There is another reason why humans don't perpetually spin their arms after a recovery. Our feet have a considerable length of contact with the surface of the floor, which was missing in your stick man sim. This extra length means your feet can apply a downward normal force near the tip of the shoes' toes to provide a countertorque from the ground [tau = r x F]. This also explains why the arm spinning is needed mostly when you are pushed backwards and not when you are pushed lightly forwards
I'm a gymnastics coach and have been teaching my students this for years. A secondary way our instincts use conservation of angular momentum is shortly after a push/fall when your brain has determined that windmilling your arms (and other counter measures) is not enough to stop your fall. It then pulls your legs in the same direction of rotation as the fall, pulling your upper body slightly in the opposite direction, making it so you land in a slight pike position roughly on your butt rather than a straight line where your head can smack into the ground (see your body position at 4:59). Its the opposite effect of doing sit ups and needing something to hold your feet down because they want to come up.
10:15 Missed another cool step here, deep tendon reflexes completely bypass your brain and make instant corrections faster than the signal can even go up your spine to your brain and back. That's the same reflexes that get tested when a doctor taps your knee or similar, that reflex is there because it's responding to that tendon stretching by instantly working to shorten it again, and there's slightly more complex reflexes that involve cross wiring between these pathways to contract some muscle groups and relax others, all entirely within the spinal cord. Your brain has to play catch-up with these as well as the fast responses it has itself.
I'm at 10:41 and this has me thinking about all the times I've dropped my phone, automatically attempted to catch it, and mid-attempt realized my initial motion input is actually going to be my demise (aka, breaking the screen by accidentally launching my phone by trying to catch it or break the fall). Interesting thought!
No robots were hacked in the making of this video.
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