# Does friction act on a wheel rolling at a constant speed

One of the things I've seemed to have taken for granted is that its the friction the floor exerts on a rolling wheel that prevents slip from occurring.

However, I ran into something that challenges that assumption: the contact point of the wheel on the floor has zero velocity relative to the floor, and no other lateral forces appear to exist. This implies that there is no friction. Otherwise the wheel would accelerate/decelerate, which there seems to be no mechanism for (ignoring drag, assuming no slip).

So, is it true to say no friction occurs on a wheel rolling at a constant speed? It is difficult to test as drag is difficult to isolate from the issue. No friction would imply that if the wheel rolled from a rough surface to a perfectly smooth surface, the wheel would not slip.

Is this effect analogous to a spring, such that if the wheel is overspinning, friction acts to slow the spinning down (spring extension, tensile force), if it underspins, friction acts to speed the spinning up (spring compression, compressive force), and a wheel spinning without slip experiences no friction (spring natural length, no force)?

• good question. i am not quiet sure about the theoretics, but in a practical situation, there would be some friction due imperfect and uncontrolled conditions. – ziggy May 9 '15 at 12:10
• Short answer is : NO. In ideal circumstances, there is no friction. Even during transition, there will be no friction. However, in practical scenarios, due to nature of contact not being point contact, friction will show up. – shivams May 9 '15 at 12:16

Maybe this thought experiment? Suppose you have a frictionless wheel and surface, in a vacuum, etc., and you spin up the wheel and push it forward so that its linear speed just matches the rotational speed and it moves along the surface with no slippage, i.e. zero net velocity at the point of contact. In this scenario, there are no forces of any kind, so teh system will continue exactly "as-is."

As you might expect, even in the absence of all other forces, any real-world materials will interact at the molecular level (van der Waals forces, perhaps) at the point of contact, leading to loss of kinetic energy.

• "In this scenario, there are no net forces of any kind". Apart from that I agree with your thought experiment. – Floris May 9 '15 at 14:18

There might be normal friction acting on the rolling wheel, namely static friction. The static friction force, $F_f$, is often written as,

$$F_f \leq \mu_s F_n,$$

where $\mu_s$ is the coefficient of static friction and $F_n$ the normal force, in this case the weight of the wheel.

Note the less-than-or-equal-to sign. The magnitude of this friction force can change depending on the other forces applied to the wheel. The friction force namely prevents the wheel from slipping. If however this force exceeds the right hand side of the equation, then the wheel will start to slip. In that case you need to use the coefficient of kinetic friction, which is typically lower. The magnitude of this force does not vary from zero to an upper limit.

When a wheel is rolling without slipping there will be another kind of friction. Namely due to the deformation of the wheel and the surface at the point (or rather the area) of contact.