# What part of a train, when as a whole it is moving forward, is moving backwards relative to the ground?

## I was thinking it had something to do with the wheels but if someone could explain it that would be great!

Dec 26, 2017

The bottom of the wheel flange.

#### Explanation:

The bottom of the wheel flange is at a greater distance from the centre of the wheel than the points at which the wheel rests on the rail.

Assuming no slippage, the distance travelled by the train is the circumference of the main part of the wheel multiplied by the number of times it turns.

Meanwhile, the edge of the wheel flange has greater circumference so any given point on the flange travels a greater distance.

So as the train moves forward with velocity $v$, the bottom of the wheel flange is moving backwards with respect to the train at velocity ${v}_{f} > v$. So in relation to the track, it is moving 'backwards' with velocity ${v}_{f} - v > 0$.

The trick here is that the particles constituting the bottom of the wheel flange do not remain at the bottom for long, so they do actually arrive at the destination with the rest of the train.