Conservative force

Conservative forces are those that possess certain properties:

• The work it does on a particle is independent of its trajectory.
• The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d_i = d_f) = 0) is zero.
• The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
• The curl of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>

When the only forces present in a system are conservative, energy is conserved.

Examples of conservative forces include:

• Gravitational force
• Force performed by a spring

Friction is an example of a non-conservative force: