# Friction in Slipping and Rolling

I'm solving a rotational motion problem that involves slipping and rolling. The problem's basic setup has a sphere rotated and then placed onto the ground, at which point it begins to acquire translational velocity. A solution in my textbook assumes the following:

"Once the ball starts rolling without slipping, there is no more frictional sliding force, and so the velocity will remain constant."

Why does friction stop exerting a force? Am I mistaken that friction exerts a force whenever an object and its surface might be distanced from each other?

• Why does friction stop exerting a force?

It doesn't! Static friction still works. The wheel is not slipping; it is rolling. At the contact point the wheel and surface stay together because of static friction. This point of the wheel doesn't slide over the surface. So no kinetic friction, but certainly static friction. If not, then how would you start your car? Your tires need grip (static friction) on the surface, and must not slip.

The quote you give does though mention constant velocity. That is the same as saying no acceleration and of course also no angular acceleration. When that is the case, which it will be after some time, all torques must sum up to zero. So, if friction is the only force that causes a torque, then friction must be zero. Friction is only making the wheel start speeding up it's rotation - it makes the wheel start to turn, when your car speeds up. But when the rotation is constant, there is no more friction - just like when the block is sliding with constant speed on the ice, or when the space shuttle is drifting at constant speed, there is no friction that brakes it.

• Am I mistaken that friction exerts a force whenever an object and its surface might be distanced from each other?

Yes, you are mistaken. If I lift a bag of potatoes from the floor, there is no friction.

But I know what you mean: what if you move the object in parallel along the surface. Still, ideally you can have a no-friction icy surface, but apart from that I guess not.

• Comments are not for extended discussion; this conversation has been moved to chat. – ACuriousMind Mar 28 '17 at 14:29

The rigid body, or ball in the picture described above has an applied force on it. The frictional force will continuously increase until it reaches a maximum static frictional force.

The static frictional force is defined by

$$f_{s,max} = \mu_s F_N$$

At that point, the object begins to slide and static friction no longer applies. Instead, between the object and the surface that it is sliding on, there is a more or less constant kinetic frictional force which can be defined by: $$f_k = \mu_k F_N$$

Am I mistaken that friction exerts a force whenever an object and its surface might be distanced from each other?

It depends on what you mean by "distanced". If the object is still in contact with a surface, it will experience friction. However, if you pull the object and lift it away from said surface, it will of course, no longer be under the influence of friction. Instead you are holding the object in a fluid (e.g. air) and depending on the applied force, can experience another non-conservative force such as air resistance.

Friction will not stop. Friction is responsible for the wheel's horizontal motion. However, the velocity will become (and remain) constant.

It's called static friction. What you don't have anymore, is kinetic friction.