Equilibrium Equations
Equilibrium Equations - Related Videos
01:30
Equations of Equilibrium in Three Dimensions
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2023
When analyzing structures or systems at rest, it is necessary to ensure they are in equilibrium. This is where the vector and scalar equations of equilibrium come into play. These equations are crucial in ensuring a structure is stable and will not collapse or fall apart. The vector and scalar equations of equilibrium provide a framework for analyzing the forces acting on a body. According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...
01:31
Alternative Sets of Equilibrium Equations
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2025
When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately. One example of such a situation can be observed in a...
02:56
Free Energy and Equilibrium
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2020
The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium). Recall that Q is the numerical value of the mass action expression...
09:05
Equilibrium and Free-body Diagrams
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2023
Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA Equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this...
02:05
Calculating Equilibrium Concentrations
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2020
Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect. A more...
FAQs
Equilibrium equations separate two independent requirements: the net external force must vanish, and the net torque must vanish. The first condition addresses translation, while the second addresses rotation. Checking both prevents an analysis from overlooking a possible motion mode, which is especially important when a loaded object is supported at multiple locations or subject to forces applied at different positions.
Taking torques about any chosen point provides a way to express rotational balance without changing the physical requirement. The selected reference point can organize the equation around the available force locations and support reactions. Because the torque sum must be zero about any point, this check tests whether the loading arrangement can produce rotational acceleration, not merely whether forces cancel.
An object can satisfy force and torque balance under specified loads, while the equations describe the balance conditions for that configuration. Their direct use is to identify whether translational and rotational accelerations are absent in the stated arrangement. This makes them a foundation for evaluating whether a structure or machine can maintain stability under its specified loads.
A practical workflow begins by representing the external loads acting on the object or structure, then writing the force-balance and torque-balance relationships. Solving those relationships gives the unknown quantities, such as support reactions. The resulting values can then be used to examine the specified static configuration and determine whether the system remains consistent with the assumed loading.
When applied loads and the system configuration are specified, equilibrium equations can determine support reactions and help evaluate stresses. The force and torque relationships connect the known loading arrangement to these unknown mechanical quantities. This allows an analysis to quantify how supports participate in maintaining the configuration and to assess loading within a structure or machine.
They are applied to static configurations in structures, machines, and other physical systems. In these settings, the equations connect specified external loading with unknown support reactions and stresses, allowing analysts to assess whether the arrangement can remain balanced. Their role is particularly important when evaluating structural or mechanical systems under stated loads and support conditions.