A 55kg runner runs around the edge of a horizontal turntable mounted on a vertic

Question

A 55kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude of 3.1m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.20rad/s relative to the earth. The radius of the turntable is 3.0m, and its moment of inertia about the axis of rotation is 120kgm^2. Find the final angular velocity of the turntable if the runner slows to a walk in such a way that she is at rest relative to the earth. I got the answer w2 = 0.793rad/s but I am not sure if it is correct or not because it said she is at rest relative to the earth. Does it mean I have to consider its as 0? Please help me! Thank you so much

Explanation / Answer

  the the and v are related

1*r=v ==> 1=v/r
the momentum before the runners stops is

1*I
when the runner stops he becomes part of the disk and the momentum is
2*(I+mr^2). These must be conserved so

1*I=2*(I+mr^2)

solve for 2=1*I/(I+mr^2) = 0.0483 rad/s

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