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I have a basic enough question. Assume that one has one of those ideal see saws, i.e. the teeter-totter pivots on point source, the balance is of uniform mass etc.

Now assume that one places an object of mass m on one end. This will force the balance to tilt on side. Now suppose that one adds another mass of m on the other side. What happens? It seems that everyone agrees that the the balance would move to the stable equilibrium, that is the middle. What I don't understand is, what is the Force that moves the teeter-totter to the middle position?

Once the second mass has been placed on the other side, the two net forces acting on the pivot is the same. And since the distance is the same, the torque is the same. So what force is it that moves the balance to the middle?

And if no such force exists then every position of the balance is valid if the two weights are equal, then how do those mass balances work?

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"It seems that everyone agrees that the the balance would move to the stable equilibrium, that is the middle."

No they don't. The see-saw will, in general, experience a force that is the gradient of the energy with respect to rotation. But if the masses are identical and placed equal distances, this gradient is zero. Thus, the see-saw will move with constant angular velocity and will not return to the middle. So, as you suggest, all angles are equilibria. You could say something tricky, like when the mass on the left moves lower the gravitational field increases a bit so actually that mass keeps accelerating down, but that's facetious.

"how do those mass balances work?"

What mass balances? If you want to know how real balances work, I presume the beam has a center of mass that is below the pivot point, so that any rotation of the beam causes a restoring torque.

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  • $\begingroup$ A finely-crafted mechanical balance is a beautiful thing. They have just enough restoring force to overcome friction in the case of equal masses, but no more than that. $\endgroup$ – user10851 Jul 27 '13 at 2:48

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