Mechanical equilibrium

An object resting on a surface and the corresponding free body diagram showing the forces acting on the object. The normal force N is equal, opposite, and collinear to the gravitational force mg so the net force and moment is zero. Consequently, the object is in a state of static mechanical equilibrium.

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.^[1]^: 39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.^[1]^: 45–46^[2]

In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent.

In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant.
In terms of velocity, the system is in equilibrium if velocity is constant. * In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero.^[2]

More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero.

If a particle in equilibrium has zero velocity, that particle is in static equilibrium.^[3]^[4] Since all particles in equilibrium have constant velocity, it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.

^ ^a ^b John L Synge & Byron A Griffith (1949). Principles of Mechanics (2nd ed.). McGraw-Hill.
^ ^a ^b Beer FP, Johnston ER, Mazurek DF, Cornell PJ, and Eisenberg, ER (2009). Vector Mechanics for Engineers: Statics and Dynamics (9th ed.). McGraw-Hill. p. 158.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Herbert Charles Corben & Philip Stehle (1994). Classical Mechanics (Reprint of 1960 second ed.). Courier Dover Publications. p. 113. ISBN 0-486-68063-0.
^ Lakshmana C. Rao; J. Lakshminarasimhan; Raju Sethuraman; Srinivasan M. Sivakumar (2004). Engineering Mechanics. PHI Learning Pvt. Ltd. p. 6. ISBN 81-203-2189-8.

[Synge-1] John L Synge & Byron A Griffith (1949). Principles of Mechanics (2nd ed.). McGraw-Hill.

[beer-2] Beer FP, Johnston ER, Mazurek DF, Cornell PJ, and Eisenberg, ER (2009). Vector Mechanics for Engineers: Statics and Dynamics (9th ed.). McGraw-Hill. p. 158.{{cite book}}: CS1 maint: multiple names: authors list (link)

[Stehle-3] Herbert Charles Corben & Philip Stehle (1994). Classical Mechanics (Reprint of 1960 second ed.). Courier Dover Publications. p. 113. ISBN 0-486-68063-0.

[Rao-4] Lakshmana C. Rao; J. Lakshminarasimhan; Raju Sethuraman; Srinivasan M. Sivakumar (2004). Engineering Mechanics. PHI Learning Pvt. Ltd. p. 6. ISBN 81-203-2189-8.

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