Rolling Ball I

Classical Mechanics Level 2

A solid ball is initially moving with a velocity of v and it is sliding with no rotational motion at t = 0 t=0 on flat ground (which you can assume to be extended to infinity).

The coefficient of kinetic friction is μ k \mu_k and coefficient of static friction is μ s > μ k \mu_s>\mu_k .

Which of the following is true after a long long time (say when the system comes to some kind of final state)?

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See Rolling Ball IIA

See Rolling Ball IIB

The ball slows down and eventually rolls without slipping at constant velocity. The ball begins to rotate faster indefinitely due to torque induced by kinetic friction. The ball continues to slip because kinetic friction is weaker compared to static friction. The ball slows down to a stops eventually due to static friction.

Max Yuen by Max Yuen , 42, USA

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1 solution

For the option given here as correct to be true, both the ball and the surface on which it moves must be rigid(i.e., nondeformable) . Otherwise the ball will stop moving ultimately, as given in the first option.

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