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One thing that helped me intuit the “sidereal” result (4) was to consider what happens as the radius of circle B approaches 0. At least in my mind, it seems pretty clear that A has to undergo at least one rotation.
That said, I am unsure that I would have caught this as a test-taker. Derek’s videos always have some “trick”, putting me on guard, but in a testing scenario I would have seen the answer for 3 with no answer for 4, marked it down, and moved on quickly.
One thing that helped me intuit the “sidereal” result (4) was to consider what happens as the radius of circle B approaches 0. At least in my mind, it seems pretty clear that A has to undergo at least one rotation.
That said, I am unsure that I would have caught this as a test-taker. Derek’s videos always have some “trick”, putting me on guard, but in a testing scenario I would have seen the answer for 3 with no answer for 4, marked it down, and moved on quickly.