a horizontal uniform disk with a mass M and a radius R = 1.2 m is free to rotate

Question

a horizontal uniform disk with a mass M and a radius R = 1.2 m is free to rotate about its central axis perpendicular to the disk's flat surface. A piece of clay with a mass m = 0.10 kg is sitting at the rim of the disk and does not slide on the disk. The moment of inertia of the disk-clay system about the central axis of the disk is I = 1.0 kg*m^2.

At time t =0 s, a constant external force, F, is applied tangentially at the rim of the disk causing the disk-clay system, initially at rest, to start rotating with a constant angular acceleration of alpha = 0.25 rad/s^2.

I need help with number 3. Please show your work.

1) What is the magnitude of tangential acceleration of the clay once the disk starts rotating?

I answered and got 0.30 m/s^2.

2) What is the centripetal force applied on the clay by the disk at t = 3.0 s?

I answered and got 0.0675 N.

3) What is the mass of the disk, M?

I am not getting the right answer for this part.

Explanation / Answer

given data
  
  
uniform disc radius R = 1.2 m, rotating about its central axis perpendicular to the disk's flat surface

mass of clay m = 0.10 kg,
mass of disc M = ?

moment of inertia of disc clay system about the central axis of the disc is I = 1.0 kg m2

3)
   we know that the moment of inertia of the uniform disc rotating about the central axis is I = 1/2 MR^2

   given that I = 1.0 Kgm2 = 1/2 (M+m)R^2
           (M+m) = 2*I/R^2
           = 2*1.0/1.2^2

           M = 2*1.0/1.2^2 - 0.1 = 1/289 kg

mass of disc is 1.289 kg

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