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A uniform wire of mass M and length d rotates in a horizontal plane about an...

A uniform wire of mass M and length d rotates in a horizontal plane about an axis passing through its center. Two small beads, each of mass m, are placed on the wire; friction between the beads and the wire is negligible. The beads are initially held on the wire by catches at a distance d/4 on either side of the center, and the system rotates with angular speed ω0. The catches are then released, and the beads slide outward along the rod.

a) Find the angular speed of the system when the beads reach the ends of the rod.

b) Find the angular speed of the rod after the beads fly off the ends.

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