Friction Required for Billiard Ball to Roll without Slipping

Thread starter domephilis
Start date May 5, 2024
Tags

Rigid body dynamics Rotational dynamics

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SUMMARY

The discussion centers on the mechanics of a billiard ball transitioning from sliding to rolling without slipping on a horizontal surface. The key equation derived is μ_k = 12v_0^2 / 49gd, where μ_k is the coefficient of kinetic friction, v_0 is the initial linear velocity, g is the acceleration due to gravity, and d is the distance traveled before rolling begins. Participants explored energy conservation principles, torque, and angular momentum to analyze the problem, emphasizing the role of friction in this transition.

PREREQUISITES

Understanding of Newtonian mechanics, specifically forces and motion.
Familiarity with the concepts of kinetic and potential energy.
Knowledge of angular momentum and torque.
Basic proficiency in calculus, particularly integration and differentiation.

NEXT STEPS

Study the relationship between linear and angular motion in rolling objects.
Learn about the conservation of energy in systems with friction.
Investigate the effects of different coefficients of friction on rolling motion.
Explore the dynamics of rigid body motion and the role of torque in rotational systems.

USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and frictional forces in mechanics.

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.