I was trying to wrap my head around this solution, and the whole idea of a car moving around a level curve, how the friction supplies the centripetal force. But I still can't wrap my head around the idea. So maybe it would help if I walk you through my logic and you can see where I went wrong in my reasoning.
You can deduce from the centripetal force requirement that while moving on a merry-go-round, there has to be some centripetal force that is keeping you moving in the circular pattern. But let's say for a moment that there's no centripetal force acting on me and I'm standing on a merry-go-round. I'll move at a constant velocity in a direction tangent to the center of the circle. "Static friction acting on an object points opposite to the direction in which the object would slide along the other object if static friction didn't exist." So I'm right now at the moment after I started sliding, sliding with a velocity vector that's orthogonal to the centripetal force. If static friction points in the opposite direction, and I'm sliding tangent to the circle, shouldn't it be pointing in the direction opposite the tangent rather than perpendicular to the tangent line?
Best Answer
If you are sliding across the surface, then "static friction" is not applicable. Consider first your motion on a merry go round without sliding. At any instant, your tangential velocity is the same as the tangential velocity of the surface under your feet. Since the two velocities are the same, no instantaneous frictional force is required to keep you moving along with the surface in that direction. Let's say that your merry go round is spinning in the x-y plane and you are at the 'top,' such that your velocity has no y component.
An instant later, the point under your feet is pulled toward the middle of the circle by the centripetal molecular forces. These forces are (at this point in the circle) completely in the y direction, but not in the x direction. However, since you are not molecularly bound to the merry go round, those forces do not affect you. So you are moving in the x direction, but not in the y direction. Now there is a small relative motion between you and the surface in the y (i.e. radial) direction. Because that is the direction if the relative motion between your feet and the merry go round, that is the direction of static friction.
Now, if you were to overcome static friction and begin sliding, the direction of kinetic friction would not be purely radial, because in addition to your radial relative motion, your tangential speed would begin to differ from that of the surface so there would be tangential frictional forces as well. But that is dependent on your position with respect to the surface is changing, which does not apply to your original question about static friction.