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Re: Rolling friction (again)



The problem is that rolling friction is a fairly common conception. It is
the force (or that component of a more general force) that is responsible
for "the _dissipation_ due to rolling", or, more accurately, for the
momentum transfer due to rolling.
The terminology may be troublesome, I think part of that is because it is
difficult to identify the cause of this force.


What would it mean to have no "rolling friction" ...
-- pure sliding, like eels on teflon, with no traction?
Certainly, there is no rolling
-- ideal rolling, like an ideal cog-wheel, with 100% traction?
Certainly, there is no dissipation at the contact points

If static friction means what I think it means,
it can't contribute to the dissipation.

Depends on which dissipation (transfer) - momentum or energy. Static
friction cannot contribute to the energy loss any more than it can
contribute to the energy gain as a vehicle accelerates. That is true. But
does that mean that static friction plays no role in accelerating the
vehicle? I really hope not.

We had a really long discussion on this one last year. The picture I took
away is that the static friction "mediates" the transfer of energy from the
fuel to the vehicle. Siilarly, the static friction can "mediate" the
transfer from bulk kinetic energy into thermal energy dissipated within the
tire walls. I would like to leave energy there and concentrate on momentum.

And it's a little obscure to talk about a variable
normal force. I assume that means it's variable
in the frame comoving with a particular patch of
rubber? It's not variable in the frame comoving
with the car chassis.

I was thinking variable over position, not in time. Is the normal force is
different between the front edge and the back edge of the contact spot?


**Does the back/forwards automatically imply friction?

Consider a very wide tire, so that the effect
of the sidewall is relatively insignificant.

Then it's not even true that there's any forward
and back motion. You can flatten a cylinder
without stretching it. Also imagine a caterpillar
tractor tread -- it flexes without stretching.

I'm not sure I follow this argument

This is true, but you can't flatten a cylinder without distorting it.
Distorting it implies that a force acted over a distance. That implies
that a force acted over a time, and that can change the momentum - even
without stretching.

If a tire is flattened, the rubber is compressed. If the distortion is
purely vertical, the compression will be greatest close to the edges. It
will try to push out and, (if they exist), may be held in place by contact
forces (i.e. with the ground)

Can a rolling tire flex on a frictionless surface?

Huh? If you smash a tire against a surface,
it will deform, whether or not it's rolling,
whether or not the surface is slippery.

Again, this is true if you smash it into a surface. Let me rephrase that
question - can a flexing tire roll on a frictionless surface? Or would the
fact that it is already squished restrict it to sliding? I really don't
know the answer to this one

Is the plane of contact (at the front and
rear contact points) parallel to the road surface?

If the road is planar and the tire is in
contact with it, surely the area of contact
must be planar.

I would think so, but imagine the tire as infinitesimal layers. The bottom
layer will be planar, the next layer is not. The forces are balanced
by "tangential" forces caused by compression, which is caused by the normal
forces. Maybe it would be simpler to consider the "plane" of contact to be
curved, neglect the internal forces and consider the "normal" force to vary
in direction with position.