The wheels have flanges on the inside edges, they keep the wheels on the rail. The wheels would not stay on the tracks without the flanges.
They have flanged wheels - so every wheel "steers", but the direction of the train is controlled by the track - thus no "steering wheel" in the cab.
So trains could stay on the track.
Gravity, same as any other train.
Almost all trains have wheels, although there do exist trains that use magnetic levitation and do not require wheels.
Maglev (magnetic levitation) trains run by way of a magnetic field generated by magnets embedded in the track. As such, they have little or no need for wheels.
Superconductors allow the train to 'float' on a layer of magnetism. Since there is no friction (as there would be with wheels on a track) - the trains can reach much higher speeds.
Yes, bullet trains have wheels. They run on rails, just as conventional railroad locomotives and cars do. The trains that operate by magnetic levitation, the so-called MagLev trains, do not have wheels as they ride on a magnetic cushion.
No, however some trains have a magnetized wheel to help grip the track. *Added - Electric trains do result in short term magnetizing of the train tracks. This can be seen on sharp curves where tiny rail slivers cling along in a magnetic pattern. In the US, trains do not have magnetized wheels, but rapid trainsit systems can include a track brake that uses a magnet to provide much faster braking than the wheels alone.
The top of the track is rounded, and the wheels on the train are also slightly rounded, at any one time there is only the surface area of a dime touching the rail, this along with incredible weight and the flange on the wheel keep the train on the track.
I'm not too sure about the advanced physics of this, but I know that it is desired for Maglev trains to not touch the track so that their speed can be maximised, and so there is no wear and tear of the track and contact. The speed would be maximised because if you don't touch the track there is no friction. Even wheels are slowed by friction so the only way to completely eliminate it is to have no friction.
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