Explanation for rolling ball

As we saw when we rolled a ball on the floor it went some distance and stopped due to tbe friction between the floor and the ball.

Let's see how it happens...

(F refers to the friction from the floor to ball)

Because of the force F, there is a unbalance force which makes a moment around the O. That's why it rolls.

From newton's law

F = ma

-F = ma(m-mass of the ball)

a = -(F/m) ----------------(A)

The acceleration "a" is a minus value. So the ball is not accelerating. It's decelerating.

Let's take it from another way...

When we take this motion, we can divide it into 2 motions
1. Linear motion
2. Rotational motion
Regarding the rotational motion...

τ = Iα
FR = Iα

a = rα

FR = Ia/R
a = FR²/I-------------------(B)

When we use equations for rotational motion, we get a plus value for "a". That means this ball is accelerating.

As we see ball never increase its velocity but in decrease its velocity. So we can understand there should be a mistake in the (B) equation. How do we define this difference?

Actually when ball rolls on the floor, the ball push the floor from its mass. Because of that following picture shows how it really happens...

The ball sinks in the floor very little which creates R and F forces from the edge of the ball. Because of the R force a moment was generated stop the motion of the ball.