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I had an interesting thought about how moments work, and if the force is carried.

If I am pushing on the handle of a door, say 10 metres away from the pivot, a force of 10 newtons, the total moment would be 100nm.

Does this mean that at every point of the door, half way for instance, the moment will be the same? Say for instance at the point 5 metres from the pivot, can you say that the moment at that point is also 100nm, and thus the force must be 50 newtons? This makes no sense, as the force applied 1cm from the pivot would be 1000 newtons.

Albeit what my teacher told me, I believe that if you half the distance from where you push, the force will also be halved, and thus the moment quartered, although I have no mathematical proof.

Thanks for your help!