BEFORE "Negotiating" a curve.

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

brian whatcott wrote:

> The short answer to why the force from the tire (or bead) changes
> direction in a turn is: "because it must!"
>
> Let me try using another model to illustrate.
> A vehicle running straight is subject to tire friction, bearing
> friction and air friction etc. These act opposite the velocity.

<snip> <snip>

This message triggered the following line of thinking. Suppose a
cylindrical wheel is set to roll on a flat horizontal surface in a
good vacuum. Its mass and radius are known and the kinetic energy,
is initially 10 J. There is no sliding, only rolling. In the ideal world
the CM would travel with a constant speed along the y axis. And the
wheel would be turning at a constant angular velocity. The radius is
such that 8 J is translational and 2 J is rotational.

But in the real world we have the process of thermalization and the
kinetic energy, K, is found to be 6 J, after the distance d=5 m was
covered (4.8 J translational + 1.2 rotational) . The kinetic energy
of the CM was reduced by dK=(8-4.8)=3.2 J. The motion picture
frames show that there were a constant acceleration (directed
toward -y). Nothing unusual so far.

According to the work-kinetic energy theorem the dK must be
associated with (or caused by , as I would prefer) the "net work
done on the center of mass". In other words, F*d must be 3.2 J
and F=(3.2)/5=0.64 N. Right or wrong?

My questions are:
1) Is there really a force F acting on the CM?
2) What is its nature? Why is it directed along -y?
3) Where is it generated? How is it generated?
4) How is it transferred to the center of mass?

The same questions can be asked about a rolling marble ball or a bead.

Ludwik Kowalski
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To understand is to find a satisfactory causal relation.
To explain is to express understanding.
To teach is to promote it.
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