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A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "free" to move in response to forces and torques it may experience.
A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing.
The 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 ...
In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.
D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing forces of inertia which, when added to the applied forces in a system, result in dynamic equilibrium. [1] [2] D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities.
For an object to be in static equilibrium, not only must the sum of the forces be zero, but also the sum of the torques (moments) about any point. For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: Σ H = 0 and Σ V = 0 , and the torque a third equation: Σ τ = 0 .
The structure has no possible states of self-stress, i.e. internal forces in equilibrium with zero external loads are not possible. Statical indeterminacy, however, is the existence of a non-trivial (non-zero) solution to the homogeneous system of equilibrium equations. It indicates the possibility of self-stress (stress in the absence of an ...