Prove that the flange of a train wheel moves backwards in respect to the ground

[porschedude]

Prove that the flange of a train wheel moves backwards in respect to the ground, using the trigonometric functions, linear and angular velocity

I really have no idea to go about doing this, all I know is that the proof involves some use of trigonometric functions, linear and angular velocity

 

[tiny-tim]

Welcome to PF!

Prove that the flange of a train wheel moves backwards in respect to the ground, using the trigonometric functions, linear and angular velocity

Hi porschedude! Welcome to PF!

Hint: All you need to know is that the wheel does not slip … in other words, the speed of the bit of the wheel which is instantaneously in contact with the rail is zero.

 

[porschedude]

Thanks, but that doesn't really prove that the wheel is moving backwards. I'm are that this can be shown by cycloids and how the outer radius actually moves backwards for an instant. But the larger part of the question is how long is the wheel traveling backwards if the train is traveling at 60 mph, but the answer can basically be found out if we prove that the wheel is going backwards,

 

[tiny-tim]

Thanks, but that doesn't really prove that the wheel is moving backwards.

Yes it does …

the wheel is rigid, and you know the velocity of its centre and of the point of contact …

just use geometry!

 

[amezcua]

Be sure to think of the "WHEEL" as the rim that rest on top of the rail and look at the bit hanging below the top edge of the rail.

 

[amezcua]

In your mind slow the train down and see the rolling surface of the wheel as a very blunt compass point .Below the rail surface a small loop will be drawn.Similarly if you ride a bike at night when they switch on neon street lights your whole wheel will go backwards.( My butterfly net is poised for all the ones that take that seriously)

 

[TVP45]

It might help to say you should pick a point on the very outer radius of the flange at the location where it is straight down for only an instant of time as a starting point for thinking about this. Look at the linear velocity of the tread and the flange for a given rpm and ask what that must mean. For this problem, treat the tread and rail as being flat in profile.