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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 equilibrium with its environment.
The moment of force, or torque, is a first moment: =, or, more generally, .; Similarly, angular momentum is the 1st moment of momentum: =.Momentum itself is not a moment.; The electric dipole moment is also a 1st moment: = for two opposite point charges or () for a distributed charge with charge density ().
The moment problem also extends to complex analysis as the trigonometric moment problem in which the Hankel matrices are replaced by Toeplitz matrices and the support of μ is the complex unit circle instead of the real line.
Moment arm diagram. A very useful special case, often given as the definition of torque in fields other than physics, is as follows: = (). The construction of the "moment arm" is shown in the figure to the right, along with the vectors r and F mentioned above. The problem with this definition is that it does not give the direction of the torque ...
In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure. [1] [2]
In physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies).
A more descriptive term is force couple or pure moment. Its effect is to impart angular momentum but no linear momentum. In rigid body dynamics, force couples are free vectors, meaning their effects on a body are independent of the point of application. The resultant moment of a couple is a special case of moment.
If a system is not in static equilibrium, D'Alembert showed that by introducing the acceleration terms of Newton's laws as inertia forces, this approach is generalized to define dynamic equilibrium. The result is D'Alembert's form of the principle of virtual work, which is used to derive the equations of motion for a mechanical system of rigid ...