The Cassette

Cassette Diagram

The cassette is the most important piece of hardware on the bike, save the derailleur. It is responsible for the gear ratios that make you move.
In this page, I'll talk about the wheel ratios, the next will tackle gear ratios.
93N are applied to the cassette, causing it to spin on the hub in the center. This makes the whole wheel spin as well.
The gear the cassette is on has a .04m radius and 27 teeth.
The wheel is a 27.5 inch wheel which means the diameter is .70m.
That gives a ratio of wheel to gear of about 4:35, which means that every inch the cassette moves, the tires move 8.75 inches.
This means that you get a lot more travel for the rotation you make.
It also mean the about 8.75 times more force is being applied to the ground than the cassette, giving you the ability to go faster than in wider gears
There is another reason why bigger gears are slower and easier to turn...