When You Shift to an Easier Gear on a Hill, You’re Doing Physics! The Bicycle and the Principle of Work
Ken Kuwako, Science Trainer. Every Day is an Experiment.
You’re panting, struggling up a steep hill. Just as you think, “I can’t do this anymore…,” you click the left-hand lever. Click! Suddenly, the desperate, heavy drag on the pedal disappears like magic! Many of you have probably been saved by this “magic,” right?But have you ever stopped to wonder? The pedaling became super light, yet now you have to pedal an awful lot just to move forward. Conversely, on a flat road, when you switch to a “heavy gear,” the pedals feel heavy, but a single push sends you zooming ahead.This difference isn’t just a feeling; it can be perfectly explained by a major rule of physics hidden in our daily lives: The Principle of Work. In this article, we’ll unlock the scientific secret hidden inside your bicycle’s gear-shifting mechanism.
What is “Work” in the World of Science?
First, let’s clarify the physics definition of “Work.” It’s a bit different from “working at the office.” In the realm of science, “Work” is a quantity calculated by: Force applied to an object $\times$ Distance moved in the direction of the force.For example, the act of “moving your bicycle (and yourself) from Point A to Point B up a hill” is exactly what qualifies as physical “Work.” And here’s the crucial part: The total amount of “Work” required to move from Point A to Point B remains the same, no matter what method you use.
No Cheating Allowed! The Universal Rule of the Principle of Work
This is where the Principle of Work comes in.
[The Principle of Work]The total amount of work required ($\text{Force} \times \text{Distance}$) remains the same, whether you use a tool or not. A tool is simply a “trade-off machine” that reduces the “Force” required in exchange for increasing the “Distance” moved, or vice versa.
You might be thinking, “Wait, aren’t tools supposed to make things easier?” That’s right—tools make things easier, but they don’t let you cheat physics.
Your bicycle’s gear-shifting mechanism (derailleur) is exactly this kind of “tool.” The necessary “Work” (getting up the hill) is fixed. The gears simply trade off your input between “Force” and “Distance” to complete that work.
| Gear State | Required “Force” (Heaviness on the Pedal) | “Distance” Pedaled (Number of Revolutions) | The Work Trade-Off |
|---|---|---|---|
| Easy Gear (Gear 1) | Small (Easy!) | Long (Lots of pedaling) | Trade “Force” for ease and “Distance” for effort |
| Hard Gear | Large (Heavy!) | Short (Fewer revolutions needed) | Trade “Distance” for ease and “Force” for effort |
The Truth About the Easy Gear: Saving Force by Earning Distance
So, why does the “easy gear” save us on those brutal hills? Climbing a steep incline requires much greater “Force” than riding on a flat surface (because you are fighting gravity). It would be impossible to push the pedals using the same “heavy gear” you use on flat ground.When you choose the “easy gear” in this situation, you are, from a physics standpoint, declaring…”I will reduce the ‘Force’ (heaviness) needed to push the pedal, in exchange for increasing the ‘Distance’ (number of revolutions) I have to pedal!”This is a brilliant, principle-of-work-based trade-off!The result is:
- Since you can reduce the force, you can actually push the pedal (it feels easier), even on a hill.
- In exchange, the distance (revolutions) is increased, so you have to pedal a lot (and you don’t move far per pedal stroke).
This is how it works.
How Gears Work: Tire Revolutions Per Pedal Stroke
How exactly does this “Force and Distance trade-off” take place? The secret lies in the gear ratio—the size difference between the front gear (chainring) attached to the pedals and the rear gear (sprocket) attached to the wheel.
- Easy Gear (for hills)
- The front gear (pedal side) is small, and
- The rear gear (wheel side) is large.
- With this combination, one full pedal revolution only turns the rear wheel a small amount (e.g., 0.8 revolutions).
- That’s why you don’t travel far per pedal stroke. But because you are only turning the wheel a “small” amount, the required “Force” is also small.
- Hard Gear (for speed)
- The front gear (pedal side) is large, and
- The rear gear (wheel side) is small.
- With this combination, one full pedal revolution turns the rear wheel a large amount (e.g., 3 revolutions).
- That’s why you zoom ahead with one pedal stroke. But in exchange for turning the wheel a “large” amount, a greater “Force” is required.
The derailleur is a marvelous invention that cleverly converts the “Force” and “Distance” we input through a combination of cogs, assisting us to achieve the necessary “Work” to reach our destination.
You’ve Been Mastering the Laws of Physics!
When you click your bicycle gear lever, you are unconsciously mastering the Principle of Work—choosing the optimal balance between the “Force” and “Distance” required at that exact moment. Choosing an easy gear on a hill wasn’t just a feeling; it was a highly scientific choice to conserve energy and smartly accomplish your “Work”! Doesn’t it change how you view your usual commute when you realize that science is hidden in something so commonplace?
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