Editing Statics (section)

{{Short description|Branch of mechanics concerned with balance of forces in nonmoving systems}}
{{About||the concept in economics|Comparative statics|the concept in exploration geophysics|Static correction (disambiguation){{!}}Static|other uses|Static analysis}}
{{distinguish|statistics}}
{{Classical mechanics|cTopic=Branches}}

'''Statics''' is the branch of [[classical mechanics]] that is concerned with the analysis of [[force]] and [[torque]] acting on a [[physical system]] that does not experience an [[acceleration]], but rather is in [[mechanical equilibrium|equilibrium]] with its environment. 

If <math>\textbf F</math> is the total of the forces acting on the system, <math>m</math> is the mass of the system and <math>\textbf a</math> is the acceleration of the system, [[Newton's second law]] states that <math> \textbf F = m \textbf a \,</math> (the bold font indicates a [[Euclidean vector|vector]] quantity, i.e. one with both [[Magnitude (mathematics)|magnitude]] and [[Direction (geometry)|direction]]). If <math>\textbf a =0</math>, then <math> \textbf F = 0</math>. As for a system in static equilibrium, the acceleration equals zero, the system is either at rest, or its [[center of mass]] moves at constant [[velocity]]. 

The application of the assumption of zero acceleration to the summation of [[Moment (physics)|moment]]s acting on the system leads to <math> \textbf M = I \alpha  = 0</math>, where <math>\textbf M</math> is the summation of all moments acting on the system, <math>I</math> is the moment of inertia of the mass and <math>\alpha</math> is the angular acceleration of the system. For a system where <math>\alpha = 0</math>, it is also true that <math> \textbf M = 0.</math>

Together, the equations <math> \textbf F = m \textbf a = 0</math> (the 'first condition for equilibrium') and <math> \textbf M = I \alpha  = 0</math> (the 'second condition for equilibrium') can be used to solve for unknown quantities acting on the system.