Calculate the radius of this rotating wheel

[MisterP]

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.

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.

 

[Orion73]

As for the rotating wheel angular speed is constant at all points, use 2.5v/r=v/(r-5).Answer obtained is 8.333334

 

[MisterP]

But the way I calculated is not right?

 

[Orion73]

How did you get the second equation??

 

[MisterP]

Dunno, just felt like that :D

 

[Delta2]

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.

 

[MisterP]

So, what is the best solution? I cannot get through..

 

[Delta2]

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

 

[MisterP]

Yes :) Thank You

 

[Chestermiller]

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?"