2290:"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
2090:
759:
1941:, 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.
1379:
772:
2023:, 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
1885:
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1914:
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
1429:
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 (−)
1999:
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
1319:
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
1697:
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1944:
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.
1351:
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
113:
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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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1880:{\displaystyle F=\left({\begin{array}{cc}f_{00}&...&f_{0j}\\f_{01}&...&f_{1j}\\...&...&...\\f_{i0}&...&f_{ij}\\\end{array}}\right)}
1686:{\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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1425:= 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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1297:(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
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1441:(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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1492:{\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
2208:(6th ed.) Hoboken, N.J.: John Wiley & Sons, 2007; p. 23.
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of a body resides. The position of the point relative to the
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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
108:{\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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2124:. Chicago: The University of Chicago Press. p.
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1433:In vector format, the moment can be defined as the
1356:of the force. This rotational tendency is known as
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1386:The magnitude of the moment of a force at a point
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2319:Beer, F.P.; Johnston Jr, E.R.; Eisenberg (2009).
870:is the total of the forces acting on the system,
34:. For the concept in exploration geophysics, see
2716:
2157:. New York: Cambridge University Press. p.
2321:Vector Mechanics for Engineers: Statics, 9th Ed
2277:
2180:(2nd ed.). Heidelberg: Springer. p.
1954:Theoria motus corporum solidorum seu rigidorum
1390:, is equal to the perpendicular distance from
1240:{\displaystyle {\textbf {F}}=m{\textbf {a}}=0}
949:{\displaystyle {\textbf {F}}=m{\textbf {a}}\,}
2392:
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2341:Encyclopedia of the History of Arabic Science
2338:Morelon, Régis; Rashed, Roshdi, eds. (1996),
2337:
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797:
1398:, multiplied by the magnitude of the force:
1247:(the 'first condition for equilibrium') and
2310:Beer, F.P. & Johnston Jr, E.R. (1992).
2385:
2371:
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790:
1126:is the moment of inertia of the mass and
945:
2229:
2115:
2041:. It has many important applications in
1905:
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1279:{\displaystyle {\textbf {M}}=I\alpha =0}
1075:{\displaystyle {\textbf {M}}=I\alpha =0}
2234:Engineering Mechanics: Statics, 12th Ed
2204:Meriam, James L., and L. Glenn Kraige.
1382:Diagram of the moment arm of a force F.
1373:
823:that is concerned with the analysis of
14:
2717:
2583:Atomic, molecular, and optical physics
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2238:. New Jersey: Pearson Prentice Hall.
2176:Geometry : our cultural heritage
2171:
2148:
1892:
486:Newton's law of universal gravitation
2258:
2165:
1995:on which a body lies determines its
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914:is the acceleration of the system,
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467:Mechanics of planar particle motion
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2312:Statics and Mechanics of Materials
30:For the concept in economics, see
25:
2736:
2358:
2120:The Beginnings of Western Science
1915:directions are equal to zero. An
1366:). Moment is also referred to as
2088:
1195:{\displaystyle {\textbf {M}}=0.}
771:
770:
757:
90:
2704:Timeline of physics discoveries
2153:A History of Natural Philosophy
1959:
1021:{\displaystyle {\textbf {F}}=0}
991:{\displaystyle {\textbf {a}}=0}
2252:
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2211:
2198:
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2109:
1948:The concept was introduced by
1043:acting on the system leads to
890:is the mass of the system and
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1:
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1304:
1099:{\displaystyle {\textbf {M}}}
960:quantity, i.e. one with both
907:{\displaystyle {\textbf {a}}}
863:{\displaystyle {\textbf {F}}}
393:Koopman–von Neumann mechanics
2261:Vector Statics For Engineers
2037:in 1647 and became known as
835:that does not experience an
461:Non-inertial reference frame
7:
2668:Quantum information science
2116:Lindberg, David C. (1992).
2064:
1437:between the radius vector,
956:(the bold font indicates a
388:Appell's equation of motion
258:Inertial frame of reference
10:
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2499:Classical electromagnetism
2344:, vol. 3, Routledge,
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29:
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2285:Morelon & Rashed 1996
2007:
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1394:to the line of action of
1165:{\displaystyle \alpha =0}
2605:Condensed matter physics
2259:Beer, Ferdinand (2004).
2230:Hibbeler, R. C. (2010).
2102:
1935:In classical mechanics,
1309:
1204:Together, the equations
551:Rotating reference frame
383:Hamilton–Jacobi equation
45:Not to be confused with
1172:, it is also true that
1139:{\displaystyle \alpha }
843:with its environment.
492:Newton's laws of motion
352:Newton's laws of motion
2689:Nobel Prize in Physics
2551:Relativistic mechanics
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2149:Grant, Edward (2007).
1975:structural engineering
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226:D'Alembert's principle
109:
38:. For other uses, see
2694:Philosophy of physics
2288:
2287:, pp. 614–642):
2218:Engineering Mechanics
2206:Engineering Mechanics
2172:Holme, Audun (2010).
1980:Strength of materials
1906:Equilibrium equations
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361:Analytical mechanics
117:Second law of motion
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2628:Atmospheric physics
2467:Classical mechanics
2395:branches of physics
2314:. McGraw-Hill, Inc.
1419:= the force applied
916:Newton's second law
839:, but rather is in
821:classical mechanics
448:Harmonic oscillator
426:Equations of motion
61:Classical mechanics
55:Part of a series on
32:Comparative statics
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1912:static equilibrium
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2648:Materials science
2615:Interdisciplinary
2573:Quantum mechanics
2330:978-0-07-352923-3
2245:978-0-13-607790-9
2191:978-3-642-14440-0
1985:center of gravity
1952:in his 1765 book
1938:moment of inertia
1931:Moment of inertia
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1119:{\displaystyle I}
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556:Centripetal force
512:Euler's equations
497:Relative velocity
273:Moment of inertia
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133:Timeline
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36:Static
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