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I remember the un-intuitive result that pure rolling without acceleration involves no friction by the law of conservation of angular momentum. Conjectures:

  1. I understand that when I'm driving a car at constant velocity on a straight, flat road, the wheels are in a state of pure rolling?
  2. One reason I have to keep expending fuel is that the tire is not in point contact with the ground, causing the normal force from the ground to be off-center, providing a decelerating torque?

Another reason I have to keep expending fuel is that there is some air-resistance.

First, are my conjectures correct? Also, in driving a vehicle in the real world under the conditions previously described, is the friction force still zero, even factoring in air-drag and real world imperfections?

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  • $\begingroup$ I remember the un-intuitive result that pure rolling involves no friction do you mean to say rolling without slipping and without acceleration? $\endgroup$ – Aaron Stevens Mar 23 at 19:39
  • $\begingroup$ Yes. I'm particularly interested in what happens when driving a car/bicycle on a straight, flat road at constant velocity. That is rolling without slipping, right? $\endgroup$ – Rohit Pandey Mar 23 at 19:41
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    $\begingroup$ The car squashes the tires as they roll along. As each part of the tire expands back to its ordinary shape after being squashed, you don't get all the energy back. $\endgroup$ – Andrew Steane Mar 23 at 19:46
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    $\begingroup$ Besides that, you also lose energy because of wheel deformations which although elastic do not return total energy, its kind of lost and spread through the wheel. $\endgroup$ – Žarko Tomičić Mar 23 at 19:46
  • $\begingroup$ Can we classify these phenomenon as being contributions by friction? $\endgroup$ – Rohit Pandey Mar 23 at 19:57
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At 60 mph on the freeway, the friction losses from an automobile are approximately 50% rolling resistance and 50% air resistance. The air resistance obviously comes from air drag, which is dependent on the shape of the vehicle, its cross-sectional area, velocity, etc. Rolling resistance comes from all of the frictional forces involved in transferring power to the driving wheels, including engine internal friction, transmission friction, drive shaft and differential friction, and deformation of tires on the road.

Regarding the tires on the road, at normal inflation pressures, the part of the tire that is not touching the road is approximately round. As the tire rotates, and a piece of the tire touches the road, it becomes flat, and the four (assuming four wheels are on the road) flat portions of the tires are what provide the traction that keep your car going in the preferred direction. Because the tires get "deformed" to provide this flat surface that you drive on, the sidewalls of the tires rapidly flex when this surface contacts the road, and then rapidly unflex as this patch of the tire leaves the road surface. This rapid flexing and unflexing heats the tires somewhat, indicating that this physical process occurs because internal friction in the tire generates heat that does not contribute to propelling your car down the road.

There is, of course, a small amount of friction involved in rolling the tires on the road that is not due to tire flexion. You maintain control of your vehicle due to this friction, and in fact, that is why carefully driven tires do not last forever. This rolling resistance is low at a constant velocity, but even so, well designed tires will only last 60,000 to 70,000 miles before the tread is worn out and new tires are required. If you want to engage in a scenario where this friction is no longer present, try driving on ice. Tire wear will practically cease on such a surface, but you will not be able to change speed or direction under these conditions, and you will soon have to replace much more than your tires.

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  • $\begingroup$ thanks David, this is a nice exposition of the topic. -NN $\endgroup$ – niels nielsen Mar 24 at 0:40
  • $\begingroup$ Thanks, nice answer. Is it fair to say that when I don't change speed or direction, the friction (not normal reaction) between tyres and ground is zero? $\endgroup$ – Rohit Pandey Mar 24 at 2:58
  • $\begingroup$ No. There is still a small amount of friction between the tires and the road. Physics books list this as coefficient of rolling resistance, and it exists even for rail cars, which use steel wheels on steel rails. $\endgroup$ – David White Mar 25 at 5:05

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