Why Does Friction Act in the Direction of Motion for a Rolling Wheel?

[gzg]

Hi. A friend of mine asked me an interesting question a couple of days ago and I've been thinking for several days but I cannot find a logical answer since I'm not taking any physics course in university. I typed physics forum in google to find the logic of the question and found here.

The question is sth like that:

We know the direction of friction force is opposite to direction of motion but let's assume just a wheel moving to right-side in a 2D world. We're expected that the direction of friction force is left-side but it didn't work like that. At the point where wheel and ground touch each other, the wheel seems like moving left; so the direction of friction force will be right-side. So it means the friction force is seen as a positive force for motion, since the direction of wheel's motion and the direction of friction force are both right-side. How could it be possible?

Finally, sorry if I wrote a word or a sentence mistake. English is not my native.

 

[Filip Larsen]

Welcome to PF.

I'm not sure I follow all the details in your descriptions, but you should know, that there are primarily two types of friction forces. Static friction which allow shearing forces between two objects that are not moving relative to each other and dynamic friction which is when there is relative motion. Usually wheels, like wheels on a car, are modeled as either rolling without slipping (using static friction) or rolling with slipping (dynamic friction). Your case seems to involve rolling without slipping?

When there is dynamical friction at play between two objects in relative motion, it is true that the friction force on each object is opposite the relative motion with respect to the other object. So if you slide a block to the right across the floor, the dynamic friction force acting on the block is pointing left and the friction force acting on the floor (which can be seen as moving left relative to the block) is pointing right. Thus the two friction forces (the one acting on the block and the one acting on the floor) are equal but in opposite direction.

 

[Doc Al]

We know the direction of friction force is opposite to direction of motion

That's not true. What is true is that friction opposes slipping between surfaces.

but let's assume just a wheel moving to right-side in a 2D world. We're expected that the direction of friction force is left-side but it didn't work like that. At the point where wheel and ground touch each other, the wheel seems like moving left; so the direction of friction force will be right-side. So it means the friction force is seen as a positive force for motion, since the direction of wheel's motion and the direction of friction force are both right-side. How could it be possible?

Let's assume that the wheel is rolling without slipping along a horizontal surface, so the only friction we need to consider is static friction. (We'll ignore the complication of 'rolling' friction, due to surface deformation.) Note that the point of the wheel in contact with the surface is (momentarily) at rest with respect to the surface.

Is the wheel accelerating? If the wheel is moving at constant speed, then the static friction at the point of contact will be zero.