Motion of an object spiraling outwards on a rotating disk with friction I recently came across the following problem:
A spinning disk has an object initially located at radius $R$. The object is moving with the same angular velocity as the disk (which I will call $ω$). There is a string tying the object to something in the center of the disk. At time  $t = 0$, the string is cut. The static friction between the object is less than the centripetal force required to keep the object in uniform circular motion (the disk's motion is constant throughout the problem), so the object begins to spiral outwards.
I am trying to find an equation for $r$ as a function of time and the initial conditions (we are given the initial radius $R$, and initial angular velocity $ω$).
In particular, I was wondering if the angular velocity of the object would be constant, what direction the friction would be directed in, and if this equation could then be applied to situations in which the disk is frictionless (by plugging in $μ = 0$ into my final equation).
Intuitively, I felt that this would somehow involve centrifugal force. Please let me know what you think.
 A: Some ideas to help you:
The angular momentum of the object will change if there is a lateral force on it. Without friction the object would move in a straight line after the string is cut - so it would move outward and thus encounter disk "going faster". This means the angular momentum of the object will increase.
A: Angular velocity of the object around the center of the disk will not be constant, but will decrease with time.  You can analyze the system in the reference frame of the rotating disk, in which the object slides over a motionless surface.  The frictional force is then very simple: it is always directed opposite to the motion of the object. There are two pseudoforces: the centrifugal force, which causes the object to move outward, and the Coriolis force, which acts perpendicular to the velocity of the object, curving it in a direction opposite to the disk rotation. 
A: I calculated that it would actually follow an elliptical path, determined by a central force of kinetic friction (as you said, less than what would be required to keep it on a circular path with the disk).  But I assumed the kinetic friction would be a central force just like the static friction would be if it were sufficient to keep the object stuck, and Ben51 's reply seems to indicate that is incorrect for kinetic friction.
My low-brow experiments with a coin and a marble on a pottery wheel seem to show some elliptical tendency, but they always end up spiraling out after a revolution or 3.  Not sure if I'm off in my calculation and it should really be a circular or elliptical spiral, or I'm just unable to control parameters tightly enough on the pottery wheel to get a sustained elliptical orbit.
I was looking for someone to corroborate my elliptical conclusion, since I'm a mathematician and not a physicist.  Would be happy to provide my calculations if anyone is interested.
