>> Won't speeding up and slowing down make the train swing out more or
>> less? (Like going round a corner in a car, if you speed up it rolls
>> more).
>>
>> In a rotating reference frame you'd be essentially turning even when on
>> a straight piece of track, so I would not say that changes in forward
>> motion won't have any effect.
>>
> Yes, to an extent, this is true. But, since the only angle its changing
> at is side to side, forward motion isn't going to have an affect
> *except* when making turns.

But as I said, in a rotating reference frame the train will be "making 
turns" all the time, even when on a straight track. So any forward/back 
acceleration will, in general, affect the side to side swinging.

You can easily see this by imagining a straight piece of track rotating 
and plotting out the course the train will take as it goes along the 
track - it will be a curve, so some sideways forces must be involved.

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