Rotating surface/friction question

[xplosiv]

Homework Statement

http://img10.imageshack.us/img10/9781/probs.jpg

The Attempt at a Solution

Hey guys, I understand how to find the static friction point (equate mv²/r to max static friction). However, I'm confused as to which direction (in to out or out to in) is the correct one ie. from kinetic slipping to 'sticking'. At the moment I'm thinking it's outside in (Jo's answer) but I can't justify it properly. Thanks!

 

[LowlyPion]

You've determined the boundary where it starts to slip. And the boundary is dependent on

μ*m*g > m*ω²*r

or

r < μ*g/ω²

This means that outside this distance it slips doesn't it? If the aim is to have it slip until it grabs then ...

 

[nlightner]

I would first like to clarify that the direction of motion is not relevant in determining the direction of friction force. Friction force always acts opposite to the direction of motion or the potential direction of motion.

In this scenario, the object is rotating on a surface, so the direction of friction force will be tangential to the surface at any given point. When the object is at the point of slipping, the direction of motion is tangential to the surface and the direction of friction force will be in the opposite direction, towards the center of rotation. This is because the object is trying to move away from the center of rotation, and the friction force is trying to oppose that motion.

On the other hand, when the object is at the point of sticking, the direction of motion is also tangential to the surface, but the object is trying to move towards the center of rotation. In this case, the friction force will act in the same direction as the direction of motion, outwards from the center of rotation. This is because the friction force is trying to prevent the object from sliding inward towards the center of rotation.

In summary, the direction of friction force will always be opposite to the direction of potential motion, regardless of whether the object is slipping or sticking. I hope this helps to clarify any confusion.