# Static and rolling friction difference

1. Dec 24, 2013

### alingy1

Is rolling friction considered static friction?
After all, the two surfaces are not moving at the point of contact.

My textbook separates static and kinetic friction.

2. Dec 24, 2013

### Panphobia

I think you are talking about something such as a cylinder rolling down on an incline? If so then only static friction is considered because it is not slipping. So yes you are right.

3. Dec 24, 2013

### alingy1

What I wrote:
My textbook separates static and [/b]kinetic[/b] friction.
What I wanted to write:
My textbook separates static and [/b]rolling[/b] friction.

4. Dec 24, 2013

### alingy1

"You are absolutely right that there is no relative motion at the point of contact, so it is not kinetic friction. It is also not static friction since the wheel is moving, though the point of contact is not; if there were no rolling friction, the wheel would continue forever on a perfectly level surface. "
-"Richard J. Plano Professor of Physics emeritus, Rutgers University"

Then:
http://www.school-for-champions.com/science/friction_rolling.htm#.UrpEQZFlPls says that it is both static and kinetic!

What is going on here!?

5. Dec 25, 2013

First you have to understand what friction is.Friction is the force resisting the relative motion of two surfaces in contact
Friction only exist between surfaces in contact.
Static friction exist between two surfaces not sliding.Kinetic friction exist between two surfaces sliding.

6. Dec 25, 2013

### ehild

What is going on here? It is the difference between a real word phenomenon and its simple model.
Imagine a wheel or ball that can roll. If both the ball and the ground are absolutely hard, neither of them deform, then the point of contact is really a single point. When that point on the ball moves with respect to the ground, (the ball slides) it is kinetic friction. If the contact point is in rest with respect to the ground, (the ball rolls) it is static friction. Both friction forces are parallel to the ground and their point of application is at the contact point.

Without any other forces parallel with the surface, kinetic friction would slow down a sliding ball.
When the ball rolls with constant velocity, the static friction is zero. When some force accelerates the rolling ball, the static friction opposes the relative motion between the ball and ground, and represents a non-zero force.

In the real word, the ball and ground both can deform and they are in contact along a surface. Your second URL explains it. See also http://www.real-world-physics-problems.com/rolling-resistance.html.

The forces along the elementary surfaces of contact add up to a force and a torque. The point of application of that force is not exactly below the centre of the ball as in case of ideal rolling, but a bit away from it, and it is not horizontal. That is rolling resistance or rolling friction. The rolling resistance will stop the rolling motion of the ball sooner or later.

ehild

7. Dec 25, 2013

### alingy1

Thanks for the detailed answer. In my physics problem (Grade 12), they give me the coefficients of static, kinetic and rolling friction. For a problem with a ball rolling, should I simply plug in F=uN, where F is the force of friction, u is the respective coefficient (in this case, rolling coefficient) and N is the normal force?

8. Dec 25, 2013

### ehild

In case of kinetic friction, F=uN. The static friction is not a defined value, uN is only the upper bound, Fs≤uN. The exact value is determined by the problem and the rolling condition. If the ball rolls on horizontal surface, and no other force acts on it, the force of static friction is zero.
As for the rolling friction, it depends how it was defined, but I think you can use F=uN.

ehild

9. Dec 25, 2013

### alingy1

So, the coefficients of rolling friction take into account the nondominant static and kinetic friction forces too?

Thank you so much. Your explanations are very clear.

10. Dec 25, 2013

### alingy1

Oh I had an interesting thought in my head. If a cylinder rolls one way, and a force is applied to it in the opposing way, would there be static friction or rolling friction?
(Sorry, I have a friction thinking cap on.)

11. Dec 25, 2013

### ehild

You need to take rolling friction into account if the problem says it so. Usually it is much less than kinetic friction.

Now, if a cylinder rolls in some direction and a force is applied in the opposite direction, the cylinder will slow down. Its linear acceleration is determined by the applied force and the static friction. ma=F +fs. The angular acceleration is α = τ(torque)/I(moment of inertia). If it goes on rolling, the angular velocity of rotation is ω=-v/R , (if you take anticlockwise rotation positive) and the angular acceleration is α = -a/R.
Assume that the force is applied at the axis of the cylinder. It has no torque with respect to the axis. The torque of the force of friction has to slow down the the rotation: fs has to point forward.

Its torque is τ=R fs, with respect to the CM. The angular acceleration is α=Rfs/I. The linear acceleration is a=-αR=-R2fs/I.
ma=F+fs= -R2fsm/I, so fs(1+mR2/I))=-F. As F points backwards, fs points forward as we supposed.

In case the force is applied somewhere else (not at the axis), its torque also counts, and you can not decide the direction of the static friction beforehand. Take on a direction for fs, write up the equation for the forces and for the torques and apply the rolling condition. You will get fs, both magnitude and direction.

ehild