Rolling without Slipping


Anyway, here goes the exercise translated from Portuguese to English:

" A solid ball with 240g of mass rolls without slipping on a horizontal surface, with a constant speed of translation of the center-of-mass. The coefficients of static and kinetic friction between the ball and the surface are, respectively, 0.32 and 0.21. Taking as positive the direction of the speed of translation of the ball, what is the friction force between the ball and the surface, in Newtons? "

My teacher is still saying the correct answer is zero. I argued with him by e-mail, anonymous, and he just ignored my arguments and said to go talk with him personally. I know he just want to humiliate me, so I want to be sure of what I am saying. He asked me jesting, in the last email, if I knew what is ABS in cars or if I knew that in snow one shall use second gear, never first. I don't know what is his point, what it has to do with this case, I think he just don't want do admit he is wrong.

In the meantime, rolling without slipping, is a very particular case that I am not sure I understand, so I am not completly sure about this. Anyway, either kinetic or static there must be a Friction! That's my point, what I have been arguing.

When doing the exercise I supposed there was another force not mentioned... and calculated the Friction with: Friction = Normal * Uk.

I just could not conceive the friction didn't exist, given the conditions.
Well, what do you say?


Your teacher is of course correct within the limits of a sliding friction discussion. Consider first static friction. Since the table is horizontal there is no component of force tangent to the surface, hence even if the coefficient of static friction were zero there would be no sliding. Therefore the static friction force is zero. Now consider kinetic friction. Look at the relative velocity between the surface of the ball and the horizontal surface. Near the point of contact the velocity is wholly normal to the plane. Even if the coefficient of kinetic friction were zero there would be no sliding. Therefore the kinetic friction force is zero.

We found the ball in a rolling state so we do not have to explain how it came to be rolling. The startup transient probably involved some sliding friction forces. Also at the next level of detail we would have to consider the fact that balls and tables in reality are somewhat deformed by their contact so that a rolling ball would eventually stop due to energy loss from this constant deformation process. The force arising from this phenomena is called rolling friction.

Where did you get this absurd notion that your teacher is your enemy? At best he is your true friend, guiding you to better understanding. At worst he is less well educated than he should be and possibly less intelligent than you are. In that case he may be defensive when challenged but is still trying his best to help.