What is the relationship between sliding and rolling motion of a ball?

AI Thread Summary
The discussion explores the relationship between sliding and rolling motion of a ball subjected to a horizontal force. Initially, the ball, at rest, receives a force that creates a counterclockwise torque, resulting in an initial angular velocity. As the ball slides, a clockwise angular velocity is generated due to its linear velocity. The key question posed is at what velocity the ball transitions from sliding to rolling, with the assumption that rolling begins when the sliding velocity becomes zero. The conversation invites further insights and comments on this dynamic interaction.
Marin
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hi there!

I considered the following problem:

a ball of radius R on a horizontal plain is at first in rest. Then it receives a horizontal force for a very short time at a point placed 1/3R from the plain and the ball starts moving with initial velocity v_0. There is also a friction when the ball slides.

the question is: at which velocity v will the ball start rolling?


here´s what I figured out:

the force initiates a torque such that the ball gets initial angular velocity w_0, counter clockwise. But the velocity v initiates another angular velocity w in clockwise direction. My assumption is that the ball will start rolling counter clockwise when the velocity v becomes 0.

what do you think?
 
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