# Law of the lever - Explained Physically

I've seen the "Archimedes Proof" of the law of the lever, and many similar ones, but...at the end of the day, all they're doing is getting observations about the way rotating bodies behave, and using those observations as axioms.

By defining torque to be the cross product of force and distance, we're just creating new terminology, but we aren't really explaining physically why it is that a force applied at a greater distance would be better at spinning something than a force applied at a lesser distance.

For example, say the green man and the pink man weigh exactly the same, but the green man is half as far from the pivot point as the pink man is. The rod will rotate towards the pink man.

Why?

I think that the reason that the green man doesn't have as much "spinning" power as the pink man does must have to do with the molecules of the bar. In a sense, the pink man will cause more bending in the bar, and it'll want to straighten out towards his direction (forgive me if that doesn't make any sense, it's just a thought).

Can someone please explain, from the approach of the atomic interactions in the rigid body connecting both the pink man and the green man to the fulcrum, and without using the concept of torque, why it is that the bar rotates towards the pink man?

And, if the torque equation could then be derived from that physical explanation, that would be awesome!

In summary, I'd like to know how to approach the concept of torque with atomic theory. I'd like to understand the interatomic electromagnetic forces in a rigid rod, how momentum travels along a rigid rod when we apply forces perpendicular to its length, and how that leads to the force being "amplified" by larger distances from the pivot point.

• What makes you think that the correct answer to "Why?" shouldn't be based on observation? Physics is a science. It describes the universe that is. All the deep and abstract concepts we work with are fundamentally descriptive (though the idea is that deeper concepts describe more of the world starting from fewer building blocks). Only you've just rejected using those more powerful tools. Nov 5, 2019 at 19:22
• To explain the value of those deeper concepts, Noether's theorem plus the isotropy of space gives the conservation of angular momentum, and that can give rise to the torque concept which answers your question in terms of deeper abstractions. But we still build on the observation that physics is isotropic (which just has to be accepted as a brute fact supported by the agreement of the deductions that follow from it with observed reality). Nov 5, 2019 at 19:30
• Maybe evaluating the different positions and seeing which has more or less potential energy might be an approach. Nov 5, 2019 at 21:25
• @dmckee thank you. You're right, and I agree with you that deducing from observed reality is a key component of physics. However, I'd still like to know how to approach this with atomic theory and consider the interatomic electromagnetic forces in a rigid rod, and how momentum travels along a rigid rod, and how that would lead to the force being "amplified" by larger distances. Nov 5, 2019 at 21:27
• For one molecular discussion of the lever rule, see pubs.rsc.org/en/content/articlehtml/2016/cp/c6cp05996a Nov 6, 2019 at 0:16

For example, say the green man and the pink man weigh exactly the same, but the green man is half as far from the pivot point as the pink man is. The rod will rotate towards the pink man.

Why?

The answer is because the pivot force acts away from the center of mass, causing a rotation.

• Why is there only translation (no rotation) when the line of action of a non-zero force goes through the center of mass?

The answer to that has to do with the definition of the center of mass. by definition, if you apply a small force on every particle in a body, it is equivalent to the total force through the center of mass. Hence why it is called center of gravity sometimes, since every particle of the body experiences gravity in the same way.

And you can intuitively understand that if all the particles experience the same small force, the body is not going to rotate. It is pushed equally everywhere in a parallel fashion.

In this scenario, the center of mass is the unique point in space where a single force through it is equivalent to a uniform distributed force over the entire body. In both cases, no rotation exists.