What's the effect of the feet distance on a person's balance in a moving train/bus?

Question

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?

Answer 1

Falling occurs if the center of mass is outside the nearest pivot point of the object.

When you place your feet apart you change your shape so the center of mass more esaily remains inside the pivots.

As you point out this only protects againts sideways motion in one direction, that denoted by a line connecting your feet.

Consequently the best orientation of that line is the one that matches the most common direction of destabilising forces.

Now to the bus. Motion is forwards or backwards, and a large component of stabalisation should be oriented that way, but not all of it, for lateral destabilising forces do occur especially when turning, and some provision should be made for them. You can move you feet to a lateral position when the vehicle is turning, and back to the direction of the vehicle afterwards However, the best overall orientation, depending on the specific details of the bus journey, is probably a diagonal line.

Answer 2

Your assumption is right, if an object is on a table, for example, if the projection (parallel to the force of gravity) on the table lays inside the portion of the object which is touching the table, then the object is in equilibrium, otherwise it will fall (if there aren't any other forces acting on the object).

This means that if the projection of your center of mass falls between your foot, then you are stable, otherwise you are unstable. In turn, if your foot are far apart, the possibility that the projection of your center of mass falls outside is small, compared with the case in which your foot are closer.

Now, since the space in which the projection can fall in order for us to be stable is a rectangle, if you face the windows, the movement of the train will move your projection of the center of mass along the longer edge of the rectangle, so you will be more stable in this configuration (it will be harder for the center of mass to fall out of this rectangle) . Moreover, if you think of our anatomy, you will realise that our movements are more rigid on our left or right side in contrast with our front or back side. This means that it is harder for us to move our center of mass from a force acting on our right/left side with respect to a force acting on our front or back side.