Turnable Angular Frequency, Torque,Inertia

1. The problem statement, all variables and given/known data
Turntable at an angular speed of Wj. Consider it to be a thin solid cylinder of mass M and Radius R. A mass m nought falls and sticks to turntable at a distance r nought from center.

a) Find new Inertia, I
b) Find new Angular Frequency, W
c) Coefficient of static friction, µ s. What is the largest r so that mass does not slide off. Assume disk is spinning at W.

2. Relevant equations
Newtons second law of motion for each of the respective bobs mass M, Moment of Inertia, angular frequency 1/2mw^2

3. The attempt at a solution
I drew the cylindrical turntable and made the equation. Because the equation for the moment of Inertia of cylinder is MR^2, the new Inertia with the additional bob of m, I got the new equation MR^2+mr^2. Could you help me find the angular frequency of this?


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