Hey all, I was wondering about something perhaps obvious to many with a mechanics/vector background. (Apologies if this is too basic compared the usual math-fun stuff.) Am wondering if there's some fundamental principle behind levers and colliding objects.. or if they're somehow describing the same thing. Here's what I mean. Take several masses on a fulcrum. A mass of 1 at distance 2 from the fulcrum plus a mass of 2 at distance 3 balances a mass of 2 at distance 4. 1x2 + 2x3 = 2x4 of 2 + 6 = 8 In other words, M1xD1 + M2xD2 = M3D3 This looks a lot like conservation of momentum (inelastic, in this case) if you replace the distances with velocities. I thought that was interesting. So I wondered... is this a coincidence? Or are these describing the same thing, conceptually? And if they're describing the same thing conceptually, then what's the kinetic energy formula equivalent? In other words, colliding objects conserve 1/2MV^2, or 1/2MVV. Replace one of the V's with a D and you get 1/2MVD. What is 1/2MVD when applied to objects balanced on each side of a fulcrum? Using the example above, the 2x4 could be balanced by 1x2 and infinitely many other mass distances: 2x4 = 1x2 + 2x3 or 2x4 = 1x2 + 1x6 etc This all balance just like many different post-collision velocity combinations will preserve momentum. But what's the kinetic energy equivalent? Am guessing there's only one solution that preserves.... something. Am not sure what it is. Rotational energy? I was about to calculate but am not sure how to start. If the lever broke above the fulcrum and the different weights began to rotate around the fulcrum they'd each have a different velocity. I suppose the bottom-line question is: if you had a mass of 2 a distance 4 from a fulcrum and a mass of 1 a distance 2 on the other side, what additional mass would you add on the side of the smaller mass (the 1) so that it not only balanced, but the x (am not sure what this would be) energy on each side was the same as well? And a related point. Rotation around a fulcrum would create a circle, obviously, which is what's created by the formula for kinetic energy. A coincidence? All the best, Gary