What Is the Final Angular Speed of a Spinning Disk with a Running Person?

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To determine the final angular speed of a spinning disk with a running person, the conservation of angular momentum principle is applied. The moment of inertia for both the person and the disk is calculated using the formula I = mr². The initial angular momentum is zero since the disk is stationary, leading to the equation 0 = I(person)ω(final person) + I(disk)ω(final disk). The person’s tangential speed and distance from the axis are used to find their contribution to the system's angular momentum. Rearranging the equations correctly allows for the calculation of the disk's final angular speed in rad/s.
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A flat uniform circular disk (radius = 4.69 m, mass = 280 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 55.0-kg person, standing 1.59 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 1.70 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.

i know that i have to use :

0=I(person)w(final person) + I(disk)w(final disk)

and i know I=mr^2

but i just don't know how to rearrange everything...correctly..
 
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