Rolling puck on a spinning disk

[Mr. T]

Homework Statement

A small puck is placed on a disk spinning with angular speed OMEGA around axis perpendicular to the disk and passing through its center. The coefficient of static friction between the disk and the puck is MU. At what distance(s) from the center of the disk will the puck be at rest?

Homework Equations

Rotational Inertia of Rotating Disk:

I=(1/2)*M*R^2

Force of Static Friction

F=MU*(NORMAL FORCE)

The Attempt at a Solution

By "at rest" I believe it means when the puck is rolling ON the spinning disk in a way that keeps it in the same place. But I have no idea how to determine the distance the puck needs to be at for that to happen.

 

[RoyalCat]

There are two possible and equivalent approaches to this problem. The first is just about applying Newton's Second Law.

Look at the puck on the spinning disk, what forces act on it? In order for it to be rotating with angular speed $$\omega$$ at a distance $$R$$ from the center of the disk, what must the force towards the center of the disk be?

The other approach involves fictitious forces. If we look at the puck from inside the rotating system, we see it at rest, but we also observe an additional force acting on it. It is "falling" outwards with a centrifugal acceleration.

The formulation of Newton's Second Law for both these systems is equivalent, find either, and apply the limitations on the static friction force, and you'll find the possible distance from the center.