Question

In a rotating body, \[\alpha = \alpha r\text{ and }\nu = \omega r.\] 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.