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A gearbox changes the relationship between engine speed and wheel speed. Follow the gear ratio to see where the extra turning force comes from.
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For a simple gear pair, tooth counts determine the speed ratio. A small driving gear turning a larger driven gear reduces output speed and increases available output torque. In an ideal lossless pair, the torque increase matches the speed reduction; a real gearbox loses some power through friction and other losses.
A lower car gear provides a larger reduction ratio. For the same engine torque, this gives more torque at the driven wheels, with the final-drive ratio also contributing. At the same road speed, the engine turns faster in the lower gear. Actual acceleration also depends on engine output at that speed, grip and vehicle load.
No. They exchange rotational speed for torque. Real gears also dissipate some input power.
With the clutch fully engaged at the same road speed, a larger reduction ratio requires more engine revolutions for each wheel revolution.
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