Re: Rolling friction (again)

["John S. Denker" <jsd@MONMOUTH.COM>]

Savinainen Antti wrote:

> 1) A car is moving at constant velocity in a level road. Rolling
> friction and air-resistance are the retarding external forces
> acting on the car. These forces must be balanced to have constant
> velocity. The balancing force is exerted by the road as well (as
> the retarding rolling friction); I would call  it static friction.
> To be more exact, static friction acts only on the wheels which are
> driven by an internal torque (in most cars only two wheels are
> driven in this manner).

The physics is fine, but the terminology strikes
me as confusing.

This causes me to revise my notes on the subject.
  http://www.monmouth.com/~jsd/physics/car-go.htm#sec-friction
I think there are four cases that need to be distinguished:
     Static friction.
     Dynamic friction.
     Ideal quasi-static rolling friction.
     Non-ideal rolling friction.
where the fourth one is newly added to the list.  The
new item is discussed in section
  http://www.monmouth.com/~jsd/physics/car-go.htm#sec-non-ideal-friction

To the extent that the rolling is ideal and quasi-static,
it does not cause any retarding force.  So I get confused
when the retarding force is called "static friction" or
anything like that.

> 2) A car is slowing down on a level road. Brakes are not applied and
> gear is not on. Then rolling friction (and air-resistance) provide
> the net force and net torque to slow down the car and the wheels.

OK.

> 3) A car is slowing down on a level road and brakes are applied in a
> way that the wheels do not lock. I assume that there is no slipping.
> In this case there is static friction in addition to rolling
> resistance in the opposite direction of the motion. The net force is
> greater than in case 2 and hence the car slows down faster.

I would have said that there is a traction force in
the rearward direction because of the braking, plus
another rearward force due to dissipation due to
nonideal roll.

> A problem arises when rolling friction is analyzed further. According
> to Swartz & Miner rolling friction is the resultant of *friction* and
> normal force which is not in line with the center of mass of the
> wheel.

Talking generically about "friction" confuses me.
There are at least three things that could mean:
 -- The traction force due to ideal natural roll
could be called friction,
 -- the traction force due to complete skidding
could be called friction, and
 -- the dissipative nonidealities associated with
the utterly nonslipping roll of a cog-wheel could
be called friction.

> They avoid talking about two friction forces: instead of
> static friction they talk about *traction*. I think that their
> approach is more coherent than the one I presented.

Traction is a fine concept, but it is _not_
synonymous with static friction or with
nonskidding motion.  A fully-locked skid or
even an unlocked skid provides a nontrivial
amount of traction.

Traction is just the force.  It is directly
connected to the momentum budget. It is only
rather indirectly connected to the energy budget.