I use metro transit train or bus for commuting to work. I have noticed that when I keep my feet almost shoulder width apart I can easily keep my balance without holding a handle or bars (and even I can hold and read a book at the same time). However, if I put my feet close to each other, keeping my balance would be much harder when the train/bus accelerates or decelerates. I have a limited knowledge of Physics so I could not come up with a convincing explanation. I just vaguely remember that, if I am right, falling and balance have something to do with the center of gravity/mass; but I am not sure how it does, of course if it does, relate to this scenario.
As a related question, I was wondering whether the direction I am facing towards also affects my balance? For example, is there any difference if I stand in the train/bus facing towards the side windows compared to the situation which I am facing towards the front/back of the train/bus?