# A wheel rolling on a horizontal flat or inclined surface

1. Apr 26, 2015

### Yam

1. The problem statement, all variables and given/known data
A wheel rolling on a horizontal flat surface at a constant velocity experiences no friction force. Why?
A wheel rolling on an inclined surface at a constant velocity experiences friction force.

2. Relevant equations

3. The attempt at a solution
A wheel rolling on a horizontal flat surface at a constant velocity experiences no friction force. I dont quite understand why there isnt any friction, i understand that the point of contact between the wheel and the surface has a velocity of zero, so it is considered not moving and thus there isnt any friction. However, doesnt it apply to the wheel on an inclined surface?

2. Apr 26, 2015

### AlephNumbers

There is certainly a static frictional force on a wheel that is rolling smoothly at a constant velocity. Otherwise it wouldn't be rolling.

3. Apr 26, 2015

### brainpushups

I'll have to disagree with you on this one. Once the wheel is rolling there is no net force on the wheel if it rolls with constant velocity . Certainly static friction is required to get the wheel to roll, but not required once it is rolling. I am, of course, referring to an ideal case.

4. Apr 26, 2015

### Yam

Yes i understand this point, but i still dont quite understand why you have friction on an inclined plane, also what kind of friction is it?

5. Apr 26, 2015

### AlephNumbers

I think that just because there is no net force, that does not mean that there are no forces acting on the wheel.

6. Apr 26, 2015

### haruspex

Even that is not strictly true. Many aircraft pre-spin their wheels for landing to reduce wear. If they happen to get it just right, there's no frictional force needed.
It says "inclined surface at a constant velocity". How that is achieved is not stated, but whatever the means there's no acceleration. Given that gravity will have a downslope component, something must oppose that.

7. Apr 26, 2015

### Yam

I made a mistake with my post.

A wheel rolling on a surface with constant acceleration experiences frictional force.

I kind of understand why.

A wheel rolling on a horizontal flat surface at a constant speed means that the wheel is pure rolling without slipping. There is no translational force present and thus there will be no friction even on the roughest surface.

On the other hand, a wheel undergoing constant acccleration means that it is undergoing up the incline with pure rolling without slipping. The maximum force of friction acting against the wheel will be mgsin(angle of incline)

Do you guys think that i am right?

8. Apr 26, 2015

### haruspex

If it's rolling on a horizontal surface at constant velocity there's no net horizontal force. If there's a frictional force it will be horizontal. What is going to balance that?

9. Apr 26, 2015

### Yam

This got me interested. How does pre-spinnign their wheel reduce wear and tear from friction?

10. Apr 26, 2015

### haruspex

Actually I just checked my claim and found that this has been proposed many times, but not implemented. Seems the extra weight of the means to do it is not justified.

11. Apr 26, 2015

### haruspex

Couldn't parse that. You don't know whether it's uphill or down.
It may be clearer/more general to think in terms of torque. If the wheel is rolling and accelerating then it has angular acceleration. That requires a torque, and friction is the only force that has a moment about the wheel's centre.
You left out $\mu$.

12. Apr 26, 2015

### Yam

hmmm.. i dont understand, wouldnt maximum friction be when

μmgcos(angle) = mgsin(angle) ?

13. Apr 26, 2015

### haruspex

OK, I see - I didn't notice you put sin, not cos.
So I change my response to:
Parallel to the slope there are two forces, mgsin(angle) and friction. If there's no acceleration then they're equal and opposite. If accelerating up slope then friction must be the larger. Friction may also be the larger if accelerating downslope very fast (faster than it would slide with smooth contact).

14. Apr 26, 2015

### Yam

Thanks for pointing this out! cheers!