Wheels, speed and relativity...

[McRhu]

From a rail's point of view, how fast are the following points on a loco wheel turning, assuming the loco is travelling at 100mph?...

a) The contact point

b) The longitudinal centrepoint of the axle

c) The top of the wheel diametrically opposite the contact point.

 

[jfollows]

0mph, 100mph & 200mph respectively, assuming no wheelslip.
Is there a reason for the question?
EG (but I didn’t need to look this up!) physics.stackexchange.com

 

[DerekC]

Is this a maths test? The answer is pretty obvious, if by "turning" you mean moving forward.

a) Stationary (because it is instantaneously in contact with the rail)

b) 100 mph (because it is attached to the frame of the loco)

c) 200 mph (because it is instantaneously moving forward by the diameter divided by the radius times the centre speed.)

The rotation speed of the wheel depends, of course, on its diameter.

 

[McRhu]

Correct of course. I must admit the notion that a point on the wheels of a fast moving vehicle could be moving at 0 mph (ie not moving relative to a certain frame of reference) fair tickled me under the oxters. (Thank you Neil deGrasse Tyson for your latest podcast.) I just thought it would be fun to share it. For those like me whose grounding in Physics and Engineering is kin to the contact point of aforesaid wheel, the principle can be demonstrated by watching the motion of a battle tank's tracks.

 

[DerekC]

A bit of graphics often helps understanding. This is a "cycloid curve" which shows the path followed by a point on rim of the wheel as it rolls along the track:



So distance along the track goes from left to right (the "x axis") and height of the point above the track goes from bottom to top (the "y axis"). The blue line shows the position of a point on the rim.

Diagram courtesy of Paul Bourke and available, with a proper mathematical explanation, here:

http://paulbourke.net/geometry/cycloid/

 

[pdeaves]

A point on the extremity of the flange would momentarily move backwards slightly, then move forward at just over twice the train speed. Flange size is small compared to wheel size so the effect is tiny but nevertheless is there.

 

[DerekC]

A point on the extremity of the flange would momentarily move backwards slightly, then move forward at just over twice the train speed. Flange size is small compared to wheel size so the effect is tiny but nevertheless is there.

True, but if you are trying to explain the principles of something, keep it simple!

 

[McRhu]

Thank you gentlemen. I appreciate your replies: the diagram does make it easier to visualise. And that point on the flange does indeed move backwards, being below the contact point which is at 0: a feature also mentioned on the podcast I was listening to. There's more to this revolving wheel mularkey than meets the eye, Horatio.