Question

In a rotating body, $\alpha =\alpha r\mathrm{and}\nu =\omega r$. Thus $\frac{\alpha }{\alpha }=\frac{\nu }{\omega }$ . Can you use the theorems of ration and proportion studied in algebra so as to write

$\frac{\alpha +\alpha }{\alpha -\alpha }=\frac{\nu +\omega }{\nu -\omega }$

Answer 1

No, we cannot use componendo-dividendo theorem of proportion here. This is because $\alpha$ and a, and v and $\omega$ are dimensionally different. Therefore, ​v + $\omega$ and/or ​$\alpha$ + a are not possible.