# The Forces of Rolling and Rolling Without Sliding

In Halliday's Fundamentals of Physics textbook the author says:

"If a wheel rolls at constant speed, it has no tendency to slide at the point of contact P, and thus no frictional force acts there."

Which got me a bit confused since i thought that the only reason for the rolling of the wheel was due to the frictional force itself. To illustrate my point, imagine a wheel in a very slippery ice (that is, with no friction at all) then, if the wheel starts to rotate on ice it would not start to roll on the ice (it would be rotating in place), that is, the rotation and translation movements are independent of each other, or is it incorrect?

Yeah, they are both true, they just kind of sound opposite without being opposite.

If you find somebody who plays pool, billiards or the like, you can ask them to show you backspin tricks and stuff like that. The way that a ball spins on a surface is not determined by its translational motion, they can be different. Pool players use the resulting friction to curve the cue ball around obstacles or ensure that after a collision the cue ball rolls into a more favorable position.

The rolling-without-slipping behavior $$\omega =v_\text{trans}/R$$ is enforced by the friction, in the sense that the friction will eventually bring it to this behavior if nothing else intervenes. Once that equilibrium has been reached, the friction has nothing else to do, it has brought the system exactly where it wants it.

So simultaneously the friction is the cause of the behavior, and the friction doesn't do anything once the behavior is established.

Just to give a totally non-physics example of this, you could punch someone every time that they say a swear word until they don't say it anymore. Once this system reaches the steady state, “the reason I don't say that word anymore is that I don't want to be punched.” / “But I have observed you for many days, getting punched does not seem to be a big problem for you!” / “Right, because I stopped saying that word!”

This is something that happens very often with all sorts of constraints, constraints very often have forces that only apply if your motion is trying to violate the constraint. So if one is trying to find out when a car falls off of a loop-de-loop, one would indirectly look for a vanishing normal force, the normal force enforces the constraint that the car does not fly outward through the loop-de-loop surface, when this vanishes it implies that the car is just barely holding on and any lower speed falls off of it.

the only reason for the rolling of the wheel was due to the frictional force itself.

I would say the reason for a change in the rolling speed of the wheel is the frictional force. You're correct that if you begin from a stopped position, that you need friction to spin it up.

But the statement seems to be talking about a situation after they are already synched up. Suppose you push a cart on a regular road. As you push it up to speed, friction gets the wheels spinning at a sufficient speed so that there is no slipping.

Then suppose the cart rolls onto an icy sheet. Even though friction has gone to zero, the wheels do not suddenly slide. The rotation continues at the same rate.