Ok I will show you how I tackle these. Once you get the hang of it, my way is really easy.
First make a list of all the rates you know that are relevant.
\(\frac{6.2 radians}{1 sec},\qquad\frac{60sec}{1min},\qquad \frac{2\pi radians}{1 revolution},\qquad \frac{1.6minutes}{1}\\ ~\\find\qquad \frac{?revolutions}{1}\\\)
Since the first 3 of these fractions have units top and bottom they can be turned upside down.
So, for example, it is correct to say 1sec/6.2 radians
You can only turn a fraction upside down if there are units both top and bottom!
Now I want to end up with revolutions on the top and I want all the other units to cancel out.
So I start with revolutions on the top and then I keep multiplying by the correct thing to cancel out the units on the bottom.
like this:
\(\frac{1 revolution}{2\pi radians}\times \frac{6.2 radians}{1 sec}\times \frac{60sec}{1min}\times \frac{1.6minutes}{1}\\ \\~\\ =\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\ =\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\ =94.7\;\;revolutions.\)
Coding:
\frac{1 revolution}{2\pi radians}\times \frac{6.2 radians}{1 sec}\times \frac{60sec}{1min}\times \frac{1.6minutes}{1}\\
\\~\\
=\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\
=\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\
=94.7\;\;revolutions.
+118727 
