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.