Algodoo

Yes, this is interesting. Nice tutorial. I never used the sum of forces as an indicator before. Here are a couple observations that might be useful:

1. "Add center axle" always puts an axle at the object's center of mass.
2. If you hang an object on a hinge, the center of mass will be vertically below the hinge after the object stops oscillating.
3. If you hang a group of objects from a hinge, the center of mass for the group will be vertically below the hinge. You can add a vertical laser to the group, pointing down directly below the hinge. Repeat this process with the hinge in a different location. The lasers will cross at the center of gravity.

The initial idea was to do it entirely with the scene paused. My method was to make a circle where the center of mass of the object is and then rotate it 180º using the axle as an axis. But it turned out easier to explain this way, I think

I concur. A similar way would be to show just the gravity vector, which starts at the center of gravity, then put the counterweight on the other side of the hinge on a line connecting the hinge and COG, and then fine tuning the counterweight mass and position so that the gravity vector originates from the center of the hinge.

I like how you did the "slide show". Very clever! Did you design that technique, or did you borrow it from someone else? Just curious.

Xray, I designed it after like 2 other complete failures at using pos on a circle and another circle hinged to it with low hingeConstant. Figured out this way would work, even though it is overcomplicated