Why do different gear ratios give different torque? Why isn’t it the faster a wheel goes the more torque it has?
In: Engineering
The physical setup should be self-explanatory. If one gear has 24 teeth and another gear has 12 teeth (of the same size), the turning the 24-gear once will turn the 12-gear twice, just because of the size difference.
Now, think about the energy you use to turn the gears, or work. The work you put in, minus the losses to friction, will be equal to the work that comes out; this is the conservation of energy. Work is also equal to the integral of force over distance; more simplified, work is equal to force multiplied by the distance this force is applied.
So if you are putting work into turning the 24-gear and the 12-gear is turning twice as fast, the work has to balance out. In order for the work to balance out, the force exerted by the 12-gear must be half of the force you’re exerting on the 24-gear. F/2 x 2D = F x D. And the same is true the other way. Each turn of the 12-gear moves the 24-gear half as far, so it must exert a force twice as large in order for the work to balance. 2F x D/2 = F x D. Torque is just rotational force.
So the gear that spins faster must produce more torque, and the gear that spins slower must product more torque.
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