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Old 2015-10-21, 05:38 PM   #64
Alan Lawrence
Join Date: Apr 2006
Location: Cambridge, uk
Posts: 54
Originally Posted by kamikaze View Post
Your assumptions only work in zero-G and are about maintaining impulse, not centre of mass.
From what I read, impulse = force * time = effect/change of momentum. So I'm not sure that's useful here...

You are not an isolated system, but subject to an external force, gravity.

By lowering your centre of mass you can leverage your potential energy to change your impulse and shift your centre of mass horizontally. If you do that right you can let gravity pull you back over the contact patch. You can straighten your body again over the patch
I kinda like that idea/explanation - you can sort of borrow time by falling, then push yourself back up when you're straight - but I'm not sure how much it explains. I think the later discussion of angular momentum is much more promising....

Originally Posted by minimalist
It's not the air resistance that makes (waving your arms) effective, it is the change in the angular momentum that it causes. By the law of conservation of angular momentum your body must rotate in the opposite direction.
That's more like it. So by waving my arms, I make my body rotate. My body would like to rotate about the same center about which my arms are rotating, but that's not possible because it's anchored at the ground. Instead, a horizontal force is exerted on my tyre, which is transmitted to the earth via friction (and thus the Earth moves, infinitesimally); and the equal-and-opposite horizontal force pushes back on me, and yes, my center of mass moves.

It has to be rotation, tho - if I just move my arms (say 5kg) horizontally (say 1m), then the equal-and-opposite force would just move my body (say 50kg) back in the opposite direction (by 10cm); I can't change my center-of-mass this way (tyre friction may stop entire body+unicycle moving by 10cm, and turn it into rotation, plus corresponding counter-rotation of the earth to preserve angular momentum, but I don't think that ends up moving my centre of mass, unless I *rotate* my arms rather than just move them across).

That's now my understanding, anyway. Thanks to all who posted in helping me get to that .
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