Direction of Rolling/Sliding Friction

[brendan3eb]

This much more of a general question that I've encountered in quite a few problems and I haven't found an answer to in my books or searching the net yet. Take, for example, a ball that has been propelled into motion by a spring gun on the floor. Initially, the ball accelerates so that the ball is in not in smooth rolling motion. I have always assumed that for this first part, before the ball conforms to smooth rolling motion, that the sliding friction force acts in the direction opposite of the displacement of the ball, and I pretty much just treat the ball like a block that is sliding on a floor with friction. Then after determining when the ball begins smooth rolling motion, I imagine that there is a static frictional force acting in the direction of displacement and opposite of the rolling of the ball.

Is this an appropriate way to describe the direction of the frictional force in rolling motion? If so, then it would be appropriate to say that the first frictional force leads to greater angular acceleration, whereas the second frictional force would lead to lesser angular acceleration in accordance to τ=Iα

 

[Doc Al]

Here's how I would describe it. Starting with a ball moving without rolling. Kinetic friction between surface and ball, which acts in a direction opposite to the ball's motion, does two things: (1) it slows down the ball (F=ma), (2) it exerts a torque on the ball starting it rotating (τ=Iα). (Note that mechanical energy is lost in this process, as usual with kinetic friction.)

At some point the translational and rotational speeds of the ball will match the conditions for rolling without slipping. At that point, assuming a horizontal surface, the friction goes to zero. As long as the ball rolls with a constant speed, no friction force is need. (If friction existed, the ball would accelerate.)

Make sense?

 

[TeaCup]

What about the ball rolling uphill or downhill? According to http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html" : "Note that the friction can be in the direction of motion (rolling downhill) or opposite to it (rolling uphill)." h

But the picture at another http://www.lastufka.net/lab/cars/why/mrollf.htm" shows that the the friction is oppose to the direction of motion when rolling downhill.

However, from my own understanding, I agree with the first website. I think if a rolling object is accelerating, then the direction of friction should be along the motion. Because I imagine the accelerating contacting part of the wheel to the ground is pushing back on the ground, which causes the ground to oppose this pushing-back, therefore exert a friction force against the contacting part, and consequently generates a friction force along the direction of motion of the rolling object. Moreover, the same friction force along the direction of motion will cause a frictional torque that will work against the torque originally causing the angular acceleration of the rolling object. (If this is true, will I glide constantly without ever stopping on a bicycle on a perfectly flat surface?)

As for decelerating...well...I'm not quite sure...I suppose the opposite exists that the contact point of the rolling object is pushing ahead of the ground and generate a friction force opposing this pushing-ahead (kind of like how when you try to slow down from a sprint that you will try to step ahead and have the friction force pushes back to slow down). Therefore, this friction force will be opposite of the direction of motion of the rolling object. But to this point...I'm not exactly sure if it's right to think that the frictional torque generated from this friction force opposite to the direction of motion will actually cause angular acceleration to the rolling object? Hmmm...

But I heard that for a bicycle, the friction associated with the back wheel is along the direction of motion, but the front wheel is opposite to the direction of motion. Is this true? If so...why? Shouldn't both wheels have frictional forces at the same direction relative to each other regardless whether the bicycle is accelerating or decelerating?

Anyway, I'm not exactly sure if I'm making sense...perhaps someone can clarify about the rolling friction when an object is rolling uphill/downhill?
Also, when I described an accelerating rolling object, I assume it's also applies to the situation of rolling downhill, and decelerating applies with rolling uphill...maybe anyone can also comment on whether this assumption is correct?

 

[Doc Al]

What about the ball rolling uphill or downhill? According to http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html" : "Note that the friction can be in the direction of motion (rolling downhill) or opposite to it (rolling uphill)." h

But the picture at another http://www.lastufka.net/lab/cars/why/mrollf.htm" shows that the the friction is oppose to the direction of motion when rolling downhill.

For the simple case of a ball rolling down a hill without slipping, the second statement is correct. The static friction acting on the ball is opposite to the motion when the ball rolls downhill. (Note that the first site goes on to discuss 'rolling' friction, which is a different thing entirely.)

However, from my own understanding, I agree with the first website. I think if a rolling object is accelerating, then the direction of friction should be along the motion.

It depends on what's making it accelerate. If you apply additional forces--such as through an axle--then you can certainly have the friction force act in the direction of the acceleration. But for the simple case of the ball rolling downhill, gravity acts down while the static friction acts up the hill (thus opposing the motion).

But I heard that for a bicycle, the friction associated with the back wheel is along the direction of motion, but the front wheel is opposite to the direction of motion. Is this true? If so...why? Shouldn't both wheels have frictional forces at the same direction relative to each other regardless whether the bicycle is accelerating or decelerating?

The back wheel is the drive wheel. By pushing the pedals you apply an external torque to the back wheel through the axle. If you are accelerating, then the friction on the back wheel acts in the direction of motion. (It's the friction force that accelerates the bike, after all.)

The front wheel is just a passive wheel--the only torque on it is due to the static friction from the road. That friction acts opposite to the direction of the bike's motion, making the wheel spin faster.

 

[TeaCup]

Thanks a lot Doc Al. I think this is giving me some quite definite answers.
However, I think I'm still a little fuzzy about when the friction moves along the direction of motion and when against it during angular acceleration. For example, what about pulling a yo-yo horizontally? In this case, isn't the string providing additional force through the yo-yo's axle but the friction will nonetheless be opposite to the motion?

I guess I haven't really grasp the pattern that determines the direction of the friction during angular acceleration...I mean, I think gravity force and force through axles are all the same...I don't really understand what is the determinative factor causing the friction to be against the direction of motion (in case of gravity) but along for some other forces.

 

[Doc Al]

However, I think I'm still a little fuzzy about when the friction moves along the direction of motion and when against it during angular acceleration. For example, what about pulling a yo-yo horizontally? In this case, isn't the string providing additional force through the yo-yo's axle but the friction will nonetheless be opposite to the motion?

It's true that for a small axle, pulling the yo-yo horizontally will produce a friction force opposite to the motion. If you use a large enough axle, you can make the friction force in the same direction as the motion. Take the case of a massless rope wound around a cylinder. If you pull the rope horizontally the friction actually increases the cylinder's acceleration.

I guess I haven't really grasp the pattern that determines the direction of the friction during angular acceleration...I mean, I think gravity force and force through axles are all the same...I don't really understand what is the determinative factor causing the friction to be against the direction of motion (in case of gravity) but along for some other forces.

There's no rule that friction always goes in the same or opposite direction as the overall motion--that depends on other factors. What is always true is that friction tends to oppose slipping between surfaces. But sometimes it's a bit tricky to figure out which way the surfaces are tending to slip.