2279:"Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic approach so that two trends - statics and dynamics - turned out to be inter-related within a single science, mechanics. The combination of the dynamic approach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. Numerous experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini may be considered the beginning of the application of experimental methods in
2079:
748:
1930:, also called mass moment, rotational inertia, polar moment of inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. The symbols I and J are usually used to refer to the moment of inertia or polar moment of inertia.
1368:
761:
2012:, is the study of fluids at rest (i.e. in static equilibrium). The characteristic of any fluid at rest is that the force exerted on any particle of the fluid is the same at all points at the same depth (or altitude) within the fluid. If the net force is greater than zero the fluid will move in the direction of the resulting force. This concept was first formulated in a slightly extended form by
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1903:
of a particle is an important concept in statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three
1418:
The direction of the moment is given by the right hand rule, where counter clockwise (CCW) is out of the page, and clockwise (CW) is into the page. The moment direction may be accounted for by using a stated sign convention, such as a plus sign (+) for counterclockwise moments and a minus sign (−)
1988:
in response to external forces. If the center of gravity exists outside the foundations, then the body is unstable because there is a torque acting: any small disturbance will cause the body to fall or topple. If the center of gravity exists within the foundations, the body is stable since no net
1308:
is the action of one body on another. A force is either a push or a pull, and it tends to move a body in the direction of its action. The action of a force is characterized by its magnitude, by the direction of its action, and by its
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While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.
1340:
In addition to the tendency to move a body in the direction of its application, a force can also tend to rotate a body about an axis. The axis may be any line which neither intersects nor is parallel to the
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such as a gravitational, electric, or magnetic field and is independent of contact with any other body; an example of a body force is the weight of a body in the Earth's gravitational field.
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application of this concept is determining the tensions of up to three cables under load, for example the forces exerted on each cable of a hoist lifting an object or of
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1869:{\displaystyle F=\left({\begin{array}{cc}f_{00}&...&f_{0j}\\f_{01}&...&f_{1j}\\...&...&...\\f_{i0}&...&f_{ij}\\\end{array}}\right)}
1675:{\displaystyle r=\left({\begin{array}{cc}x_{00}&...&x_{0j}\\x_{01}&...&x_{1j}\\...&...&...\\x_{i0}&...&x_{ij}\\\end{array}}\right)}
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states that the moment of a force about any point is equal to the sum of the moments of the components of the force about the same point.
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1414:= the perpendicular distance from the axis to the line of action of the force. This perpendicular distance is called the moment arm.
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1286:(c. 287–c. 212 BC) did pioneering work in statics. Later developments in the field of statics are found in works of
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is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the
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torque acts on the body. If the center of gravity coincides with the foundations, then the body is said to be
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is produced by direct physical contact; an example is the force exerted on a body by a supporting surface. A
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for clockwise moments, or vice versa. Moments can be added together as vectors.
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The application of the assumption of zero acceleration to the summation of
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Branch of mechanics concerned with balance of forces in nonmoving systems
1430:(the vector from point O to the line of action), and the force vector,
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Mariam
Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in (
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of a body at rest: it represents an imaginary point at which all the
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1481:{\displaystyle {\textbf {M}}_{O}={\textbf {r}}\times {\textbf {F}}}
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Statics is used in the analysis of structures, for instance in
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is the angular acceleration of the system. For a system where
2197:(6th ed.) Hoboken, N.J.: John Wiley & Sons, 2007; p. 23.
1980:
of a body resides. The position of the point relative to the
2050:
were also major figures in the development of hydrostatics.
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is generated by virtue of the position of a body within a
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Forces are classified as either contact or body forces. A
97:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
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is the summation of all moments acting on the system,
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2113:. Chicago: The University of Chicago Press. p.
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1422:In vector format, the moment can be defined as the
1345:of the force. This rotational tendency is known as
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1375:The magnitude of the moment of a force at a point
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2308:Beer, F.P.; Johnston Jr, E.R.; Eisenberg (2009).
859:is the total of the forces acting on the system,
23:. For the concept in exploration geophysics, see
2146:. New York: Cambridge University Press. p.
2310:Vector Mechanics for Engineers: Statics, 9th Ed
2277:
2169:(2nd ed.). Heidelberg: Springer. p.
1943:Theoria motus corporum solidorum seu rigidorum
1379:, is equal to the perpendicular distance from
1229:{\displaystyle {\textbf {F}}=m{\textbf {a}}=0}
938:{\displaystyle {\textbf {F}}=m{\textbf {a}}\,}
2367:
2330:Encyclopedia of the History of Arabic Science
2327:Morelon, Régis; Rashed, Roshdi, eds. (1996),
2273:
786:
8:
1387:, multiplied by the magnitude of the force:
1236:(the 'first condition for equilibrium') and
2299:Beer, F.P. & Johnston Jr, E.R. (1992).
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2030:. It has many important applications in
1268:{\displaystyle {\textbf {M}}=I\alpha =0}
1064:{\displaystyle {\textbf {M}}=I\alpha =0}
2223:Engineering Mechanics: Statics, 12th Ed
2193:Meriam, James L., and L. Glenn Kraige.
2097:
1371:Diagram of the moment arm of a force F.
812:that is concerned with the analysis of
112:
48:
2572:Atomic, molecular, and optical physics
2227:. New Jersey: Pearson Prentice Hall.
2165:Geometry : our cultural heritage
475:Newton's law of universal gravitation
7:
1984:on which a body lies determines its
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903:is the acceleration of the system,
888:
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456:Mechanics of planar particle motion
64:
2301:Statics and Mechanics of Materials
19:For the concept in economics, see
14:
2109:The Beginnings of Western Science
1904:directions are equal to zero. An
1355:). Moment is also referred to as
2077:
1184:{\displaystyle {\textbf {M}}=0.}
760:
759:
746:
79:
2693:Timeline of physics discoveries
2142:A History of Natural Philosophy
1010:{\displaystyle {\textbf {F}}=0}
980:{\displaystyle {\textbf {a}}=0}
1937:The concept was introduced by
1032:acting on the system leads to
879:is the mass of the system and
1:
1088:{\displaystyle {\textbf {M}}}
949:quantity, i.e. one with both
896:{\displaystyle {\textbf {a}}}
852:{\displaystyle {\textbf {F}}}
382:Koopman–von Neumann mechanics
2250:Vector Statics For Engineers
2026:in 1647 and became known as
824:that does not experience an
450:Non-inertial reference frame
2657:Quantum information science
2105:Lindberg, David C. (1992).
1426:between the radius vector,
945:(the bold font indicates a
377:Appell's equation of motion
247:Inertial frame of reference
2730:
2488:Classical electromagnetism
2333:, vol. 3, Routledge,
33:
18:
2274:Morelon & Rashed 1996
1383:to the line of action of
1154:{\displaystyle \alpha =0}
2594:Condensed matter physics
2248:Beer, Ferdinand (2004).
2219:Hibbeler, R. C. (2010).
1924:In classical mechanics,
1193:Together, the equations
540:Rotating reference frame
372:Hamilton–Jacobi equation
34:Not to be confused with
1881:
1161:, it is also true that
1128:{\displaystyle \alpha }
832:with its environment.
481:Newton's laws of motion
341:Newton's laws of motion
2678:Nobel Prize in Physics
2540:Relativistic mechanics
2285:
2138:Grant, Edward (2007).
1964:structural engineering
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508:Simple harmonic motion
421:Euler's laws of motion
215:D'Alembert's principle
98:
27:. For other uses, see
2683:Philosophy of physics
2276:, pp. 614–642):
2207:Engineering Mechanics
2195:Engineering Mechanics
2161:Holme, Audun (2010).
1969:Strength of materials
1895:Equilibrium equations
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180:Statistical mechanics
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1363:Moment about a point
1311:point of application
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585:Angular acceleration
577:Rotational frequency
357:Lagrangian mechanics
350:Analytical mechanics
106:Second law of motion
59:
2617:Atmospheric physics
2456:Classical mechanics
2384:branches of physics
2303:. McGraw-Hill, Inc.
1408:= the force applied
905:Newton's second law
828:, but rather is in
810:classical mechanics
437:Harmonic oscillator
415:Equations of motion
50:Classical mechanics
44:Part of a series on
21:Comparative statics
2673:History of physics
1901:static equilibrium
1888:Varignon's theorem
1882:Varignon's theorem
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753:Physics portal
367:Routhian mechanics
242:Frame of reference
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2688:Physics education
2637:Materials science
2604:Interdisciplinary
2562:Quantum mechanics
2319:978-0-07-352923-3
2234:978-0-13-607790-9
2180:978-3-642-14440-0
1974:center of gravity
1941:in his 1765 book
1927:moment of inertia
1920:Moment of inertia
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1336:Moment of a force
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1108:{\displaystyle I}
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872:{\displaystyle m}
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808:is the branch of
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550:Centrifugal force
545:Centripetal force
501:Euler's equations
486:Relative velocity
262:Moment of inertia
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2493:Classical optics
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1982:foundations
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671:Clairaut
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315:Velocity
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170:Kinetics
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122:Timeline
2714:Statics
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2545:Special
2403:Applied
2209:, p. 24
2115:108-110
1396:·
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1030:moments
987:, then
806:Statics
726:Koopman
686:Poisson
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