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My answer to this after reading the question was 1, because by definition it is one revolution. So I thought that was trick, and the answer essentially is none

My answer to this after reading the question was 1, because by definition it is one revolution. So I thought that was trick, and the answer essentially is none of the above. But there is a lot more nuance here than just that with multiple definitions of revolution versus rotations, and sidereal time is where this answer can get weird.

HarHarVeryFunny 3y ago
The only ambiguity there would be revolution/rotation about what center - the small disk's own center or the center of the large one. It seems pretty obvious they are expecting you to calculate something, so assuming this is a trick question and the answer is 1 would seem a risky interpretation, and anyways wasn't one of the answer options.
- matt-attack 3y ago
  But isn’t that precisely the distinction between rotation and revolution already provides? When I first read it I thought, well they used the word revolution so clearly the answer is 1. If they had stated “rotations” then the answer is obviously 4. It’s pretty ridiculous they couldn’t use the right word when the distinction was taught back it elementary school during the discussion of the motion of the earth.
  - HarHarVeryFunny 3y ago
    But why is it obviously 4 ? Is it equally obvious that if the small disk was rolling around the inside of the large disk then the answer would be 2 ? If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive. btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!
    - matt-attack 3y ago
      The way I think of it, is if the outer circle is just sliding with friction such that the same point of the little circle is in contact with the big circle, it would undergo a single full rotation. Or is you slid a box along the surface of the drum, it would naturally undergo a single rotation. So then when add in the "rolling", you get the 3.
wlonkly 3y ago
Well, it depends on which definition you use. If you consider the circles planets, then it's one revolution by the astronomical definition. If you consider them gears, then it's 4 revolutions by the mechanical definition.

HarHarVeryFunny 3y ago

The only ambiguity there would be revolution/rotation about what center - the small disk's own center or the center of the large one. It seems pretty obvious they are expecting you to calculate something, so assuming this is a trick question and the answer is 1 would seem a risky interpretation, and anyways wasn't one of the answer options.

matt-attack 3y ago
But isn’t that precisely the distinction between rotation and revolution already provides? When I first read it I thought, well they used the word revolution so clearly the answer is 1. If they had stated “rotations” then the answer is obviously 4. It’s pretty ridiculous they couldn’t use the right word when the distinction was taught back it elementary school during the discussion of the motion of the earth.
- HarHarVeryFunny 3y ago
  But why is it obviously 4 ? Is it equally obvious that if the small disk was rolling around the inside of the large disk then the answer would be 2 ? If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive. btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!
  - matt-attack 3y ago
    The way I think of it, is if the outer circle is just sliding with friction such that the same point of the little circle is in contact with the big circle, it would undergo a single full rotation. Or is you slid a box along the surface of the drum, it would naturally undergo a single rotation. So then when add in the "rolling", you get the 3.

wlonkly 3y ago

Well, it depends on which definition you use. If you consider the circles planets, then it's one revolution by the astronomical definition. If you consider them gears, then it's 4 revolutions by the mechanical definition.