I was pleasantly surprised when I found a problem actually asking for angular speed, omega, in your text. I might have know they would mess it up. The answer they gave was the frequency, about 500 Hz. The angular speed is of course 2pi times as great.
The solution uses the idea that it makes one eighth of a rotation in the time it takes light to travel 35 km out and 35 km back. This is about 2.33 E-4. so frequency = 1/8 x 1/2.33E-4
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