Editing Statics (section)

==Background==

===Force===
''[[Force]]'' 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 ''point of application'' (or ''point of contact''). Thus, force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action.<ref>Meriam, James L., and L. Glenn Kraige. ''Engineering Mechanics'' (6th ed.)  Hoboken, N.J.: John Wiley & Sons, 2007; p. 23.</ref>

Forces are classified as either contact or body forces. A [[contact force]] is produced by direct physical contact; an example is the force exerted on a body by a supporting surface. A [[body force]] is generated by virtue of the position of a body within a [[force field (physics)|force field]] 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.<ref>''Engineering Mechanics'', p. 24</ref>

===Moment of a force===
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 [[line of action]] of the force. This rotational tendency is known as ''[[moment of force]]'' ('''M'''). Moment is also referred to as ''torque''.

====Moment about a point====
[[File:Diagram of the moment arm of a force F.svg|thumb|Diagram of the moment arm of a force F.]]
The magnitude of the moment of a force at a point ''O'', is equal to the perpendicular distance from ''O'' to the line of action of ''F'', multiplied by the magnitude of the force: {{nowrap|1=''M'' = ''F'' &middot; ''d''}}, where

: ''F'' = the force applied
: ''d'' = the perpendicular distance from the axis to the line of action of the force. This perpendicular distance is called the moment arm.

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 (−) for clockwise moments, or vice versa. Moments can be added together as vectors.

In vector format, the moment can be defined as the [[cross product]] between the radius vector, '''r''' (the vector from point O to the line of action), and the force vector, '''F''':<ref>{{cite book|last=Hibbeler|first=R. C.|title=Engineering Mechanics: Statics, 12th Ed.|url=https://archive.org/details/staticsstudypack00russ|url-access=registration|year=2010|publisher=Pearson Prentice Hall|location=New Jersey|isbn=978-0-13-607790-9}}</ref>

:<math>\textbf{M}_{O}=\textbf{r} \times \textbf{F}</math>
:<math>r=\left(
\begin{array}{cc}
 x_{00} & ...  & x_{0j}\\
 x_{01} & ...  & x_{1j}\\
 ... & ... & ... \\
  x_{i0} & ...  & x_{ij}\\
 
\end{array}
\right)</math>
:<math>F=\left(
\begin{array}{cc}
 f_{00} & ...  & f_{0j}\\
 f_{01} & ...  & f_{1j}\\
 ... & ... & ... \\
  f_{i0} & ...  & f_{ij}\\
 
\end{array}
\right)</math>
:

====Varignon's theorem====
''[[Varignon's theorem (mechanics)|Varignon's theorem]]'' 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.

===Equilibrium equations===
The [[mechanical equilibrium|static equilibrium]] 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 directions are equal to zero. An [[engineering]] 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 [[guy wires]] restraining a [[hot air balloon]] to the ground.<ref>{{cite book|last=Beer|first=Ferdinand|title=Vector Statics For Engineers|publisher=McGraw Hill|year=2004|isbn=0-07-121830-0}}</ref>

===Moment of inertia===
In classical mechanics, ''[[moment of inertia]]'', 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.

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.

The concept was introduced by [[Leonhard Euler]] in his 1765 book ''Theoria motus corporum solidorum seu rigidorum''; he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.