When a person runs, especially if they're springing, their forearms go in front of them, sometimes even becoming horizontal. So, you won't get an energetic sprint look by just rotating the same arm sprite, you'll need to do some foreshortening.
(A similar thing also happens with legs, one leg goes in front of the other, but that's not very visible from the side so you'll only need to worry about this when doing front/back views.)