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A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is internal. Gear $1$, gear $3$ and arm $OP$ are pivoted to the ground at $O$. Gear $2$ is carried on the arm $OP$ via the pivot joint at $P$, and is in mesh with the other two gears. Gear $2$ has $20$ teeth and gear $3$ has $80$ teeth. If gear $1$ is kept fixed at $0\:\text{rpm}$ and gear $3$ rotates at $900\:\text{rpm}$ counter clockwise $\text{(ccw)}$, the magnitude of angular velocity of arm $OP$ is _____________________ $\text{rpm}$ (in integer)

 

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