# Why is is harder to get an object to slide than it is to roll given that $\mu_s>\mu_k$?

I learned that rolling involves the coefficient of static friction unlike sliding that involves the coefficient of kinetic friction. It's known that the coefficient of static friction is always higher than the coefficient of kinetic friction. This should result in rolling to be more difficult than sliding as it involves higher frictional force, which is not the case in real life.

Edit Thanks for your answers, but I am lost indeed in those details you mentioned. Let me rephrase the question. Assume a single car tire on a horizontal surface in two situations not attached to anything: 1- It's rolling (µs is involved) 2- It's sliding (µk is involved) since Fsmax=µsN (where Fsmax is the maximum static friction and µs is the coefficient of static friction), Fk=µkN (where Fk is the kinetic friction and µk is the coefficient of kinetic friction), and µs > µk, I can assume that the tire will experience higher frictional force while rolling than while sliding. This conclusion is totally counterintuitive to me.

Additional Info: Please put my question in context with the following quote of my physics teacher. "If you lock your wheels driving down the road on dry concrete if they are sliding, or skidding, you will have less friction than if they are rolling. (µs > µk) This is in theory the idea of antilock breaking systems (ABS) in cars; they cause intermittent lockage of breaks to keep the wheeling rolling intermittently to prevent sliding and thus provide higher friction force (stoppage force) using μs instead of μk."

• I have edited my answer accordingly Mar 23, 2020 at 18:49

You are making the typical mistake that because $$f_\text{k}=\mu_\text kN$$ that means that $$f_\text s=\mu_\text sN$$. However, this is not true. In general we have $$f_\text s\leq\mu_\text sN$$, i.e. the maximum static friction force is $$\mu_\text sN$$. Once the static friction force would need to be larger than this value to prevent slipping, then we get slipping. Therefore, $$\mu_\text s>\mu_\text k$$ really leads to the statement

This should result in getting an object to start to slide to be more difficult than sustaining sliding, as it involves higher frictional force

The rolling part of your question is somewhat irrelevant, since this is true for the relative motion between the surfaces at the point(s) of contact irrelevant of what the rest of the body is doing. However, what is important to realize for your system is that it is much easier to get the object to roll than it is to slide because once you apply some force to the object, static friction will start acting as well, thus providing a torque and causing the object to roll.

So, in this particular instance, your confusion probably arises from equating rolling to overcoming the static friction force; they are not the same thing. Overcoming the static friction force is harder than maintaining sliding, but rolling is something different.

If you want to look at exploring the nature of the static friction force for a rolling object when another external force is applied to that object, check out my answers for the following posts

Response to Edited Question

Assume a single car tire on a horizontal surface...I can assume that the tire will experience higher frictional force while rolling than while sliding. This conclusion is totally counter-intuitive to me.

If you are trying to accelerate the car with a large enough magnitude so that the friction between the tire and the road is at its maximum value, then yes, that friction force will be larger than the friction force if there was sliding. However, this does not have to be the case at all points during driving (I would guess most of the time the car is never close to this point in usual, safe driving conditions). You seem to be thinking that if static friction is involved it must be at its maximum value, or that if rolling is occurring that static friction is at its maximum value. Both assumptions are false in general.

Please put my question in context with the following quote of my physics teacher. "If you lock your wheels driving down the road on dry concrete if they are sliding, or skidding, you will have less friction than if they are rolling. (µs > µk) This is in theory the idea of antilock breaking systems (ABS) in cars; they cause intermittent lockage of breaks to keep the wheeling rolling intermittently to prevent sliding and thus provide higher friction force (stoppage force) using μs instead of μk."

In this case we are talking about being right at the interface between slipping and not slipping, so indeed we want to focus on the maximum value of the static friction force. If the brakes try to stop the wheels too quickly, then the required static friction force to prevent slipping increases, thus increasing the ability of slipping. Anti-lock brakes therefore try to prevent this.

The coefficient of static friction gives an estimate of the maximum value of the static friction force between two surfaces. The actual static force can be anything less than that. If a car is accelerating, static friction pushes it forward. If it is braking, the force is backward. The size of the force depends on the torque on the wheel from the engine or brakes. (If the force reaches its maximum, you go into a skid.) Neglecting other forces, the friction would be zero if the velocity is constant. (In rolling, there is a retarding force associated with the deformation of the two surfaces.)