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Problem Posts |  |
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QUESTION
(Original) Three identical cylindrical barrels with radius $\sqrt{3}$ are placed tangent to each other (represented by circles $c_{1}$ , $c_{2}$ , $c_{3}$ .) A metal sheet $AB$ is placed just touching $c_{1}$ and $c_{3}$. A coin $c$ with radius $2-\sqrt{3}$ is placed on the floor tangent to $c_{2}$ and $c_{3}$ (see the diagram), and rolled without slipping about the barrels (so that the coin is rotating clockwise), going through plank $AB$, until it returns to its starting point. How many radians has the coin rotated? (For example, half a turn is $\pi$ .)
(Original) Three identical cylindrical barrels with radius $\sqrt{3}$ are placed tangent to each other (represented by circles $c_{1}$ , $c_{2}$ , $c_{3}$ .) A metal sheet $AB$ is placed just touching $c_{1}$ and $c_{3}$. A coin $c$ with radius $2-\sqrt{3}$ is placed on the floor tangent to $c_{2}$ and $c_{3}$ (see the diagram), and rolled without slipping about the barrels (so that the coin is rotating clockwise), going through plank $AB$, until it returns to its starting point. How many radians has the coin rotated? (For example, half a turn is $\pi$ .)
Separate the coin's rotation into two 'components'.
