how does a train stay on the tracks?

Gravity.

Really?

Yes.

Have a close look at the wheels of a train and you will see that the inside of the wheel has a lip(flange) that goes on the inside of the track. This plus gravity keep it on the track.

Search google images for “train track and wheel”

They don’t turn sharply enough, at a fast enough speed for their inertia to pull them from the track. With the lip on the inside of the wheel its easier for the trains momentum to continue in a relatively straight manner along the rail that gently guides it.

Its really just a simple math equation.

no no no lol
trains, stay on their track because their rims are slightly tapered. =D my teacher mr. daly told me =D

hahahaha, im afraid your all misinformed especially mr.equation man (spargett).
look up Youtube.com/richardfeynmantrain if you want the right answer,but if ye couldnt be bothered heres my attempt. PLEASE READ!!!!!!!
the inside lip is only a safety device, if it was only thing keeping the train on, wouldnt there be a loud noise all the time right. if you look closely (again) you will see that the actual wheel is sloped, meaning that the circle area on the outer rim is smaller then the circle area on the inside (beside the lip/flange), so whenever a train is going round a corner the momentum makes the train shift either left or right depending on what direction the corner is going. by this shift the wheel on the inside has a smaller distance to travel then the outside which is on a bigger circumference. thus bring the train round the corner without the use of the lips. the train sways to and fro and eventually staightens out again.