Record and turntable, Physics help. I need the solved equations, but cannot get them right for some reason.?

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Part A

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

Express ωf in terms of It, Ir, and ωi.

Part B

Because of friction, rotational kinetic energy is not conserved while the disks’ surfaces slip over each other. What is the final rotational kinetic energy, Kf, of the two spinning disks?

Express the final kinetic energy in terms of It, Ir, and the initial kinetic energy Ki of the two-disk system. No angular velocities should appear in your answer.

Answer:

A) ωf = ωi * It / (It + Ir)

B) Ki = ½ * It * ωi²

Kf = ½ * (It + Ir) * ωf² = ½ * (It + Ir) * [ωi * It / (It + Ir)]² → some (It + Ir) cancel

Kf = ½ * ωi² * It² / (It + Ir) = ½ * It * ωi² * It / (It + Ir)

Kf = Ki * It / (It + Ir)

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