Friction Required for Billiard Ball to Roll without Slipping

Thread starter domephilis
Start date May 5, 2024
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Rigid body dynamics Rotational dynamics

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A billiard ball with an initial linear velocity v_0 and zero angular velocity rolls on a horizontal surface with a coefficient of friction mu_k, eventually rolling without slipping after traveling a distance d. The relationship derived shows that mu_k equals 12v_0^2 divided by 49gd. The discussion emphasizes using energy principles to relate initial and final velocities, while also addressing the role of friction and torque in the motion. Participants explore the conservation of energy and the complexities of angular momentum, particularly in relation to the frictional forces acting on the ball. The conversation highlights the challenges in deriving the necessary equations and understanding the dynamics involved in the transition from sliding to rolling motion.

May 6, 2024

domephilis

One last thing I'd like to post on this thread. I have found the following explanation from Doc AI in response to this thread (https://www.physicsforums.com/threads/linear-and-angular-acceleration.184624/):

"The article is correct. The linear acceleration of the center of mass just depends on the net force on the object, not on where the force is applied. The angular acceleration about the center of mass depends on where the force is applied. (Both statements are just consequences of Newton's 2nd law.)

Realize that the work you do on an object is force times the distance that the contact point moves. When you push the object with an off-center force the contact point moves more (compared to an equal on-center force), thus it takes more work to maintain the force--that extra work goes into the rotational energy."

I think this really cleared it up for me intuitively. In my understanding, torque explains the "how" of the motion of an object, but F=ma is true regardless of how the motion occurs internally. The important thing for energy conservation is that the movement of the contact point is not the same as the movement of the CM. Hope this helps.