Conservative force

Conservative forces are those that possess certain properties:^[1]

• 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. .
• The curl of the force, is zero,

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: