Joey, stands at rest at the outer edge of the frictionless merry-go-round of Figure 9.27. The merry-goround is also at rest. Joey then begins to run around the perimeter of the merry-go-round, finally reaching a constant speed, measured relative to the ground, of \(5.0 \mathrm{~m} / \mathrm{s}\). What is the final angular speed of the merry-go-round?

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EXAMPLE 9.10 Period of a merry-go-round Joey, whose mass is 36 kg, stands at the center of a 200 kg merry- go-round that is rotating once every 2.5 s. While it is rotating, Joey walks out to the edge of the merry-go-round, 2.0 m from its center. What is the rotational period of the merry-go-round when Joey gets to the edge? PREPARE Take the system to be Joey + merry-go-round and assume frictionless bearings. There is no external torque on this system, so the angular momentum of the system will be con- served. As shown in the visual overview of FIGURE 9.27, we model the merry-go-round as a uniform disk of radius R = 2.0 m. From Table 7.1, the moment of inertia of a disk is disk MR. If we model Joey as a particle of mass m, his moment of inertia is zero when he is at the center, but it increases to mR when he reaches the edge. = 014 found. FIGURE 9.27 Visual overview of the merry-go-round. After: WY Before: Wi R M Known Find: T T = 2.5 s m = 36 kg M = 200 kg R = 2.0 m