Consider a searchlight on the ground that casts a spot on a cloud (1000 mathrm{~m}) overhead. If

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Consider a searchlight on the ground that casts a spot on a cloud \(1000 \mathrm{~m}\) overhead. If the searchlight is rotated rapidly-say, \(30^{\circ}\) in \(1 \mu \mathrm{s}\)-how fast does the spot move in the Earth reference frame? Is this a violation of special relativity?

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