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Take a break and walk to the bathroom without moving your hands. What does it feel like the right answer might be?
I know it's difficult, but why? Does is have anything to do with physics?
Balance: balance will be maintained. Try running with your hands tied to your sides and you'll find out for yourself why.
I know the facts. I want to know the physics.
Lets consider this then as a torque problem. Lets look at what you look like from the front:|dw:1343295702478:dw| Ok, so you see when you lift your leg, the other leg becomes like a fulcrum while anything pointing out perpendicular from it becomes a lever arm. The weight of your entire leg is pulled down by the force of gravity, and causes a torque to cause you to tip over. So to have a net torque of zero, you move your arm on the other side of your body to counteract it by helping you tip in the other direction so they cancel out. Of course in reality it doesn't take very long to take a step, and a lot of that falling motion can be used to walk forward. So yeah, quick and dirty example, hope that makes sense, I can add more if you're interested.
This question is associated with Bio mechanics. So, in order to mantain the balance our body naturally move our hands and arms too back and forth.
Here's a pretty good explanation which makes the most sense to me: http://www.cosmosmagazine.com/news/2888/why-we-swing-our-arms-when-we-walk