Apparent force: Difference between revisions

Latest revision as of 21:29, 13 January 2024

(Also fictitious force, inertial force, transport force.) A force (mass times an acceleration) introduced on the side of an equation on which all supposedly real forces appear.

For Newton's dynamical law of motion for a body of mass m acted on by a force F,

to be valid requires that the acceleration a be specified relative to an inertial reference frame. If the acceleration in a noninertial reference frame (e.g., a rotating reference frame) is a*, then

and the previous dynamical equation may be written

where the quantity - ma_i is the inertial or apparent force and a_i is the inertial acceleration. Examples of apparent forces are the centrifugal force and the Coriolis force. Within classical (Newtonian) mechanics inertial forces are fictitious, merely masses times accelerations. But in general relativity, inertial forces are equivalent to real forces resulting from interactions between bodies because it is impossible to distinguish between inertial and gravitational accelerations; both are independent of the mass of the body.
See apparent gravity.
Symon, K. R. 1960. Mechanics. 2d ed., . p. 271.
Bergmann, P. G. 1942. Introduction to the Theory of Relativity. 155–156.

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 |Definitions={{Definition
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+|Meaning=(Also fictitious force, inertial force, transport force.) A force (mass times an [[acceleration]])  introduced on the side of an equation on which all supposedly real forces appear.
-(Also fictitious force, inertial force, transport force.) A force (mass times an [[acceleration]])  introduced on the side of an equation on which all supposedly real forces appear.<br/> For Newton's dynamical law of motion for a body of mass ''m'' acted on by a force '''F''',  <blockquote>[[File:ams2001glos-Ae23.gif|link=|center|ams2001glos-Ae23]]</blockquote> to be valid requires that the acceleration '''a''' be specified relative to an [[inertial reference frame]]. If  the acceleration in a noninertial [[reference frame]] (e.g., a rotating reference frame) is '''a'''&#x0002a;, then  <blockquote>[[File:ams2001glos-Ae24.gif|link=|center|ams2001glos-Ae24]]</blockquote> and the previous dynamical equation may be written  <blockquote>[[File:ams2001glos-Ae25.gif|link=|center|ams2001glos-Ae25]]</blockquote> where the quantity - ''m'''''a'''<sub>''i''</sub> is the inertial or apparent force and '''a'''<sub>''i''</sub> is the inertial acceleration. Examples  of apparent forces are the [[centrifugal force]] and the [[Coriolis force]]. Within classical (Newtonian)  mechanics inertial forces are fictitious, merely masses times accelerations. But in general relativity,  inertial forces are equivalent to real forces resulting from interactions between bodies because it is  impossible to distinguish between inertial and gravitational accelerations; both are independent of  the mass of the body. <br/>''See'' [[apparent gravity]].<br/> Symon, K. R. 1960. Mechanics. 2d ed., . p. 271. <br/> Bergmann, P. G. 1942. Introduction to the Theory of Relativity.  155&ndash;156.
+|Explanation=For Newton's dynamical law of motion for a body of mass ''m'' acted on by a force '''F''',  <blockquote>[[File:ams2001glos-Ae23.gif|link=|center|ams2001glos-Ae23]]</blockquote> to be valid requires that the acceleration '''a''' be specified relative to an [[inertial reference frame]]. If  the acceleration in a noninertial [[reference frame]] (e.g., a rotating reference frame) is '''a'''&#x0002a;, then  <blockquote>[[File:ams2001glos-Ae24.gif|link=|center|ams2001glos-Ae24]]</blockquote> and the previous dynamical equation may be written  <blockquote>[[File:ams2001glos-Ae25.gif|link=|center|ams2001glos-Ae25]]</blockquote> where the quantity - ''m'''''a'''<sub>''i''</sub> is the inertial or apparent force and '''a'''<sub>''i''</sub> is the inertial acceleration. Examples  of apparent forces are the [[centrifugal force]] and the [[Coriolis force]]. Within classical (Newtonian)  mechanics inertial forces are fictitious, merely masses times accelerations. But in general relativity,  inertial forces are equivalent to real forces resulting from interactions between bodies because it is  impossible to distinguish between inertial and gravitational accelerations; both are independent of  the mass of the body. <br/>''See'' [[apparent gravity]].<br/> Symon, K. R. 1960. Mechanics. 2d ed., . p. 271. <br/> Bergmann, P. G. 1942. Introduction to the Theory of Relativity.  155&ndash;156.
 }}
 }}