A turntable that turns 7 revolutions each second is located on top of a mountain. Mounted on the turntable is a laser that emits a bright beam of light. As the turntable and laser rotate, the beam also rotates and sweeps across the sky. On a dark night, the beam reaches some clouds 10 km away.
(a) How fast does the spot of laser light sweep across the clouds?
km/s
(b) How fast does the spot of laser light sweep across clouds that are 20 km away?
km/s
(c) At what distance will the laser beam sweep across the sky at the speed of light (the speed of light is 300,000 km/s)? (In Chapter 15 we will learn that no material can travel at the speed of light; here we have a nonmaterial spot. Not only can it travel at the speed of light, at greater radial distances the nonmaterial spot can travel faster than the speed of light!)
km
c) In Euclidian space, the beam remains straight and r = V/ω = 300000/14π = 6821 km.
In reality, the coherent beam will severely distort as the distance approaches 6821 km and may not be recognizable as light at all.
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