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MATHS
Asked by Diana

In an arrangement of stacked gears used to slow down a fast-moving motor whilst increasing the torque, the second large gear rotated once every 9 seconds, calculate how long it takes the other gears to rotate?

For this question you need to know that power is always conserved for highly efficient gears. A consequence of this means that the ratio of the speeds of two gears is equal to inverse of the ratio of the two diameters of the gears or the inverse of the number of teeth. That is to say if we have two gears, 1 and 2 and we have gear 1 with 50 teeth and gear 2 with 5 teeth, Teeth(1)/Teeth(2) = 10 = Speed(2)/Speed(1). Therefore gear 2 is travelling 10 times more quickly than gear 1. For your question you need to convert 9 times per second into radians per second, (x2pi) and then look at either the number of teeth on your gears or the diameter of your gears to solve.

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Cameron Brown
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