B Calculating Rod Speeds with Algebraic Formulas

[demackison]

I am trying to create a formula for a spreadsheet to calculate values and it has been thirty years since high school algebra. Here are the formulas I need to rearrange.

w=(d/r)/t
v=d/t

w is an unknown constant and I have values for v₁ and r₁
I need the formula to spit out v₂ if I input r₂ in the spreadsheet

 

[fresh_42]

it has been thirty years since high school algebra.

We normally don't give away ready made answers, but in this (very simple) case I'll make an exception, as it seems, that a tutorial on how to deal with quotients might not be appropriate in your case. But in general please use our homework section for these kind of questions, the automatically inserted template and especially tell us, what you don't understand, i.e. where you got stuck and why.

$w=(d/r)/t = \dfrac{\frac{d}{r}}{\frac{t}{1}}=\dfrac{d}{r} \cdot \dfrac{1}{t}= \dfrac{d}{r\cdot t}=\dfrac{d}{t} \cdot \dfrac{1}{r}=\dfrac{v}{r}$.

So if $\dfrac{v_1}{r_1}=w= \dfrac{v_2}{r_2}$ then $v_2= \dfrac{v_1}{r_1}\cdot r_2 = \dfrac{v_1 \cdot r_2}{r_1}$.

 

[demackison]

Thanks!

 

[demackison]

Thanks!

I had converted to d/r * t/1, in error.

 

[fresh_42]

Thanks!

Only if $\frac{d_1}{r_1}=\frac{d_2}{r_2}$ but you haven't explained anything about the assumptions which are allowed or not, especially nothing about $d$. That's why I said: If $\frac{v_1}{r_1}=\frac{v_2}{r_2}$. I cannot know.

 

[demackison]

The formula was for a rod swinging around an axis with the speed of one end of the rod known. In essence, the spreadsheet will show what various longer or shorter rods will do to the speed at the other end.

Don't worry, this will be checked by an actual engineer before anything is implemented. :)