Dynamics - Rock in tire tread *please check answer*

[bodaciousllam]

I really have no idea if I even went about this problem right, maybe some of you wonderful people can help me out.

Homework Statement

http://img217.imageshack.us/img217/9358/wheeljk9.jpg

The Attempt at a Solution

http://img220.imageshack.us/img220/179/50999155cw8.th.jpg

 

[PhanthomJay]

Welcome to PF! Your solution looks good! Note that the friction force in your diagram,
2(F_f), acts radially inward on the pebble; but you also show a friction force in what you are calling the 'theta' direction (parallel to the rotation axis), which is zero, because there is no acceleration in that direction.

 

[bodaciousllam]

Jay,

Thanks, but I can't figure out why the answer came out negative, unless it means I have the friction vectors pointing the wrong way, but that doesn't make sense to me intuitively.

And the theta friction force was just something I forgot to erase

 

[PhanthomJay]

Oh, yeah, I missed your minus sign. The plus and minus sign difficulties are typical of all Physics problems. Actually, as your sketch shows. there are 2 Normal forces acting on the pebble; they act in opposite directions, each pointing toward the pebble, so that one value is negative (-323 N), and the other is positive (+323 N). The normal forces act toward the object they act on. It's probably better to just give the magnitude of the normal force, and show the direction in a sketch. Note that the friction forces on the pebble act radially inward, as they must in order to keep the pebble moving in the circle, in the inward direction of the centripetal acceleration. When the static friction force is not sufficient to produce the inward centripetal acceleration, that is, when the rpm exceeds 4000rpm, the pebble is flung off in a direction tangent to the circular path.