A Ball is rolling on a flat surface

[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 ?

 

[A.T.]

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 ?

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

 

[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.

 

[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 ;-).

 

[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.

 

[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.

 

[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 :
$$mgh = \frac{mv^2}{2} + \frac{I\omega ^2}{2}$$
?

 

[Tazerfish]

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 :
$$mgh = \frac{mv^2}{2} + \frac{I\omega ^2}{2}$$
?

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).

 

[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.

 

[vanhees71]

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 :
$$mgh = \frac{mv^2}{2} + \frac{I\omega ^2}{2}$$
?

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

 

[rcgldr]

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 :
$$mgh = \frac{mv^2}{2} + \frac{I\omega ^2}{2}$$
?

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

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.