A homogeneous sphere of mass m and radius a is welded to a rod AB of negligible

Question:

A homogeneous sphere of mass m and radius a is welded to a rod AB of negligible mass, which is connected by a clevis to a vertical shaft AC. The rod and sphere can rotate freely about a horizontal axis at A, and shaft AC can rotate freely about a vertical axis. The system is released in the position β = 0 with an angular velocity φ0 about the vertical axis and no angular velocity about the horizontal axis. Knowing that the largest value of β in the ensuing motion is 30?, determine

(a) The initial angular velocity φ0,

(b) The value of φ when β = 30?.