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

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The discussion focuses on calculating the final angular speed of a spinning disk when a person runs on it. The disk has a radius of 4.69 m and a mass of 280 kg, while the person weighs 55.0 kg and runs at a tangential speed of 1.70 m/s. The conservation of angular momentum principle is applied, using the equation 0 = I(person)ω(final person) + I(disk)ω(final disk), where I represents the moment of inertia calculated as I = mr². The challenge lies in rearranging the equation to solve for the final angular speed of the disk.

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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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