Mechanical equilibriumIn classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. 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. 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.
Thermodynamic equilibriumThermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of matter nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.
WeightIn science and engineering, the weight of an object is the force acting on the object due to acceleration or gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Yet others define it as the magnitude of the reaction force exerted on a body by mechanisms that counteract the effects of gravity: the weight is the quantity that is measured by, for example, a spring scale.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
TorqueIn physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). It describes the rate of change of angular momentum that would be imparted to an isolated body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point.
Economic equilibriumIn economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers.
Dynamic equilibriumIn chemistry, a dynamic equilibrium exists once a reversible reaction occurs. Substances transition between the reactants and products at equal rates, meaning there is no net change. Reactants and products are formed at such a rate that the concentration of neither changes. It is a particular example of a system in a steady state. In physics, concerning thermodynamics, a closed system is in thermodynamic equilibrium when reactions occur at such rates that the composition of the mixture does not change with time.
DynamometerA dynamometer or "dyno" for short, is a device for simultaneously measuring the torque and rotational speed (RPM) of an engine, motor or other rotating prime mover so that its instantaneous power may be calculated, and usually displayed by the dynamometer itself as kW or bhp. In addition to being used to determine the torque or power characteristics of a machine under test, dynamometers are employed in a number of other roles.
General equilibrium theoryIn economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts with the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant.
SystemA system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity.
ForceIn physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.
GroupoidIn mathematics, especially in and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: Group with a partial function replacing the binary operation; in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation on the morphisms, called inverse by analogy with group theory. A groupoid where there is only one object is a usual group.
Equilibrium constantThe equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture.
Body forceIn physics, a body force is a force that acts throughout the volume of a body. Forces due to gravity, electric fields and magnetic fields are examples of body forces. Body forces contrast with contact forces or surface forces which are exerted to the surface of an object. Normal forces and shear forces between objects are surface forces as they are exerted to the surface of an object. All cohesive surface attraction and contact forces between objects are also considered as surface forces.
Free body diagramIn physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a 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). The body may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems.
Center of massIn physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion.
Quotient groupA quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying elements that differ by a multiple of and defining a group structure that operates on each such class (known as a congruence class) as a single entity.
State functionIn the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system.
Shear forceIn solid mechanics, shearing forces are unaligned forces acting on one part of a body in a specific direction, and another part of the body in the opposite direction. When the forces are collinear (aligned with each other), they are called tension forces and compression forces. William A. Nash defines shear force in terms of planes: "If a plane is passed through a body, a force acting along this plane is called a shear force or shearing force." This section calculates the force required to cut a piece of material with a shearing action.
Conversion of unitsConversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Unit conversion is often easier within the metric or the SI than in others, due to the regular 10-base in all units and the prefixes that increase or decrease by 3 powers of 10 at a time. The process of conversion depends on the specific situation and the intended purpose.
