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Rolling friction (again)



Rolling friction has been discussed earlier in this list (I had a large number of hits which I read through). I checked John Denker's web page (http://www.monmouth.com/~jsd/physics/car-go.htm) and read again what Swartz & Miner (1998, 93-96) had to say about rolling friction. I still feel that I need some advice from colleagues.

Let's consider the following cases.

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).

According to this analysis the road exerts two frictional forces on the wheels in the opposite directions. Of course torques due to static and rolling friction with respect to the axle must be zero as well.

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.

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.

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. 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.

Have I made mistakes in the analysis? What do you think would be an appropriate level of discussion in high schools? I would like to address rolling friction in teaching even though it is not exactly part of the Finnish or International Baccalaureate syllabuses. Traction is not mentioned in any high school physics books I have read.

Regards,

Antti Savinainen
Kuopion Lyseo High School/IB
Finland
Homepage: <http://kotisivu.mtv3.fi/physics/>

Reference:

Swartz, C. and Miner, T. (1998). Teaching Introductory Physics - A sourcebook. Spinger-Verlag, New York.