Conservative force

A force whose work between two points is independent of the path taken. Equivalently, its work around every closed path is zero.

Potential energy: A scalar quantity associated with a system’s configuration that can be converted into other forms of energy. A conservative force’s work equals the decrease in potential energy.
Gravitational force: The attractive interaction between masses, described classically by Newton’s law of universal gravitation. In Newtonian mechanics, gravity near Earth is modeled as a conservative force.
Work (physics): The transfer of energy when a force acts through a displacement. Path independence is a claim about the work done by a force.
Nonconservative force: A force whose work generally depends on the path taken between two points. It is the direct opposite of a conservative force’s path-independent work.
Scalar potential: A scalar field whose spatial gradient can define a vector field. The negative gradient of a scalar potential gives a conservative force.
Electrostatic force: The force between stationary electric charges, described by Coulomb’s law. For stationary charges, this force has a scalar electric potential.
Path independence: A property in which an accumulated quantity depends only on endpoints, not on the route between them. It is the defining condition for work by a conservative force.
Conservative vector field: A vector field expressible as the gradient of a scalar potential, with sign convention chosen for the application. Conservative forces are a physical instance of this broader mathematical structure.
Gradient: A vector of spatial derivatives that points toward the steepest increase of a scalar field. Its relation to potential energy expresses the local direction and strength of the force.
Hooke's law: A relation stating that an ideal spring’s restoring force is proportional to its displacement from equilibrium. An ideal spring force is conservative, with elastic potential energy.

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