As a bicycle shop, we get that same question from customers quite often: "Why do bicycles have gears?" or "What are gears used for?"
We have decided to come up with a long version of the answer as well as a short version. Before we start with the long answer, let us define some terms, and that is the 3 stages of riding a bicycle.
Coming back to the main topic - why do bikes have gears? Remember that torque is required for starting the bicycle from rest? At low gear, the bike will be able to convert most of the the cyclist's pedaling effort into torque, which gets the bike moving. At the same time, very little speed is achieved, but that is not a problem at all: we need to get the bike moving first so and we will worry about going fast later (albeit only for a few seconds)
If, at this point, the gear is raised (or commonly known as "change to higher gear"), a small percentage of the same pedaling effort is now not used in generating torque but used in generating speed instead. The result is that the bike goes faster and faster. When the bike is moving sufficiently fast, miraculously, the need for torque becomes zero, or is no longer required; At the highest gear, your pedaling effort is completely (well, almost) converted to speed and that is how you reach your cruising cadence.
So here is the short answer: When the bike is at zero or low speed, low gear is necessary so that your pedaling effort is converted to torque, which starts the bike moving. After the bike has started moving, high gear is necessary to convert your pedaling effort into speed, which makes the bike move faster. The lower the gear, more torque. The higher the gear, more speed. Anything in between - a mix of some torque and some speed.
How about riding a bike that has a fixed gear (commonly known as "fixies" or mistakenly known as "no gear")? It is possible to ride a bike with only a single gear (and that gear is usually the highest gear). As you might have imagined, there will be no "low gear" to help the cyclist convert that cycling effort into torque and therefore it is pretty hard (double or even triple the usual strength) to get a fixie to start moving or to accelerate. After the huff and puff and the fixie has gained sufficient speed, most pedaling effort is then converted into speed (due to the high gear that is present) and therefore fixes can usually maintain the same high speed with most other bikes.
Tip: Riding up a steep slope requires low gears as well. Since there is a downwards gravitational force that is pulling the cyclist back, a low gear is necessary to convert as much pedaling effort as possible to keep the bike moving. Speed is not the crucial factor when climbing steep slopes.
Now you may ask questions along the line of "Why do low gears generate more torque and less speed?" or "Why do high gears generate more speed and less torque?". This is akin to asking "Why does sugar taste sweet?" We may need to refer you to some physicist or chemist..
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