A homogeneous disk of radius 9 in. is welded to a rod AG of length 18 in.

Question:

A homogeneous disk of radius 9 in. is welded to a rod AG of length 18 in. and of negligible weight which is connected by a clevis to a vertical shaft AB. The rod and disk can rotate freely about a horizontal axis AC, and shaft AB can rotate freely about a vertical axis. Initially rod AG is horizontal (θ0 = 90?) and has no angular velocity about AC. Knowing that the smallest value of θ in the ensuing motion is 30?, determine

(a) The initial angular velocity of shaft AB,

(b) Its maximum angular velocity.