# Understanding Gears & Machines: Force & Distance

• Jimmy87
In summary: Thanks Haruspex! The makes a lot of sense. The only thing that now confuses me is when people explain how this applies to bicycles. You have just confirmed that the linear distance must be the same on the two gears but the angular distance is more for the smaller gear. When people explain how low and high gears work they compare the LINEAR distance of the wheel (using its radius) to the LINEAR distance of the pedal. So if the wheel does 4 rotations for every one rotation of the pedal (small driving gear at the pedals and large driven gear at the back) the wheel covers more linear/circumference distance than the pedal. Why does linear distance work in this case but not in the example in the original
Jimmy87

## Homework Statement

I am really struggling to understand gears and how they can multiply force or speed. I was reading over this physics link (http://www.tutorvista.com/content/physics/physics-i/power-energy-machines/gears.php).

## The Attempt at a Solution

I'm confused about the whole "force x distance" idea. In this link it says cog A rotates twice for every turn of cog B so must be moving faster which I get. However it then talks about cog A moving twice the distance and so experiences half the force. My line of thinking is that the circumference is smaller on the smaller cog so although it is moving faster it is still covering the same distance as the larger cog in terms of circumference so then wouldn't the forces have to be the same? I thought the forces would be the same anyway because of Newton's 3rd law. Wouldn't a tooth of cog A exert a force on a tooth of cog B and cog B exert and equal and opposite force back on cog A?

Jimmy87 said:

## Homework Statement

I am really struggling to understand gears and how they can multiply force or speed. I was reading over this physics link (http://www.tutorvista.com/content/physics/physics-i/power-energy-machines/gears.php).

## The Attempt at a Solution

I'm confused about the whole "force x distance" idea. In this link it says cog A rotates twice for every turn of cog B so must be moving faster which I get. However it then talks about cog A moving twice the distance and so experiences half the force. My line of thinking is that the circumference is smaller on the smaller cog so although it is moving faster it is still covering the same distance as the larger cog in terms of circumference so then wouldn't the forces have to be the same? I thought the forces would be the same anyway because of Newton's 3rd law. Wouldn't a tooth of cog A exert a force on a tooth of cog B and cog B exert and equal and opposite force back on cog A?

I am not surprised the text at that link confuses you. It is nonsense.
Yes, the distances moved are the same, and the forces the gears exert on each other are the same (simple action and reaction).
The article should be discussing torque, not force. The purpose of meshing two gears of different sizes is to increase or decrease the torque.

Instead of force x distance it should look at torque x angular distance (which also equals work done).
Since the linear distance the gears move is the same, the gear with the greater radius rotates through a smaller angle, so experiences the greater torque.

Jimmy87
haruspex said:
I am not surprised the text at that link confuses you. It is nonsense.
Yes, the distances moved are the same, and the forces the gears exert on each other are the same (simple action and reaction).
The article should be discussing torque, not force. The purpose of meshing two gears of different sizes is to increase or decrease the torque.

Instead of force x distance it should look at torque x angular distance (which also equals work done).
Since the linear distance the gears move is the same, the gear with the greater radius rotates through a smaller angle, so experiences the greater torque.

Thanks Haruspex! The makes a lot of sense. The only thing that now confuses me is when people explain how this applies to bicycles. You have just confirmed that the linear distance must be the same on the two gears but the angular distance is more for the smaller gear. When people explain how low and high gears work they compare the LINEAR distance of the wheel (using its radius) to the LINEAR distance of the pedal. So if the wheel does 4 rotations for every one rotation of the pedal (small driving gear at the pedals and large driven gear at the back) the wheel covers more linear/circumference distance than the pedal. Why does linear distance work in this case but not in the example in the original post? In this second bicycle example can we now use "force x distance" to say when the wheel covers more linear distance there would be less force from wheel on the road and vice versa there would be more force required at the pedals and less linear distance?

Jimmy87 said:
Why does linear distance work in this case but not in the example in the original post?
Gears are connected in either of two ways: by meshing teeth (or, equivalently, sharing a chain that meshes with teeth on both), or by sharing an axle. In the former case, the linear distances are the same but the angular distances are different. In the latter case, the angles are the same and the linear distances differ. A gear train works by alternating the two cases. Going from the pedals to the wheel involves both.

Jimmy87 and jbriggs444
haruspex said:
Gears are connected in either of two ways: by meshing teeth (or, equivalently, sharing a chain that meshes with teeth on both), or by sharing an axle. In the former case, the linear distances are the same but the angular distances are different. In the latter case, the angles are the same and the linear distances differ. A gear train works by alternating the two cases. Going from the pedals to the wheel involves both.

Thanks again. After reading around more I am getting more and more worried. My textbook says the exact same thing as the website if I am understanding everything you have said. I took a picture of the start of the gears section from my textbook and attached it and would really appreciate it if you could quickly see if it is correct. It clearly shows two interlocking gears in figure 4 and that the larger gear with twice the diameter has twice the FORCE but shouldn't this be twice the torque and the SAME force for an interlocking gear? This is supposed to be the official textbook for our course! I am worried now what to do. Do I learn it the incorrect way?

Many thanks again!

#### Attachments

• Gears - Textbook.docx
419.9 KB · Views: 196
Jimmy87 said:
Thanks again. After reading around more I am getting more and more worried. My textbook says the exact same thing as the website if I am understanding everything you have said. I took a picture of the start of the gears section from my textbook and attached it and would really appreciate it if you could quickly see if it is correct. It clearly shows two interlocking gears in figure 4 and that the larger gear with twice the diameter has twice the FORCE but shouldn't this be twice the torque and the SAME force for an interlocking gear? This is supposed to be the official textbook for our course! I am worried now what to do. Do I learn it the incorrect way?

Many thanks again!
You are right, this textbook commits the same blunder.
What textbook is it?

Jimmy87
haruspex said:
Thanks for the link. I have written to OUP.

Thanks, hopefully it won't be in the exam just a textbook mistake. Although on the exam website it does say under that module "students should understand how ratios can enable gears and levers to work as force multipliers" so looks like could be on the exam like that as well. :(

Thanks for all your help haruspex ! :)

Thanks for posting this as my kids are also doing GCSE physics next year. I best check which exam board they are using to see if it's the same.

## 1. What are gears and how do they work?

Gears are mechanical components that consist of toothed wheels that mesh with one another to transmit force and motion. They work by transferring rotational motion from one shaft to another, often changing the speed and direction of the rotation.

## 2. How does the force applied to gears affect their motion?

The force applied to gears determines the amount of torque that is produced. Torque is the force that causes an object to rotate around an axis, and it is directly proportional to the force applied and the distance from the axis of rotation.

## 3. How does the distance between gears affect their performance?

The distance between gears, also known as the gear ratio, determines the speed and torque of the output gear. A smaller gear ratio results in a higher speed and lower torque, while a larger gear ratio results in a lower speed and higher torque.

## 4. What are some common applications of gears?

Gears are used in a wide range of machines and devices, including cars, bicycles, clocks, and industrial machinery. They are also commonly used in manufacturing processes, such as in gear cutting and gear hobbing.

## 5. How do gears and machines relate to the concept of work and energy?

Gears and machines are essential in the concept of work and energy as they allow us to efficiently transfer and transform energy. By using gears, we can increase or decrease the force and distance involved in doing work, making it easier to complete tasks and conserve energy.

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