# B A Ball is rolling on a flat surface

1. Sep 14, 2017

### atos

Let's say we have a rolling without slipping (e.g. mentioned ball) on flat surface.
Does it mean that the ball will accelerate to infinity ?

2. Sep 14, 2017

### A.T.

Why would it accelerate at all? Is it an incline?

3. Sep 14, 2017

### atos

No, it's a flat surface. But it seemed to me that since we have static friction, it means that the angular and linear acceleration is non-zero.

4. Sep 14, 2017

### vanhees71

If it's friction it's decelerated (on the average) and thus coming to a halt. Roll a ball on a flat surface, and you can even observe this in Nature ;-).

5. Sep 14, 2017

### atos

Ok, but I've heard that's because of rolling resistance (rolling friction) and not the static friction. I assume that we have situation without rolling resistance.

6. Sep 14, 2017

### vanhees71

Any friction conteracts the motion and thus leads to deceleration. This must be so, because as a dissipative process friction leads to an energy loss of the moving object, heating up the environment.

7. Sep 14, 2017

### atos

Now I'm really confused. So why can we use the principle of conservation of energy, for example when the ball rolls down an incline :
$$mgh = \frac{mv^2}{2} + \frac{I\omega ^2}{2}$$
?

8. Sep 14, 2017

### Tazerfish

We can use the equation as an approximation.
There will be frictive losses which you could represent with an extra term on the right, but we don't know how big they will be and in most cases, friction is fairly negligible

As to your previous question, obviously the ball won't accelerate.
It would violate conservation of energy and momentum as well as intuition...
or have you ever seen a ball start to roll for no apparent reason?

Static friction does not apply any net force or torque to a resting ball.

Only a rolling ball will experience friction (in the direction opposite to its movement).

9. Sep 14, 2017

### rcgldr

In the case of a ball rolling on a flat horizontal surface, and absent any forces such as rolling resistance or aerodynamic drag, then static friction is zero. The ball continues to roll at constant velocity.

Last edited: Sep 14, 2017
10. Sep 15, 2017

### vanhees71

Very simple: You neglect friction here. Since the constant force is obviously conservative then the energy-conservation law holds.

11. Sep 15, 2017

### rcgldr

Static friction is not ignored, as static friction is what causes the ball to roll instead of slide. Since the ball is not sliding, then there are no losses related to friction. The idealizations here are that there is no rolling resistance, and there is no aerodynamic drag. Static friction doesn't cause a loss of mechanical energy; it just converts some of the gravitational potential energy into angular kinetic energy as the ball rolls down the inclined plane.