A bicycle can be thought of as a simple machine. A lever is a rigid body pivoted on a fixed fulcrum. A seesaw is an example of a lever. On a seesaw, if a heavy person is at one end and a lighter person is at the other end, the heavy person can keep the lighter one suspended in the air. But, what happens if the heavier person moves closer to the center? Eventually, a point will be reached where the two people will balance each other. If the heavier person moves still closer, the lighter person can now keep the heavier one up in the air.
Levers use the principle that force times distance of the effort equals force times distance of the resistance. If a person applies a fifty pound force four feet from the fulcrum, he can move a two hundred pound weight which is one foot from the fulcrum.
Force times distance is also the formula for work. Work is the product of the force applied to an object by an outside agent and the distance through which the force acts on the object. It is important to remember distance. The lighter force must move through a greater distance. If you are using a crowbar to move a rock you may move one foot to move the rock one inch. The work remains the same. If the force increases the distance decreases, and vice versa.
A ten speed uses gears, where a gear can be thought of as a spinning lever. A gear is a wheel with projections on it called teeth. On a bicycle, these teeth are on the edge of the wheel. This type of gear is called a spur gear. When you talk about force when you are using gears, you talk about torque. Torque is a force that can produce rotation. Torque is equal to the distance from the point of application of the force to the center of rotation multiplied by the component of force perpendicular to this distance.
On a bicycle, the teeth are connected by the chain. The rider makes the front gears go around, which drives the chain, which turns the rear gears. The rear gears are fixed on the wheel. When the rear gears turn, the wheel turns. It is important to realize how the chain works. A link of chain fits over a tooth in a gear. A movement of one link in the chainwheel causes a movement of one link in the freewheel. With gears if torque increases then speed decreases.
My bicycle has a 40-50 combination of teeth on the chainwheel. Does this mean that I travel fifty inches for every revolution of the pedals? No, it means that one revolution of the pedals causes the chain to move fifty links. The distance I travel depends on how many teeth are on the gear in the back wheel. One of the sprockets on my freewheel has thirteen teeth. One revolution of the crank will turn my rear wheel 3.84 times. Since the diameter of my tires is twenty-seven inches, I will travel 84.78 inches.