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We've just studied rolling without slipping and I was having some trouble deciding the direction of the frictional force in some cases. So I pondered a little bit and recalled how you choose the direction of friction for "normal" translation without rotation:
Hope I didn't forget anything. Anyway, when rolling without slipping, the friction is static, so I presumed this static friction should have the same rules for deciding its direction than static friction in "normal" translation. And this worked! When I solved some exercises with this method, I got the right answer.
This even explains that weird fact that when rolling downhill, friction is uphill, but when rolling uphill, friction is also uphill. This is because whether the body is rolling uphill or downhill, the only resultant force parallel to the surface is Mgsin([tex]\theta[/tex]), [tex]\theta[/tex] the angle of the incline, and this is always directed downhill, so the opposing static friction would always be uphill. Problem solved, right?
Then, my professor gives us a test with a question about a yo-yo that rolls without slipping, which is having its string pulled by someone. The question came with the following free-body diagram:
[PLAIN]http://img12.imageshack.us/img12/5923/diagramso.png
Which doesn't make sense! The tension force exerted by the string is to the left; the friction should be to the right! Argh!
So HOW exactly do you predict the direction of friction when rolling without slipping?
Thanks.
- If the friction is static, then its direction is opposed to the tendency of movement (direction of the resultant of the forces parallel to the surface). So if the body has a tendency to move toward the right (there's a resultant to the right), then the static friction will be directed to the left.
- If the friction is kinetic, then its direction is opposed to the direction of motion parallel to the surface. So if the body is moving to the right, the kinetic friction is to the left.
Hope I didn't forget anything. Anyway, when rolling without slipping, the friction is static, so I presumed this static friction should have the same rules for deciding its direction than static friction in "normal" translation. And this worked! When I solved some exercises with this method, I got the right answer.
This even explains that weird fact that when rolling downhill, friction is uphill, but when rolling uphill, friction is also uphill. This is because whether the body is rolling uphill or downhill, the only resultant force parallel to the surface is Mgsin([tex]\theta[/tex]), [tex]\theta[/tex] the angle of the incline, and this is always directed downhill, so the opposing static friction would always be uphill. Problem solved, right?
Then, my professor gives us a test with a question about a yo-yo that rolls without slipping, which is having its string pulled by someone. The question came with the following free-body diagram:
[PLAIN]http://img12.imageshack.us/img12/5923/diagramso.png
Which doesn't make sense! The tension force exerted by the string is to the left; the friction should be to the right! Argh!
So HOW exactly do you predict the direction of friction when rolling without slipping?
Thanks.
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