Conservative force field ↩

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created: 2022-07-01 22:44:16
modified: 2022-07-01 22:57:41

Let's consider a force field

, where the force only depends on the position.

is conservative, if everywhere its curl vanishes (aka it is a conservative vector field).

In this case, the work done on a moving particle between positions and does not depend on the path taken, only on the start and endpoints. This is equivalent to saying that the work done around a closed path vanishes.

Potential energy

For conservative fields, the work done can be characterized by the difference in potential energy between the start and end points.

Which also equals the negative of the change in kinetic energy, due to the work theorem.