Show all work please! Thank you! A 55 kg runner runs around the edge of a horizo

Question

Show all work please! Thank you!

A 55 kg runner runs around the edge of a horizontal turntable mounted on a vertical, Motionless axis through its center. The runner's velocity relative to the earth has magnitude of 3.1 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.20 rad/s relative to the earth. The radius of the turntable is 3.0 m, and its moment of inertia about the axis of rotation is 120kg-m^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.

Explanation / Answer

using law of conservation of angular momentum

L1 = L2

I1*w1 - (m*v*r) = I2*w2

(120*0.2)-(55*3.1*3) = I2*w2

I2 = I1+(m*r^2) = 120+(55*3^2) = 615 kg-m^2

then
(120*0.2)-(55*3.1*3) = 615*w2

w2 = -0.792 rad/s

So the answer is w2 = 0.792 rad/s

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