Several bacteria, such as Escherichia coli and Salmonella typhimurium, are self-propelled using their flagella in a very particular way. We analyze the mechanics of this phenomenon, taking into account the geometry of these propellers. The dependence of the speed of the bacterium on the configuration of the flagellum is found in a simple way. By using similar artifices, we also describe the mechanics of the opposite effect, that is, the rotation acquired by a helix when it is towed through a fluid in the axial direction at low Reynolds number.

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