Problem 36 in Chapter 2 relates to the Gedanken experiment in whichlight is shin

Question

Problem 36 in Chapter 2 relates to the Gedanken experiment in whichlight is shined towards the moon. Due to the rotation of the moonthe light flashes across the moon. In this case the floodlight is400km above the Earth. The only other information is that the lightsource rotates with a frequency of 100 Hz. The question asks howfast does the light flash across the surface. My best guess is touse the velocity addition equation. In order to do this the linearvelocity of the moon surface must be determined and a few othervalues must be looked up. My confusion is what is the stationaryreference frame. I am guessing the floodlamp. If so then is theinertial moving reference frame the Moon surface or the lightbeam?
Is this question asking for the velocity of the light along thesurface of the moon or the speed vector sum of the separatedirectional velocities? Also the text in the chapter seems tosuggest that the result is larger than the speed of light. Also ananswer would be helpful to check once I get started solving theproblem.

Another idea I had was to use physics I and angular speed and thedistance to find the speed of the light at the distance of themoon.

Explanation / Answer

From the earth, the spot of light would appear to be travelingfaster than the speed of light. . The moon is roughly 1.25 light seconds from earth (I alwaysremember that it takes 1.25 seconds for a radio transmission to getto the moon - it is the only way I can remember how far away itis). The circumference of its orbit is roughly c = 2 1.25 l-s c = 7.85 l-s . Since the rotation rate is 100Hz, the apparent speed of thedot would be v. = 7.85 c-s * 100 Hz v = 785 c Darn fast. . This is completely beyond the question. But at thisspeed, you would actually see two dots on the moon. You wouldfirst see the dot near the middle of the moon. It wouldimmediately break apart with one dot going in the direction ofrotaion of the laser and the other dot would go even faster in theother direction. This is caused by the radius of themoon. The center is closer to us than the edge so we wouldsee the center first. I worked out the mathmatics of thisonce.

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