Finding revolution of different sized wheels

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Discussion Overview

The discussion revolves around a problem involving the calculation of the number of revolutions made by the rear wheel of a penny farthing bicycle, given the number of revolutions of the front wheel and their respective radii. Participants explore different methods for solving the problem, including a shortcut and a more detailed approach using the formula s = rθ.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a shortcut method to find the number of revolutions by using the ratio of the radii of the wheels and multiplying it by the number of revolutions of the front wheel.
  • The same participant attempts a more detailed calculation using the formula s = rθ, converting revolutions to radians and back, but encounters a discrepancy in their answer.
  • Another participant questions the calculation of a specific division, prompting a clarification about the use of π in the conversion from radians to revolutions.
  • A later reply reveals that a calculation error occurred due to a misunderstanding of how to input the multiplication in a calculator.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method used, but there is agreement on the final corrected answer of 974 revolutions after addressing the calculation error.

Contextual Notes

There are indications of confusion regarding calculator input and the conversion process between radians and revolutions, which may affect the understanding of the problem-solving approach.

Who May Find This Useful

This discussion may be useful for students working on similar physics problems involving rotational motion and conversions between different units of measurement.

slambert56
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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 the 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.
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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.
 

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