# Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]

John Taylor's Classical Mechanics says this...

I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the second condition is not? And if so, how are the forces in that situation non-conservative even if they satisfy the second condition?

• Possible duplicates: physics.stackexchange.com/q/528336/2451 , physics.stackexchange.com/q/27896/2451 Sep 16 at 14:34
• Does this answer your question? Why can't conservative forces depend on velocity? Sep 16 at 15:01
• I don't like the phrase "or any other variable" in condition one. The electric force depends on a particle's charge, in addition to its position, for example. Sep 16 at 15:10
• @BobD My question is more like, can there be force fields which satisfy the second condition without satisfying the first? And if this is not possible then the condition 1 is superfluous. As Adriano Del Vincio said in his answer that we can have time varying force fields which do not satisfy the first condition but they do satisfy the second condition at any fixed time.Considering a fixed time to check the second conditon is kinda logical otherwise consider this... the same path from A to B will lead to different work done on the particle depending on how fast the particle goes from A to B. Sep 17 at 7:19
• @BobD So are there other examples? Sep 17 at 7:21