Angular Speed of Disk with 260 kg Mass and 69 kg Person

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To find the angular speed of the disk when a person runs on it, the conservation of angular momentum principle is applied. The initial angular momentum of the system is zero since the disk is stationary. As the person runs with a tangential speed of 3.10 m/s, their angular momentum can be calculated using their mass and distance from the axis. The resulting angular speed of the disk can then be determined by equating the angular momentum of the person to that of the disk. This approach illustrates the relationship between linear and angular motion in a rotating system.
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A flat uniform circular disk (radius = 1.90 m, mass = 260 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 69.0-kg person, standing 1.97 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.10 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.

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