When a ball rolling without slipping along an inclined plane reaches the bottom, it has a linear velocity $v$ and angular velocity $\omega\ =v/r$ at the bottom. Then it continues its motion on the horizontal floor. At the moment it reaches the bottom, the point of contact of the ball with the floor is at rest, and there is no external force that could cause slipping. We can think that in this case there would not be any friction. But if there is no friction, the ball will continue to move FOREVER, which apparently does not happen. What is the explanation?
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1 Answer
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You're right, in the ideal situation there would be no frictional force and the ball would continue rolling for ever. The reason real balls come to rest is because their weight either causes the surface they're on to deform slightly, or causes the ball itself to deform slightly. Think, for example, of rolling a ball on a thick carpet or on sand. As the ball rolls, it squishes down the surface in front of it. The surface, in turn, pushes back on the ball (Newton's 3rd law). That's the force that brings the ball to rest. (Of course, the ball can also slow down if the surface is not perfectly level, and no real surface is.)
The next order effect is probably air friction, but this is also very tiny if the ball is small and is not moving very fast. It might, however, be the dominant force on a very rigid, light-weight ball rolling on a very rigid surface.
