The spool has a mass of 60 kg and a radius of gyration k_G = 0.3 m. If it is released from rest, determine how far its center descends down the smooth plane before it attains an angular velocity of ω = 6 rad/s. Neglect friction and the mass of the cord which is wound around the central core.

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0.3 m G 0.5 m A 30°