Calculating Law of Levers Moments

[The P-manator]

When you calculate the two moments for the law of the levers, they are supposed to be the same, right?

 

[HallsofIvy]

I think you had better give us more information on the problem! My first thought was that if you are talking about two different moments on two different levers, then, no, they don't have to be the same!

I like to think of it in terms of conservation of energy: Work done on the lever is the force you apply times the distance that end of the lever moves and that must be equal to the work done by the lever: the force the lever applies times the distance the end of the lever doing the work moves. I think you will find that that is the same as saying that the two moments (of the two ends of the same lever!) must be the same.