Discovering Friction Directions: An Overview

[josendk]

why are there directions of friction true? (picture below, they are all standing on a flat table and there is static friction)

[URL]http://www.upload3r.com/serve/230511/1306176168.jpg[/URL]

how can I in the future easyli see where the friction is going, so I don't have to write up these three everytime:

sum of F = m*a
sum of tau = I * alpha
a = R*alpha

 

[tiny-tim]

welcome to pf!

hi josendk! welcome to pf!

(have a tau: τ and an alpha: α )

you can find the direction of friction by first finding the direction (clockwise or anti-clockwise) of the torque of F about the point of contact

 

[josendk]

thank you for the welcoming and the reply :)

they all rotate clockwise but the friction does not have the same direction in all three examples, can you explain that?

 

[yster]

I was going to say that the friction is in opposite direction to where they are most likely to go but the third one confuses me. The 1st and 2nd card will obviously move to the right if the force is big enough so friction is to the left. I find it hard to tell the direction in which the 3rd one witt move.

Tiny-Tim the torque looks clockwise about the point of contact in all three cases to me? Please explain why the the third case has friction in the opposite direction.

My thoughts are that yoyo will not move horizontally and will rotate so the friction opposes this rotation instead of the movement

 

[josendk]

to clear things up my professor did this experiment in class last semester and when you pull up, it will rotate clockwise, if you pull at a 45 degree angle it will NOT roll, but slip instead.

Actually it is number 2 I have a hard time understanding because the torques from the center of the yo-yo go the same way :s
My logic would be that they would have to oppose each other as in 1 and 3.

the picture is from my physics-book university physics solutions

 

[tiny-tim]

they all rotate clockwise but the friction does not have the same direction in all three examples, can you explain that?

hi josendk!

yes, in all three cases, the yoyo accelerates clockwise, and so must roll and accelerate to the right

in the third case (F vertical), isn't it obvious the friction must be to the right (because the friction is the only horizontal force)?

in the other two cases, we need to do a bit of thinking to find the direction of friction …

assuming the yoyo is accelerating, if the ground suddenly turned to frictionless ice, what would happen? the force F would want to linearly accelerate it at F/m, but it would want to rotationally accelerate it at Fr/I …

(r is the height of F above the centre)

these match (and the yoyo will continue to roll despite the lack of friction) if F/m = RFr/I, ie I/mR² = r/R

I/mR² is usually about 1/2, so if F is less than about 3R/2 up from the table (r < R/2), then the LHS wins, ie the linear acceleration wins, the yoyo wants to move faster than the rolling rate for its angular speed will let it, ie the bottom of the yoyo wants to slip forward, and so the friction is backward (but gets less as r+R approaches 3R/2)