What is the final angular velocity, ωf, of the two disks?

Consider a turntable as a circular disc of inertia 0.142 kg⋅m2 rotating at a constant angular velocity of 4.80 rad/s2 around an axis passing through the center and perpendicular to the plane of the disc (the “primary axis of disk symmetry”). The disc axis is vertical and the disc is supported by frictionless bearings. The turntable motor is off, so no external torque is applied to the shaft.
Another disk (a register) is placed on the first so that it falls coaxially (the axes coincide). The moment of inertia of the disc is 8.60×10−2 kg⋅m2. The initial angular velocity of the second disk is zero.

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