Calculate the radius of this rotating wheel

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Homework Help Overview

The discussion revolves around calculating the radius of a rotating wheel, where the linear speeds of two points on the wheel are compared. The original poster states that one point's speed is 2.5 times that of another point, which is positioned 5 cm closer to the center of the wheel.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationships between the linear speeds and distances of the points on the wheel, with attempts to set up equations based on these relationships. Questions arise regarding the validity of the equations used and the methods of solving them.

Discussion Status

Participants are engaged in checking each other's calculations and reasoning. Some guidance has been offered regarding the correctness of the equations and the values derived from them, but there is no explicit consensus on the best approach to analyze the problem.

Contextual Notes

There is a mention of using Cramer’s rule for solving the equations, and some participants express uncertainty about their calculations and the assumptions made in setting up the problem.

MisterP
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Homework Statement


Calculate radius of rotating wheel. Linear speed of point "a" (red dot) is 2.5 times faster than linear speed of point "b"(blue dot) that is 5cm closer to center of wheel. Right answer is 8.33cm. I drew a sketch without linear line.
rotating-wheel.sized.jpg


Homework Equations

The Attempt at a Solution


So, I tried to make this equation system consisting 2 equations..
a - b = 5
a - 2.5b = 0

I used Cramer`s rule to solve this.
wheelrotationab.sized.jpg
 

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As for the rotating wheel angular speed is constant at all points, use 2.5v/r=v/(r-5).Answer obtained is 8.333334
 
But the way I calculated is not right?
 
How did you get the second equation??
 
Dunno, just felt like that :D
 
You have done something wrong , the solution you calculated ##a=5,b=3.33## does not satisfy the first equation which is ##a-b=5##. It doesn't satisfy the second equation too which is ##a-2.5b=0##. Check again your work for calculating a, it should be ##a=8.333## the value for b seems correct to me.
 
So, what is the best solution? I cannot get through..
 
The solution is ##a=8.33,b=3.33##. You have made a mistake in calculating ##\nabla_a##,this determinant is equal to 12.5 and not 7.5
 
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Yes :) Thank You
 
  • #10
MisterP said:
So, what is the best solution? I cannot get through..
Your question should not be "what is the best solution?" Your question should be "what is the correct way to analyze this problem?"
 

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