How does one moving slowly cause the others to go faster and faster?
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A wheel converts rotation at its axle into linear motion at a point along its circumference (the distance around the outside of a circle).
A bigger wheel has a greater circumference than a smaller wheel.
Gears are wheels whose edges touch. As gears turn, adjacent edges pass the point of contact at the same speed. The circumference of the smaller wheel is shorter, so a particular tooth it will come around to the point of contact again sooner than the corresponding tooth on the bigger gear.
Every time a particular tooth passes the point of contact, the gear has turned another full revolution. So the bigger gear (which has a larger circumference and more teeth) takes longer to compete a full revolution than a smaller gear with fewer teeth.
Gears have teeth to keep their relative rotation in perfect aligmment and to transfer torque from one gear to the next.
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