NationMaster - Encyclopedia: Inertial frame of reference

An inertial frame of reference, or inertial reference frame, is one in which Newton's first and second laws of motion are valid. In other words, a reference frame that is neither rotating nor accelerating. Image File history File links No higher resolution available. ... This article is about inertia as it applies to local motion. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—i.e. in a straight line and at constant speed. Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... In physics, force is anything that can cause a massive body to accelerate. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... Rest in physics and in the technical sense of geometric mensuration denotes a particular relation between a pair of observers. ... This article does not cite any references or sources. ...

1 Equivalence of inertial reference frames
2 Inertial frames in classical mechanics
3 Einstein's theory of special relativity
4 Einstein’s general theory of relativity
5 See also
6 External links
7 References

Equivalence of inertial reference frames

A fundamental principle of all physics is the equivalence of inertial reference frames. In practical terms, this equivalence means that scientists within an enclosed box moving uniformly cannot determine their velocity by any experiment done exclusively inside the box.

By contrast, bodies are subject to so-called fictitious forces in non-inertial reference frames; that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames. Therefore, scientists within a box that is being rotated or otherwise accelerated (except by gravity) can measure their acceleration and angular velocity by observing the motion of an un-restrained body inside the box. A fictitious force is an apparent force that acts on all masses in a non-inertial frame of reference, e. ... In theoretical physics, a common coordinate system or frame of reference, that refers to a non-inertial state of motion can be referred to as a noninertial frame (as opposed to an inertial frame). ... In physics, force is anything that can cause a massive body to accelerate. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... Centrifugal force (from Latin centrum centre and fugere to flee) is a term which may refer to two different forces which are related to rotation. ... In physics, the Coriolis effect is an inertial force first described by Gaspard-Gustave Coriolis, a French scientist, in 1835. ... A rotating frame of reference is a coordinate system that describes how physics appears when measured against a hypothetical network of rigid rulers extending from a rotating body. ... Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...

Inertial frames in classical mechanics

Classical mechanics assumes the equivalence of all inertial reference frames, and makes one additional assumption, namely, that time flows at the same rate in all reference frames. This corresponds to Newton's concepts of absolute space and absolute time. Given these two assumptions, the coordinates of the same event (a point in space and time) described in two inertial reference frames are related by a Galilean transformation Classical mechanics (also called Newtonian mechanics) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... In physics, the notion of absolute space underlies the laws of classical physics of Isaac Newton. ... The absolute time is a hypothetical time that either runs at the same rate for all the observers in the universe or the rate of time of each observer can be scaled to the absolute time by multiplying the rate by a constant. ... The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. ...

$mathbf{r}^{prime} = mathbf{r} - mathbf{r}_{0} - mathbf{v} t$

$t^{prime} = t - t_{0}$

where $mathbf{r}_{0}$ and $t 0$ represent shifts in the origin of space and time, and $mathbf{v}$ is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time between two events ( $t 2 - t 1$ ) is the same for all inertial reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, $left| mathbf{r}_{2} - mathbf{r}_{1} right|$ ) is also the same. The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... Distance is a numerical description of how far apart objects are at any given moment in time. ...

Einstein's theory of special relativity

Einstein's theory of special relativity likewise assumes the equivalence of all inertial reference frames, but makes a different additional assumption, namely, that the speed of light is the same when measured in all inertial reference frames. This second assumption leads to counter-intuitive effects that have been verified experimentally, including: â€œEinsteinâ€ redirects here. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... â€œLightspeedâ€ redirects here. ...

time dilation (moving clocks tick more slowly)
length contraction (moving objects are shortened in the direction of motion)
relativity of simultaneity (simultaneous events in one reference frame are not simultaneous in almost all frames moving relative to the first).

These effects are expressed mathematically by the Lorentz transformation Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ... Length contraction, according to Albert Einsteins special theory of relativity, is the decrease in length experienced by people or objects traveling at a substantial fraction of the speed of light. ... The relativity of simultaneity is the dependence of the notion of simultaneity on the observer. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ...

$x^{prime} = gamma left(x - v t right)$

$y^{prime} = y$

$z^{prime} = z$

$t^{prime} = gamma left(t - frac{v x}{c^{2}}right)$

where shifts in origin have been ignored, the relative velocity is assumed to be in the $x$ -direction and the factor $γ$ is defined

$gamma stackrel{mathrm{def}}{=} frac{1}{sqrt{1 - v^2/c^2}} = frac{c}{sqrt{c^2 - v^2}} ge 1$

The Lorentz transformation is equivalent to the Galilean transformation in the limit $c rightarrow infty$ or, equivalently, $v rightarrow 0$ (low speeds). The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. ...

Under Lorentz transformations, the time and distance between events may differ among inertial reference frames; however, the Lorentz scalar distance $s 2$ between two events is the same in all inertial reference frames A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ... In physics a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. ...

$s^{2} = left( x_{2} - x_{1} right)^{2} + left( y_{2} - y_{1} right)^{2} + left( z_{2} - z_{1} right)^{2} - c^{2} left(t_{2} - t_{1}right)^{2}$

where $c$ is the speed of light. From this perspective, the speed of light is only accidentally a property of light, and is rather a property of spacetime, a conversion factor between conventional time units (such as seconds) and length units (such as meters). â€œLightspeedâ€ redirects here. ... This article does not cite any references or sources. ... For other uses of this term, see Spacetime (disambiguation). ... Conversion of units refers to conversion factors between different units of measurement for the same quantity. ... Look up second in Wiktionary, the free dictionary. ... â€¹ The template below (Unit of length) is being considered for deletion. ...

Einstein’s general theory of relativity

Einstein’s general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Euclidean geometry with a curved non-Euclidean metric. In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity. For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry describes hyperbolic, elliptic and absolute geometry, which are contrasted with Euclidean geometry. ... In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ... In differential geometry, the geodesic deviation equation is an equation involving the Riemann curvature tensor, which measures the change in separation of neighbouring geodesics. ...

However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a “local theory”. (However, this refers to the theory’s application rather than to its derivation.)

External links

Stanford Encyclopedia of Philosophy entry

References

Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics, 2nd ed. (Freeman, NY, 1992)
Albert Einstein, Relativity, the special and the general theories, 15th ed. (1954)
Henri Poincaré, (1900) "La theorie de Lorentz et la Principe de Reaction", Archives Neerlandaises, V, 253–78.

Categories: Frames of reference | Classical mechanics | Introductory physics | Relativity | Astrodynamics John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ... â€œEinsteinâ€ redirects here. ... Jules TuPac Henri PoincarÃ© (April 29, 1854 â€“ July 17, 1912) (IPA: [][1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ...

Results from FactBites:

NationMaster - Encyclopedia: Inertial reference frame (667 words)
	In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force.
	Frames of reference are especially important in special relativity, because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another reference frame.
	An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g.

Inertial frame of reference - Biocrawler (976 words)
	All reference frames that move with constant velocity and in a constant direction with respect to any inertial frame of reference are members of the group of inertial reference frames.
	The group of inertial frames of reference is the only group of frames of reference in which the same laws of motion hold.
	Special relativity not only identified the Lorentz transformations as the appropriate transformations between inertial frames of reference, it also brought the perception that the 'laws holding good' for all members of the group of inertial frames of reference also includes the laws of electrodynamics, not just the laws of kinematics.

More results at FactBites »

COMMENTARY

Share your thoughts, questions and commentary here

Want to know more?
Search encyclopedia, statistics and forums:

Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 0825, y

Contents

Equivalence of inertial reference frames GA_googleFillSlot("encyclopedia_square");