# Finding revolution of different sized wheels

• slambert56
In summary, the correct number of revolutions for the small wheel of a penny farthing bicycle is 974, which can be obtained by dividing the big wheel radius by the small wheel radius and multiplying by the number of revolutions of the big wheel. The formula used is s=rθ, where s is the distance traveled, r is the radius, and θ is the angle in radians. However, in this case, the mistake was made of not multiplying by 2π to convert from radians to revolutions, resulting in the initial incorrect answer of 9614 revolutions. Once this mistake was corrected, the correct answer of 974 revolutions was obtained.

#### slambert56

Ok the answer in the back of my book says 974 revolutions and a very short hand way to get that is divide the big wheel radius by the small wheel radius to get 3.53 so i can just multiply 3.53 times the 276 rev to get 974 rev. But I tried a long way using the s=rtheta formula b/c on a test I probably can't get all points without using a formula. I got a different answer and I don't know why. Any help would be greatly appreciated!

Here is the question and my work is in the picture.
A penny farthing bicycle(has a large front wheel and a small rear wheel). On a sunday ride teh front wheel(r=1.20m) makes 276 revolutions. How many revolutions does the rear wheel(r=.340m) make?
Okay so I simply use the formula s=r times theta. I know to use this formula I have to have radians and I converted and then at the end convert back to revolutions. i rev=2pie radians.

Now I first found the total distance traveled by the big wheel by finding s which is the distance and this is the same for the small wheel so i just plugged it in. Am I missing something?? THANKS.
http://img94.imageshack.us/img94/7942/002oek.jpg [Broken]

Last edited by a moderator:
You should post this in the homework section.
How did you get that 6120 divided by 2π is 9614? What value of π are you using?

I just divided 6120 by 2pie just to convert radians into revolutions. 1 rev= 2 pie radian

My question was about your numbers. How much is 6120 divided by 2π?

ahhhhh okay when i typed it into my calculator as (2pie) and it didnt multiply apparently. Its 974. Thanks for catching my dumb mistake. I thought it would automatically multiply but I have to put in the sign. :yuck:

## 1. How do you find the revolution of a wheel?

To find the revolution of a wheel, you first need to know the circumference of the wheel. Then, you can calculate the number of revolutions by dividing the distance traveled by the circumference of the wheel.

## 2. Can you use the same formula for all sized wheels?

Yes, the formula for finding the revolution of a wheel can be used for all sized wheels as long as the circumference is known. However, the distance traveled will vary depending on the size of the wheel.

## 3. Is the revolution of a wheel affected by its size?

Yes, the size of the wheel does affect its revolution. A larger wheel will cover more distance in one revolution compared to a smaller wheel.

## 4. What other factors can affect the revolution of a wheel?

In addition to size, other factors that can affect the revolution of a wheel include the surface it is rolling on, the weight placed on the wheel, and any friction or resistance present.

## 5. How can the revolution of a wheel be measured accurately?

The revolution of a wheel can be measured accurately by using a revolution counter or by marking the starting and ending points of the wheel's rotation and counting the number of revolutions in between.