Physics "Teeter-Totter" Balance Simulator
The settings allow you to have the plank supported by some short columns, place weighted objects at different points, and then remove the supports, so you can estimate the amount of change that will take place and then see if you got it right. On different levels, you can move people, bricks, and lots of different objects around and make a game out of achieving just the right balance. It's also a lot less dangerous than the teeter-totters I remember on the playground.
It is written in HTML5, so it should play just fine on iPads and other Apple products as well as any computer running Windows.
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