# Question regarding a rolling ball

1. Oct 1, 2012

### aftershock

Hi,

This has been bugging me for a little while now. Imagine a ball is rolling along on a rough surface without slipping. Under ideal conditions it will just continue rolling indefinitely right?

However, if you were to draw a free body diagram the normal and gravitational force would cancel out and you'd have friction. How does friction not cause the velocity of the ball to change when it's the only force acting?

2. Oct 1, 2012

### Jolb

The frictional force on the ball only arises when the ball slides. A rule of thumb is that the frictional force is proportional to the difference in velocity between the surfaces in contact. There is no frictional force on the ball when the ball rolls without slipping, because the point on the ball touching the surface has zero velocity relative to the surface. This is the reason why cars use wheels rather than something that slides--e.g. skis.

3. Oct 1, 2012

### aftershock

Can you expand on this a little? It's my understanding that the frictional force only does work when the ball slides. If the ball is rolling the friction force is still acting (even though it does no work) otherwise the ball would just spin around in place instead of rolling along.

4. Oct 1, 2012

### dipole

Well, what is work? It's equal to the change in energy. If friction can't do work on a rolling ball, how can it change its energy and slow it down?

Basically, friction creates a torque on the ball initially giving it some angular momentum about it's center of mass, but once the ball is rolling without slipping, there is no more force - the ball is just rolling freely and feels no friction.

Real balls slow down because as they roll over little bumps and irregularities on a surface they rub and scrape against them.

5. Oct 2, 2012

### Jolb

Imagine we had a ball rolling on a table in the International Space Station (there is no "gravity"; everyone in the station feels zero g's). The ball continues to roll along the table until it reaches the edge of the table. What happens once it rolls off the table? Does it stop rolling the instant it passes the edge of the table? That is what you suggest.

In reality, the ball would continue to "roll" as if it were still in contact with a fictitious table along the same linear trajectory it was following when it left the table. This is because the ball feels no torque and thus continues at a constant angular velocity, as dipole has explained.

6. Oct 2, 2012

### sophiecentaur

The model of a rolling ball with friction needs to include a description of what causes the friction. The interface between ball and table must have finite thickness and that implies a variation of relative speeds over that small distance. (Radius and circumference) it's the same with gear teeth, which always rub a bit and lose energy during rotation. This could imply some energy loss with rotation.

7. Oct 2, 2012

### mikeph

+Even if completely smooth, the ball and table will deform in such a way that the ball's centre of mass is always slightly rolling uphill. The constant deformation will cause a slow transfer of kinetic energy into heat.

8. Oct 2, 2012

### Naty1

what ideal conditions?

this is not an 'ideal condition.

Post #7 hits the nail on the head, but also is not 'ideal conditions'....

More here:

http://en.wikipedia.org/wiki/Rolling_friction

some practical insights are included like:

9. Oct 2, 2012

### aftershock

Let me rephrase my question.

Imagine the ball is rolling along at 10 m/s to the right and I draw a free body diagram. I would have the normal force up, the gravitational force down, and the frictional force to the left.

If I add all the forces up I would have a net force of friction. If I set that equal to ma I'd be wrong since the ball is rolling at a constant 10 m/s. What's wrong with this?

10. Oct 2, 2012

### Staff: Mentor

Why are you assuming a friction force?

11. Oct 2, 2012

### aftershock

If the friction force wasn't present wouldn't the ball spin in place instead of rolling forward?

12. Oct 2, 2012

### Staff: Mentor

No. Once the ball is rolling without slipping along a horizontal surface there is no friction force involved. (Except for the dissipative 'rolling friction', which I assume you wish to ignore.)