# Runner on a turntable

1. Apr 9, 2016

### reminiscent

1. The problem statement, all variables and given/known data
A 55 kg 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 3.1 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 120 kg-m2. 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.

2. Relevant equations
ΔL = 0
L1 = L2

3. The attempt at a solution
This was ripped off from a problem in the book that asked for "the final angular velocity of the system if the runner comes to rest relative to the turntable," which I did just that, but I just noticed that this problem's last sentence is a different variation (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.")
Here is what I did - should I change anything at the end?

2. Apr 10, 2016

### haruspex

Your working is not easy to read (posting images is for diagrams and printed/typed matter) and you do not define your variables, which makes it hard to follow.

3. Apr 10, 2016

### reminiscent

Well T stands for turntable and R stands for runner. L1 was the initial and L2 was the final. L1 consisted of the angular momentums of both the turntable and runner. I treated them as a system at the end having the same angular velocity.

4. Apr 10, 2016

### reminiscent

Can anyone tell me what I did wrong?

5. Apr 10, 2016