Ideal Wheels: was( L2-"Negotiating" a curve.)

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

The teaser
> Putting it all together:  An ideal wheel *never* dissipates
> energy.  If you
> put a force on it in the direction where it can roll, it just
> rolls (no
> force).  If you put a force on it in the other two
> directions, it resists
> the force (no motion).  No matter how you slice it, there's
> no force dot
> displacement.

I assume many of you have tried to deal with the following conundrum:

perfect rolling motion for an ideal wheel:

perfect rolling = no relative motion at the point of contact

ideal wheel = a rigid circular type object.

Consider two cases: (in both cases, straight line motion of the cm of the
wheel)

1) V_cm of wheel is constant

Force: gravity and an upward pointed normal force that cancels out.

Is there a static friction force or not?  I'd have to say no, since the a_cm
is zero.

2) Wheel is speeding up

There must now be a forward static friction force to account for the
non-zero a_cm.  But this force give a torque in the wrong sense and would
serve to slow down the rotation of the wheel.

Explanations??

I wonder if it means that it is impossible to have perfect rolling motion of
a rigid body (a single point (perhaps line)) *in principle*.

Thoughts?   I no this is an old problem, and the only way I've seen it
treated in a few textbooks, is to simply say the wheels aren't rigid, and
explore the consequences.

Joel