...
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Angular Velocity: Encyclopedia Ii - Angular Velocity - Vector Angular Velocity.
Angular velocity is the vector physical quantity that represents the process of rotation (change of orientation) that occurs at an instan...
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Coordinate System: Encyclopedia Ii - Coordinate System - Examples
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
r...
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Dot Product: Encyclopedia Ii - Dot Product - The Dot Product In Physics
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 an...
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Weber-fechner Law: Encyclopedia Ii - Weber-fechner Law - Background
Stevens' power law is generally considered to provide a more accurate and/or general description, although both the Weber–Fechner law a...
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Weber-fechner Law: Encyclopedia Ii - Weber-fechner Law - Economics
In 1889, the Austrian economist Friedrich Wieser, in "Natural Value," coined the phrase marginal utility for a closely-related phenomenon...
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Scientific Notation: Encyclopedia Ii - Scientific Notation - Using Scientific Notation
Scientific notation - Converting.
Multiplication and division by 10 are easy to perform both with the mantissa and with the exponential...
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Scientific Notation: Encyclopedia Ii - Scientific Notation - Description
In scientific notation numbers are written as where the exponent b is an integer and a is any real number. The number represented by a i...
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Permittivity: Encyclopedia Ii - Permittivity - Permittivity Measurements
The dielectric constant of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated ...
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Angular Velocity: Encyclopedia Ii - Angular Velocity - The Non-circular Motion Case
If the motion of a particle is described by a position vector-valued function r(t) — with respect to a fixed origin — then the angula...
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Weber-fechner Law: Encyclopedia Ii - Weber-fechner Law - A Non-fechnerian Interpretation Of Weber's Results
In 1890, the American psychologist William James described Fechner's writings on the subject of Weber's results as "patient whimsies" and...
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Permittivity: Encyclopedia Ii - Permittivity - Vacuum Permittivity
The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity, (also called dielectric constant...
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Intensive Quantity: Encyclopedia Ii - Intensive Quantity - Combined Intensive Quantities
If a set of parameters, {ai}, are intensive quantities and another set, {Aj}, are extensive quantities, then the function F({ai},{Aj}) is...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Definition
Heat capacity is mathematically defined as the ratio of a small amount of heat δQ added to the body to the corresponding small increase ...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Heat Capacity At Absolute Zero
From the definition of entropy
we can calculate the absolute entropy by integrating from zero temperature to the final temperature Tf
...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Dimensionless Heat Capacity
The dimensionless heat capacity of a material is
where
C is the heat capacity of a body made of the material in question (J·K−1)
n...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Specific Heat Capacity
The specific heat capacity of a material is
which in the absence of phase transitions is equivalent to
C is the heat capacity of a...
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Dot Product: Encyclopedia Ii - Dot Product - Proof Of The Geometric Interpretation
Note: This proof is shown for 3-dimensional vectors, but is readily extendable to n-dimensional vectors.
Consider a vector
Repeated ap...
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Dot Product: Encyclopedia Ii - Dot Product - Generalization
The inner product generalizes the dot product to abstract vector spaces, it is normally denoted by <a, b>. Due to the geometric int...
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Heat Capacity: Encyclopedia Ii - Heat Capacity - Heat Capacity Of Compressible Bodies
The state of a simple compressible body with fixed mass is described by two thermodynamic parameters such as temperature T and pressure P...
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Permittivity: Encyclopedia Ii - Permittivity - Explanation
In electromagnetism one can define an electric displacement field D, which represents how an electric field E will influence the organiza...
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Noether's Theorem: Encyclopedia Ii - Noether's Theorem - Applications
The formal statement of the theorem derives an expression for the physical quantity that is conserved — and hence also defines it (actu...
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Noether's Theorem: Encyclopedia Ii - Noether's Theorem - Mathematical Statement Of The Theorem
Informally, Noether's theorem can be stated as (technical fine points aside):
To every differentiable symmetry generated by local action...
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Dot Product: Encyclopedia Ii - Dot Product - Properties
The following properties hold if a, b, and c are vectors and r is a scalar.
The dot product is commutative:
The dot product is bilinea...
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