The first and second equilibrium conditions are specified in a particular frame of reference. The first condition involves only forces and is therefore independent of the origin of the reference system. However, the second condition concerns the torque, which is defined as a cross product, where the position vector enters the equation with respect to the axis of rotation of the point where the force is applied. Therefore, the torque depends on the position of the axis in the reference system. However, if the rotational and translational equilibrium conditions apply simultaneously in one frame of reference, they also apply to any other frame of reference, so that the net torque about each axis of rotation is always zero. The explanation is quite simple. Market equilibrium conditions highlight some important implications of the implementation of the CGT proposal. First of all, the price of a CGT is always the cost difference between green and non-green electricity. This means that the GCT market is efficient in that consumers equate their social impact of purchasing green electricity with the additional cost of that electricity. Using the free body diagram, we identify the force quantities and and the corresponding lever arms and We can now explicitly write the second equilibrium condition (figure) with respect to the unknown distance x: In Eqs. (127) and (128) Ka are the equilibrium constants of the chemical reaction and aieq and ai(α)eq are the activities at equilibrium concentrations of the reactants. With the concept of standard reaction enthalpies, standard Gibbs reaction energies and standard entropies (Section III), μi⊖(p, T) quantities can be calculated using tabular standard values (at 25 °C and 1 atm) and cp or Vi functions. Phase transitions on the integration path should be considered using the corresponding transfer quantities ΔH(α → β) or ΔV(α → β). In many balance situations, one of the forces acting on the body is its weight. In free-body diagrams, the weight vector is attached to the body`s center of gravity. For all intents and purposes, the center of gravity is identical to the center of mass, as you learned in Linear Moment and Collisions about linear momentum and collisions. Only in situations where a body has a large spatial range, so that the gravitational field is unequal throughout its volume, are the center of gravity and the center of mass located at different points. In practical situations, however, objects as large as ships or cruise ships are also in a uniform gravitational field on the Earth`s surface, with acceleration due to gravity having a constant magnitude of In these situations, the center of gravity is identical to the center of mass. Therefore, in this chapter, we use the center of mass (CM) as the point where the weight vector is attached.

Remember that CM has a special physical meaning: when an external force is exerted on a body exactly at its CM, the body as a whole undergoes a translational movement and such a force does not cause rotation. Due to the non-thermal equilibrium method for thin film deposition, there are unique phase control methods for composite thin films. One is quenching after spray separation, the other is interrupted separation by spraying. Under equilibrium conditions, magnetic flux penetrates the mass of a Type II superconductor above the lower critical field Hc1(0) ∼ 10–20 mT for many high-field materials. At H>Hc1, this magnetic flux is present in the form of a hexagonal network of quantized vortex lines. Each vortex is a tube with the radius of the London magnetic penetration depth λ(T) in which shielding currents flow around a small non-superconducting nucleus of radius ξ(T), where the coherence length ξ(T) at T = 0 quantifies the size of the Cooper pairs. Bulk vortices are present when the Ginzburg–Landau parameter κ = λ/ξ exceeds 2−1/2, as is characteristic of many superconducting compounds, especially extreme type II superconductors such as Nb3Sn or high-Tc stratified cuprates with κ = 20–100. The flux generated by shielding currents in a vortex is equal to the flux quantum φ0=2.07×10−15Wb, so that the vortex density n = B/φ0 is proportional to the magnetic induction B. Superconductivity is destroyed when normal nuclei overlap in the upper critical field, Hc2(T)=φ0/2πμ0ξ2(T). In isotropic superconductors such as Nb-Ti and Nb3Sn, the vortex lines are continuous, but in high-Tc anisotropic compounds such as Bi2Sr2Ca2Cu3Ox and Bi2Sr2CaCu2Ox, the vortex lines consist of stacks of weakly coupled pancake vortices whose circulation currents are mainly limited in the CuO2 superconducting planes.

A body moving in a circle of constant velocity is in rotational equilibrium. The second equilibrium condition states that the net torque acting on the object must be zero. We substitute these components under equilibrium conditions and simplify. We then obtain two equilibrium equations for stresses: just as an object in translational equilibrium can be at rest or moving at constant translation speed, an object in rotational equilibrium can also rotate at constant angular velocity. This article focuses solely on static equilibrium and the conditions that must be met to achieve static equilibrium. Static equilibrium and dynamic equilibrium occur when the object is at rest and moving in a constant-speed reference coordinate system. If the net result of all external forces (including moments) acting on an object is not zero, Newton`s second law applies. In this case, the object of a mass is not in the state of equilibrium and undergoes an acceleration that has the same direction as the resulting force or moment.