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A uniform rod of mass 250 g and length 75 cm is free to rotate in...

A uniform rod of mass 250 g and length 75 cm is free to rotate in a horizontal plane around a fixed vertical axis through its center, perpendicular to its length. Two small beads, each of mass 25 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rod’s center, 9 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 7.5 rad/s. When the catches are released, the beads slide outward along the rod.

a) What is the rod’s angular velocity, in rad/s, when the beads reach the ends of the rod?

b) What is the rod’s angular velocity, in rad/s, if the beads fly off the rod?

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