# Rolling and Friction

My prof really confused me.

Given a rolling sphere, which way does the friction point to?

http://img187.imageshack.us/img187/7968/rolling1.png [Broken]
http://img338.imageshack.us/img338/8753/rolling2.png [Broken]

I think it probably matters if the ball is purely rolling or partially skidding, but I'm not sure which direction friction points to in either case.

So can someone please tell me under which cases the friction will point which way?

Thanks!

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Oddbio
Gold Member
First think, which way is the ball rolling? not rotating, I mean if it were moving which was is it going?

Then you know that the ball will eventually slow down due to friction so therefore, the force must be in the opposite direction.

This would be the second picture (bottom) in your image.

However, this is not your usual static or kinetic friction. Here you will have rolling friction, because the ball is not sliding. and the coefficient for that will be much smaller than for other forms of friction.
Which is why it is more efficient to role something than to drag it along.

Oddbio
Gold Member
Just to clear up any confusion (and maybe this is why you were confused). The force should NOT be at the bottom of the ball. So, although, the correct drawing is the bottom one, that drawing makes it look like the force is acting to increase rotation, but this is not so. Draw the force from the center of the ball to the left.

So, you mean that the friction does not act on the bottom contact point of the ball? Or are you saying that because the ball is rolling, it has both pure rotational and pure translational motion, and the translational motion is being slowed by the friction whereas the rotational motion is not affected?

See my old prof told us that the second diagram is correct, but the newer (and more reputable) prof told us that the first one is correct because that friction force would try to slow down rotation.

diazona
Homework Helper
Or are you saying that because the ball is rolling, it has both pure rotational and pure translational motion, and the translational motion is being slowed by the friction whereas the rotational motion is not affected?
That one, more or less. Technically the force has to act through a point of contact, but it would be quite complicated to try to think about it 100% correctly. Nobody really understands just how friction works in detail.
See my old prof told us that the second diagram is correct, but the newer (and more reputable) prof told us that the first one is correct because that friction force would try to slow down rotation.
As far as I know, they can both be correct. If the ball is slipping while rolling, then kinetic friction acts against the relative motion between the ball and the ground. In that case the frictional force will slow down the rate of rotation. But if the ball is rolling without slipping, kinetic friction will be absent and you'll be able to observe the weaker effect of rolling friction, which acts to slow down the translational motion of the ball. Or more precisely, it slows both the translational and rotational motions in the same way, so that the ball continues to roll without slipping.

Oddbio
Gold Member
The problem lies with what you are thinking of the force as acting on, and it should be as diazona stated.

Keep in mind, that for the first diagram you must consider the force acting on the edge of the ball, going in the opposite direction of rotation which will slow the ball down. But in the second diagram you must consider the force as acting at the center of the ball (on the entire ball) slowing down it's motion.

The translational and rotational motion should be thought of as separate. So, from experience we know that if you roll a ball it will slow down, in this case it is moving to the right and therefore it will have an acceleration to the left (slowing down), and so the net force will be to the left. If you look at the first diagram you can see that either it is saying the ball will speed up to the right (which can't happen) or that the force is acting on the rotational motion only. In that case you will have to find a way to connect the rotational motion with the translational motion.

Also, probably the most important point is that the equation to find the force of rotational friction from the coeficient of rotational friction does not depend on the body's rotation. You simply treat it as a point particle moving under a force opposing motion (just like kinetic friction), of course in reality this assumes that the ball is rolling without slipping. However, if the ball is rolling and slipping then you will have two different equations of friction to find, which would be rolling and kinetic friction, and they would both point in the same direction. At any rate, this all suggests that the second diagram is the more convenient one to use. (placing the friction force arrow at the center of the ball for clarity)

let me clear you on this:

1.)Case1: If u push a wheel by a certain force. Then friction acts opp to direction of your push and it is friction therfore which rotates the ball by producing torque.

2.)Case2: But if you rotate the ball by giving the ball a torque by your hands then friction will act in the direction of rotation, then friction will tend to move the ball forward and the ball will roll on the surface because u provided it torque and friction provided it forward push.

Case 1 is equivalent to sliding and rotation.
CAse 2 is equivalent to pure rolling.

Oddbio
Gold Member
Friction can never give the ball a "forward push". It always acts to oppose motion only.

Friction can never give the ball a "forward push". It always acts to oppose motion only.
As an extension of this into another topic because of the sometimes difficult rules involving friction...

Suppose we have an object that we are holding in our hand and our hand is parallel to the floor. We are not in motion. Our hand is supplying the a force up equal to mg where m is the mass of the object. No vertical or horizontal motion.

Then we take a step forward.

The object in our hand would have a change in kinetic energy as we step forward. In this case friction between our hand and object would be doing + work on the object? correct or please help me if I am thinking about this improperly?

Same idea as an object in the bed of a truck at rest. As the truck accelerates forward, friction supplies the force that changes the kinetic energy in the object in the bed of the truck?

Oddbio
Gold Member
You are right, I didn't think of that.
But in this problem I do not believe it is possible for that to happen unless the surface on which the ball is resting is moving.

Perhaps I just misunderstood what R Power was saying.

You are right, I didn't think of that.
But in this problem I do not believe it is possible for that to happen unless the surface on which the ball is resting is moving.

Perhaps I just misunderstood what R Power was saying.
Well relative to the bed of the truck or hand, static friction is not supplying a forward force it seems because the object is not accelerating relative to the bed of the truck. I believe if the object was slipping in the back of the truck, the force of friction would be in the opposite direction in relation to the motion of the truck. So I am getting mixed up a bit also. I understand the rotational stuff. I was just trying to think about a different situation. Problem is frame of reference.