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The speed of the rod is proportional to the number of teeth on the cog and that which is driving the cog. If the driver remains the same then in order for the driver and the cog to mate one typically needs to reduce the number of teeth on the cog when it is made smaller. Thus the ratio of the teeth on the driver to that on the cog is increased as will its speed.

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Q: Would a rod being turned by a cog go faster if the cog turning the rod was smaller or bigger?
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