What role does static friction force play for a rolling object? How can I know what direction it points?

Question

Fundamentally, what does a friction force do for a rolling object? I am very confused by the way my textbook explains it. In my textbook , it says: A wheel rolling on a horizontal flat surface at a constant velocity experiences no friction force. Why? On the same surface, there is an acceleration of the wheel pointing to the right (probably caused by a force), so the ball is angularly accelerating in the clockwise direction. In this case, a friction force appears, and it is also pointing to the right. How come? What does the friction do for this wheel? On an inclined plane, a ball freely rolls down the surface. The direction of friction is up the ramp, which confuses me because in the previous example the friction force was in the direction of the wheel's acceleration. And there is a difference if a wheel is freely rolling and if there is a torque acting on the ball's center of mass. WHY??? What does friction do in these cases? How does it cause an object to roll?

Answer 1

"A wheel rolling on a horizontal flat surface at a constant velocity experiences no friction force. Why?"

The statement does not mention a driving force, so we have to presume there isn't one. This would be similar to when an object is briefly pushed by a force and then slides over a horizontal, frictionless surface at constant velocity: no force is required to keep it going (as per Newton's first law of motion). Given the lack of a driving force, IF there were a friction force on the wheels, it would be the only force acting, and would therefore slow down the object, which would contradict "rolling... at a constant velocity."

"On the same surface, there is an acceleration of the wheel pointing to the right (probably caused by a force), so the ball is angularly accelerating in the clockwise direction. In this case, a friction force appears, and it is also pointing to the right. How come?"

Presumably, a torque is being applied to the wheel (misquoted here, I think, as a "ball") by some kind of drive shaft, not shown. The torque causes an angular acceleration (α), by definition. If the wheel is to continue rolling without slipping, the linear acceleration (a) of the wheel has to keep pace with the angular acceleration, so that a = rα (a condition of rolling without slipping) remains true.

The way this is accomplished is that, as the surface of the wheel accelerates rotationally and tries to slip over the surface, a (static) friction force engages to keep this from happening. Since the surface of the wheel tries to move past the surface opposite the way the wheel is rolling, the friction force engages to prevent this by pointing in the opposite direction, IN the direction the wheel is rolling. This is just like when you walk. When you want to move forward, you try to slide your foot backward over the surface you are on, and the friction force which prevents that acts in the opposite direction and pushed you forward (to see this even more clearly, imaging trying the same thing on ice; your foot would just slip backward).

"On an inclined plane, a ball freely rolls down the surface. The direction of friction is up the ramp, which confuses me because in the previous example the friction force was in the direction of the wheel's acceleration. And there is a difference if a wheel is freely rolling and if there is a torque acting on the ball's center of mass. WHY???"

This is a very good question, and made me think for a bit about something I had not considered before. The difference in this case is that, for the ball on the ramp, there is from outside force trying to pull it forward. This is the force of gravity down the plane. In the previous example, the cause of the wheel's rolling was (presumably) from an internal torque sent to the wheel through a drive shaft. So, effectively, FIRST the wheel started to rotate, and THEN friction engaged to make rolling without slipping happen (as described above). The wheel first tried to rotate, and thus slide (backward) over the surface, as we do when we walk. The friction force engaged to prevent that (thus providing a friction force FORWARD on the object), and this caused the rolling without slipping. This was the result of internally-generated torque.

But in this case, the driving force is coming from outside the object, and trying to make it slide down the incline. Once the object tries to slide, the friction force (which always opposes motion or attempts at motion) engages to oppose that, meaning it points opposite the direction of motion. Because friction then becomes to only force on the ball NOT acting through the center of mass (gravity does act through the center of mass), it provides a torque around the center of mass. Thus, the object then begins to roll (without slipping, if the conditions are right).

So, in this case, the object tries to slide first, which friction prevents, and that leads to rolling.

This is analogous to a similar situation in linear motion. As mentioned above, if you are walking, you are pushing your feet backward on a surface, and, as they try to slide backward over the surface, static friction engages with an opposing force forward to prevent that, driving you forward. However, if someone (or something) is trying to drag you forward, but you are not sliding, static friction is engaging backward to prevent you from sliding forward. The key difference is how and from where the driving force (or torque, in the rolling cases) is being generated.

Answer 2

Friction is simply the force between 2 objects which either causes or resists relative lateral motion between them. The most common usage is "sliding" friction, referring to 2 objects that have relative motion along a common plane. The term "rolling friction" applies to any combination of things that resists or causes motion in a "rolling" interface.

"lateral" is used here to define motion that is perpendicular to whatever force hold the objects in contact....eg a block on a table held in place by gravity.

Static friction applies when there is no relative motion and the friction force is simply resisting any relative motion. Moving ( or "dynamic" ) friction applies whenever there is relative motion. Depending on the nature of the surfaces, static and dynamic friction can be very different.

Many physics problems state that friction should be ignored. This is done to simplify the problem in the interests of demonstrating a specific principle.

The universal rule for this kind of problem is to draw a picture and label all the relevant forces. Then recognize that any acceleration must be due to a "net force" which is the sum of any forcing functions and of any forces that might resist motion / acceleration.