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During analysis of rolling motion, why do we consider coefficient of friction as that of static friction and not kinetic friction?

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    $\begingroup$ Are we talking about rolling or about circular motion? I suspect you're talking about rolling, and if you are, think about how tires behave on ice... $\endgroup$ – Jerry Schirmer Jun 5 '13 at 10:49
  • $\begingroup$ Since you're talking about rolling motion, it might be useful to understand how gears work. $\endgroup$ – Mike Dunlavey Jun 5 '13 at 15:29
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Like @Jerry said, this is all to do with how a wheel works (or similar rolling object; a giant meatball for example). This figure should help:

enter image description here

As you can see from the image, we consider static friction because while the whole meatball may be in motion, the part touching the ground (the only part friction can act on) is not moving relative to the ground. If it were moving, this would be considered sliding. If you've ever driven a meatball on ice, you'd agree that sliding is definitely a bad thing.

In fact, the entire reason your meatball can roll around is due to static friction. When you apply a torque on the meatball, it wants to rotate on the spot. Without static friction, it would do just that and there would be no net forward motion. However, static friction causes the part of the meatball touching the ground to stay in one place. But the meatball still has a torque, so it will rotate; it rotates with a forward motion as long as it can't overcome static friction where it "meats" the ground. If your meatball ever starts to slip, then we discuss kinetic friction, which is usually less than static friction. This means the forward force you could potentially apply to your meatball is severely reduced and it would go nowhere (but it would go there fast!).

Static friction. That's how I roll!

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  • $\begingroup$ Minor nitpick: Road tires have tread only to displace surface rainwater. This is why racing drivers use slicks on dry days. On dry days, treads reduce static friction, not increase it. $\endgroup$ – RedGrittyBrick Jun 5 '13 at 14:25
  • $\begingroup$ @RedGrittyBrick I stand corrected. Thanks, I'll get rid of that. Is it then why they're made of rubber? $\endgroup$ – Jim Jun 5 '13 at 15:07
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Static friction is for when two surfaces do not move relative to one another (no rubbing), whereas kinetic friction is for when two surfaces do move relative to one another (rub against one another). For rolling motion a good starting place for understanding which is relevant is to think about a tire on a car.

Kinetic friction is appropriate when the tire on a car is not getting enough traction and it spins without the car moving forward, as say can happen on ice, because then there is rubbing of the tire tread on the ice (which are the two relevant surfaces in this case).

But if the tire "rolls without slipping", on say a dry road, then static friction is appropriate because there is no relative motion between the tire tread and the road (which are the two relevant surfaces in this case). To see that there is no relative motion in this case think of a tire rolling without slipping as being like the tracks on a tank (compare this picture of a flat tire to this track simulation video): where the tire meets the road it is slightly deformed to be flat on the road and this flat part and the road do not have any motion between them (there is no rubbing of these two surfaces).


You might also find it helpful to look at the two animated GIFs here.

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The idea is that the bottom of the wheel is actually stationary, which is often hard to get your head around. Here's a great analogy, though: walking.

When you walk, do both of your feet move at the same speed? Of course not! You wouldn't be walking if they were. If you really pay attention to your feet, one foot is actually stationary (relative to the ground) while the other one is moving much faster than your overall motion.

The same thing happens between the top and bottom of a tire. The top point is moving in the same direction (relative to the car) as the car is moving (relative to the ground), so it's moving twice as fast as the car (relative to the ground). The bottom point is moving in the opposite direction, so it's stationary (relative to the ground). On average, every point on the wheel will move at the same velocity as the car, so don't worry about logic breaking your tires. :)

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I usually consider a rolling friction coefficient which is different from the static and the sliding friction.

The reason is because the elastic deflection of a rolling element imparts resistance what is non-linearly proportional to the applied (contact) load.

For steel over steel depending on lubrication conditions a typical value us $\mu_{roll}=0.008$

The static friction is used to determine the available traction, beyond which slipping will occur. When pushing a bowling ball, if you push slightly it will roll, but if you push with more force that static friction times weight then the ball will slide and roll.

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  • $\begingroup$ rolling friction and static friction both exists in this scenario and both do very different things. The question pertains to the friction (resistance to sliding) between the rolling object and the surface. Not the combined forces from resistance to being compressed then separated from the surface and resistance from the bearings/axel, which is closer to what rolling friction is $\endgroup$ – Jack Dozer Jun 5 '13 at 13:49

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