Just once more, an illustration of what I wrote up in post 762 (
https://www.physicsforums.com/showpost.php?p=2052782&postcount=762 )
of the basic kinematics of a wheel rolling without slipping on a surface.
I realize that my orientations are the opposite of all videos here, sorry about that. The principle should remain, though.
In as much I can find references on the web, here is one:
http://dept.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_3.html
(although it only treats rolling without slipping on a stationary surface, not a moving one).
There is an educational paper here:
http://www.iop.org/EJ/article/0143-0807/24/6/001/ejp3_6_001.pdf?request-id=4c8428fa-8110-4545-9d19-1b1284d162f3
(although it centers more on the study of acceleration)
Another reference is this, where you see the superposition of rotation and translation:
http://cnx.org/content/m14311/latest/
(note especially equation (3) )In any case, these sources indicate that the motion of individual points of a rigid body (such as a wheel) is given by the vectorial superposition of the translational motion of its center, and the rotational motion around that center.
I try to illustrate that in the picture (it was the calculation done in post 762).
From that, we see that the point of contact (wheel side) has the velocity of w . R + v_x which must - rolling without slipping - have exactly the same velocity as the point of contact (surface side), which is the linear velocity v_tread.
So we have that R.w + v_x = v_tread.
From which:
w = (v_tread - v_x)/R
Note, btw, that the TOP point of the wheel has a velocity of v_x - R . w.
Depending on whether v_x is larger or smaller than R.w, this point moves forward or backwards.
