Solving Angular Speed of a Circular Disk

[teddygrams]

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..

 

[member 553083]

The angular speed of the disk is given by:w(final disk) = (I(person)w(final person)) / I(disk)where I(person) = 55.0 kg * 1.59 m^2 = 87.45 kgm^2I(disk) = 280 kg * 4.69 m^2 = 1319.2 kgm^2w(final person) = 1.70 m/sSubstituting in the above equation gives:w(final disk) = (87.45 kgm^2 * 1.70 m/s) / 1319.2 kgm^2 = 0.15 rad/s