Re: "Negotiating" a curve. EUREKA?

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

Replying to John_D (see below) and to Leigh.

The last think I want to do is to include the gyroscopic effects.
On the contrary, I want to eliminate everything but the most
essential. Yes the wheels of the tricycle are massless.

Reading the books recommended by Leigh was not very
helpful, as far as this physics problem is concerned, but they
were interesting and promoted some thinking. I am still
uncertain about the

> I say again the non-rigidity [of wheels with respect to the
> platform and the road] is not essential to understanding
> the problem as originally posed.

A. Sharp does show the turning tricycle (Figure 187) but
the front wheel is parallel to the back wheels. How can it be?
And I can not accept this --> " A horizontal force, F2, applied
at G [CM], necessary to give the body its circular motion, is
supplied by the horizontal component of the reaction of the
saddle on the rider." The net force acting on the center of
mass must be described as a vector sum of all external forces.
The force of the saddle acting on the body of the rider is not
an external force.

But I am not a member of the Nitpicker's Society. So what
is the problem? Why is a tricycle turning when its front
wheel is not parallel to its back wheels? Everybody knows
the answer, it turns because the front wheel is turned. What
can be more simple than this? I agree. Turning the wheel is
the cause of turning.

The issue is to explain this in terms of an FBD (free body
diagram). How to explain the net force in terms of individual
external forces? This should be in textbooks in which the
"negotiation of a curve" is used as an illustration. The authors
should either explain the net force or use other illustrations.
It would be very useful if somebody could produce here a
satisfactory explanation for a student of an introductory
physics course.
Ludwik Kowalski

To understand is to find a satisfactory causal  relation which is
objectively correct. To explain is to express that understanding.
To teach is to promote understanding.
*************************************************
John Denker wrote:

> At 04:35 PM 11/6/99 -0500, Ludwik Kowalski wrote:
> > John_D would probably say (and I was saying the
> > same thing the other night) that forces in the bearing
> > are internal and that only external forces matter.
>
> Sometimes I would say that.  Gyroscopic precession can be considered
> a consequence of "internal" forces, and there are cases where it matters.
> But in this case it doesn't matter much.
>
> > This
> > would certainly be the case if the wheels were locked.
> > Then I realized that wheels are not rigid and that the
> > FBD can not be used, except for the rigid platform.
> > I have to think about the situation again. Reading the
> > books recommended by Leigh will be the first step.
>
> I say again the non-rigidity is not essential to understanding
> the problem as originally posed.
>
> Suggestion:  start by considering the limit where the wheels have
> negligible mass.  Then they contribute nothing to the kinematics, other
> than to constrain the motion of the rest of the tricycle.
>
> Indeed if the rolling motion of the wheels is keeping you from seeing the
> kinematics of the original problem, replace the wheels by beads sliding
> on wires (three straight wires for the non-turning case, and three curved
> wires for the turning case).