We swing our arms because of Newton’s Third Law of Motion: “If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.”
If you push someone forward then you are pushed back as well. This principle also applies within our bodies, so if you swing your heavy leg forward then doing so will tend to push your hip backwards, rotating the hip and by extension your torso. Then when you swing your other leg forward it will rotate your hips and torso the other direction.
Rotating your torso back and forth is wasteful in terms of energy use, and it throws off your hips from allowing you to walk straight. To help counteract this we swing our arms opposite to the way our legs move, so if you are swinging your right leg forward you will be swinging your right arm back. Your arms aren’t as heavy as your legs so it doesn’t completely counteract the motion but it does help, as you can tell if you try walking with your arms held still.
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