"Power (physics) In physics, power is the rate of doing work or transferring heat, the amount of energy transferred or converted per unit time. Having no direction, it is a scalar quantity. In the International System of Units, the unit of power is the joule per second (J/s), known as the watt in honour of James Watt, the eighteenth-century developer of the condenser steam engine. Another common and traditional measure is horsepower (comparing to the power of a horse). Being the rate of work, the equation for power can be written: As a physical concept, power requires both a change"
"Dimensionless quantity In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. It is also known as a bare number or pure number or a quantity of dimension one and the corresponding unit of measurement in the SI is one (or 1) unit and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This"
"Dimensionless physical constant In physics, a dimensionless physical constant, sometimes called a fundamental physical constant, is a physical constant that is dimensionless. It has no units attached and has a numerical value that is independent of the system of units used. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of . The term ""fundamental physical constant"" is often used to refer to the dimensionless constants, but has also been used (primarily by NIST and CODATA) to refer to certain universal dimensioned physical constants, such as the speed of light ""c"", vacuum permittivity ""ε"", Planck"
"Magnitude (mathematics) In mathematics, magnitude is the size of a mathematical object, a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs. The Greeks distinguished between several types of magnitude, including: They proved that the first two could not be the same, or even isomorphic systems of magnitude. They did not consider negative magnitudes to be meaningful, and ""magnitude"" is still chiefly used in contexts in which zero is"
"tensors, pseudotensors and curvilinear coordinates. For an introduction based on the example of particles following circular orbits about a large mass, nonrelativistic and relativistic treatments are given in, respectively, Newtonian motivations for general relativity and Theoretical motivation for general relativity. In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A vector is what is needed to ""carry"" the point to the point ; the Latin word ""vector"" means ""one who carries"". The magnitude"
"Physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum ""c"", the gravitational constant ""G"", the Planck constant ""h"", the electric constant ""ε"", and the elementary charge ""e"". Physical constants can take many dimensional forms: the speed"
"and that the ten kilogram block has a volume of one cubic foot, then it can be deduced that the twenty kilogram block has a volume of two cubic feet. The concept of size is often applied to ideas that have no physical reality. In mathematics, magnitude is the size of a mathematical object, which is an abstract object with no concrete existence. Magnitude is a property by which the object can be compared as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects"
"consider a spinless particle, for which it turns out that the mixing can be specified by some arbitrary choice of gauge θ(""x""), where an angle θ = 0° represents 100% A and 0% B, θ = 90° means 0% A and 100% B, and intermediate angles represent mixtures. According to the principles of quantum mechanics, particles do not actually have trajectories through space. Motion can only be described in terms of waves, and the momentum ""p"" of an individual particle is related to its wavelength λ by ""p"" = ""h""/""λ"". In terms of empirical measurements, the wavelength can only be"
"Massless particle In particle physics, a massless particle is an elementary particle whose invariant mass is zero. The two known massless particles are both gauge bosons: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, gluons are never observed as free particles, since they are confined within hadrons. Neutrinos were originally thought to be massless. However, because neutrinos change flavor as they travel, at least two of the types of neutrinos must have mass. The discovery of this phenomenon, known as neutrino oscillation, led to Canadian scientist Arthur B. McDonald and Japanese scientist Takaaki Kajita"
"Magnitude (astronomy) In astronomy, magnitude is a unitless measure of the brightness of an object in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus. The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. The brighter an object appears, the lower the"
"""covariant"". A third concept related to covariance and contravariance is invariance. An example of a physical observable that does not change with a change of scale on the reference axes is the mass of a particle, which has units of mass (that is, no units of distance). The single, scalar value of mass is independent of changes to the scale of the reference axes and consequently is called ""invariant"". Under more general changes in basis: Curvilinear coordinate systems, such as cylindrical or spherical coordinates, are often used in physical and geometric problems. Associated with any coordinate system is a natural"
"Singularity (mathematics) In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. For example, the real function has a singularity at ""x"" = 0, where it seems to ""explode"" to ±∞ and is not defined. The function ""g""(""x"") = |""x""| (see absolute value) also has a singularity at ""x"" = 0, since it is not differentiable there. The algebraic curve defined by formula_2 in the (""x"", ""y"") coordinate system has a singularity"
"direction as their momentum are called ""right-handed"" and otherwise they are called ""left-handed"". When a particle is massless, the direction of its momentum relative to its spin is frame independent, while for massive particles it is possible to 'overtake' the particle by a Lorentz transformation flipping the helicity. Chirality is a technical property (defined through the transformation behaviour under the Poincaré group) that agrees with helicity for (approximately) massless particles and is still well defined for massive particles. In many quantum field theories, such as quantum electrodynamics and quantum chromodynamics, left- and right-handed fermions are identical. However, the Standard Model's"
"either derive their values from the mathematics of the theory, or accept their values as empirical. Dimensionless physical constant In physics, a dimensionless physical constant, sometimes called a fundamental physical constant, is a physical constant that is dimensionless. It has no units attached and has a numerical value that is independent of the system of units used. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of . The term ""fundamental physical constant"" is often used to refer to the dimensionless constants, but has also been used (primarily by NIST and CODATA) to refer to"
"motion is a two-dimensional vector (because it excludes the component in the direction of the line of sight) and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion is due north, 90 degrees meaning the motion is due east, and so on), and the second quantity is the motion's magnitude, typically expressed in arcseconds per year (symbol arcsec/yr, as/yr) or milliarcsecond per year (mas/yr). Proper motion may alternatively be defined by the angular changes per year in"
"motion. The first use of ""momentum"" in its proper mathematical sense is not clear but by the time of Jenning's ""Miscellanea"" in 1721, five years before the final edition of Newton's ""Principia Mathematica"", momentum or ""quantity of motion"" was being defined for students as ""a rectangle"", the product of and , where is ""quantity of material"" and is ""velocity"", . Momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If is"
"that has a dimensionless value of approximately 10. Other dimensionless constants are the measure of homogeneity in the universe, denoted by ""Q"" which is explained below by Martin Rees, the baryon mass per photon, the cold dark matter mass per photon and the neutrino mass per photon. Barrow and Tipler (1986) anchor their broad-ranging discussion of astrophysics, cosmology, quantum physics, teleology, and the anthropic principle in the fine structure constant, the proton-to-electron mass ratio (which they, along with Barrow (2002), call β), and the coupling constants for the strong force and gravitation. Martin Rees, in his book ""Just Six Numbers"","
"identity, also known as ""Lagrange's formula"" may be remembered as ""BAC minus CAB"", keeping in mind which vectors are dotted together. This formula finds application in simplifying vector calculations in physics. In physics, vector 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, independent of the coordinate system. Examples include: For vectors with complex entries, using the given definition of the dot"
"Angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a system remains constant unless acted on by an external torque. In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector p = ""m""v. This definition can be applied to each point in continua like solids or fluids, or physical"
"is a geometric object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction that the arrow points. The magnitude of a vector a is denoted by formula_7. The dot product of two Euclidean vectors a and b is defined by where is the angle between a and b. In particular, if a and b are orthogonal (the angle between vectors is 90°) then due to formula_9 At the other extreme, if they are codirectional, then the angle between them is 0° and"
"G-factor (physics) A g""-factor (also called g"" value or dimensionless magnetic moment) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or nucleus. It is essentially a proportionality constant that relates the observed magnetic moment ""μ"" of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton. The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by where μ is the spin magnetic moment of the particle, ""g"" is"
"missing particle. In those cases when the momentum along one direction cannot be measured (i.e. in the case of a neutrino, whose presence is only inferred from the missing energy) the Transverse mass is used. In a two-particle collision (or a two-particle decay) the square of the invariant mass (in natural units) is The invariant mass of a system made of two massless particles whose momenta form an angle formula_8 has a convenient expression: In particle collider experiments, one often defines the angular position of a particle in terms of an azimuthal angle formula_9 and pseudorapidity formula_10. Additionally the transverse"
"a given application), deviations from Newtonian mechanics become apparent and can be quantified by using the Parameterized post-Newtonian formalism. In that case, General relativity (GR) becomes applicable. However, until now there is no theory of Quantum gravity unifying GR and QFT in the sense that it could be used when objects become extremely small and heavy.[4][5] In special relativity, the momentum of a particle is given by where ""m"" is the particle's rest mass, v its velocity, ""v"" is the modulus of v, and ""c"" is the speed of light. If ""v"" is very small compared to ""c"", ""v""/""c"" is"
"some of the light. Furthermore, many people find it counter-intuitive that a high magnitude star is dimmer than a low magnitude star. Magnitude (astronomy) In astronomy, magnitude is a unitless measure of the brightness of an object in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus. The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example,"
"and magnitudes are constants. The magnitude of the acceleration of an object is the magnitude |A| of its acceleration vector. It is a scalar quantity: A relative position vector is a vector that defines the position of one point relative to another. It is the difference in position of the two points. The position of one point ""A"" relative to another point ""B"" is simply the difference between their positions formula_23 which is the difference between the components of their position vectors. If point ""A"" has position components formula_24 If point ""B"" has position components formula_25 then the position of"
"about that axis (using the right-hand rule to determine direction). This entity is called an axis-angle. Despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded and in this case commutativity appears. Several ways to describe angular displacement exist, like rotation matrices or Euler angles. See charts on SO(3) for others. Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix."
"Momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If is an object's mass and is the velocity (also a vector), then the momentum is In SI units, it is measured in kilogram meters per second (kg⋅m/s). Newton's second law of motion states that a body's rate of change in momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial"
"as a redshift and analyze the effect in terms of scenarios (b) or (d). In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = ""mv"". It is a ""conserved"" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that"
"Motion (physics) In physics, motion is a change in position of an object over time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, time, and speed. Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame. If the position of a body is not changing with respect to a given frame of reference (reference point), the body is said to be ""at rest"", ""motionless"", ""immobile"", ""stationary"", or to have constant (time-invariant) position. An object's motion cannot change unless it"
"mathematical properties of invariance in tensor mathematics, and are frequently used in electromagnetism, special relativity, and general relativity. Invariant (physics) In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation. In the current era, the immobility of Polaris (the North Star) under the diurnal motion of the celestial sphere is a classical illustration of physical invariance. Another example of a physical invariant is the speed of light under a Lorentz transformation and time under a Galilean transformation. Such spacetime transformations represent shifts between the reference frames of different observers. By Noether's"
"in numeric quantities, usually measurements, by a factor of 10—that is, a difference of one digit in the location of the decimal point. Magnitude (mathematics) In mathematics, magnitude is the size of a mathematical object, a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs. The Greeks distinguished between several types of magnitude, including: They proved that the first two could not be the same, or even isomorphic systems"
"their center of gravity, an example later raised by Albert Einstein in his development of general relativity. A more recent form of these objections was made by Ernst Mach. Mach's principle proposes that mechanics is entirely about relative motion of bodies and, in particular, mass is an expression of such relative motion. So, for example, a single particle in a universe with no other bodies would have zero mass. According to Mach, Newton's examples simply illustrate relative rotation of spheres and the bulk of the universe. When, accordingly, we say that a body preserves unchanged its direction and velocity ""in"
"algebra, we retain only first order terms, so formula_9. Since there is no acceleration in the formula_10 or formula_11 direction due to a displacement in the radial direction, the other radial terms are zero: formula_12. Similarly, we can compare the gravitational force on two nearby observers lying at the same radius formula_13 but displaced by an (infinitesimal) distance ""h"" in the formula_10 or formula_11 direction. Using some elementary trigonometry and the small angle approximation, we find that the force vectors differ by a vector tangent to the sphere which has magnitude By using the small angle approximation, we have ignored"