Rearranging angular velocity equation to make $T$ the subject I want to rearrange the formula for angular velocity $\omega = \dfrac{2\pi}{T}$, to make $T$ the subject as I wish to find the period.
Would the correct answer be $T = \frac{\omega}{2\pi}$ or would it be $T = \frac{2\pi}{\omega}$? 
And is there a certain rule you should follow when rearranging ?
 A: From 
$$
\frac{a}{b}=\frac{c}{d} \tag1
$$ by multiplying out $(1)$ by $bd$ one gets
$$
ad=bc\tag2
$$ by dividing $(2)$ by $cd$ one gets
$$
\frac{a}{c}=\frac{b}{d}. \tag3
$$ Applying it to
$$
w=\frac{2\pi}{T}
$$ one gets
$$
T=\frac{2\pi}{w}.
$$
A: It is quite simple. You have $\omega = \dfrac{2\pi}{T}$ since you want to make T the subject, multiply the whole equation by T and you will get $$\omega{\cdot T} = \dfrac{2\pi}{T}{\cdot T} = 2\pi$$
On bringing ${\omega}$ on right you will have $T = \frac{2\pi}{\omega}$
A: Starting with $$\omega = \dfrac{2\pi}{T}$$ First multiply both sides by $T$:
$$\omega\color{red}{\cdot T} = \dfrac{2\pi}{T}\color{red}{\cdot T} = 2\pi$$
Divide both sides by $\omega$ to isolate $T$ on the left:
$$\color{red}{\frac{\color{black}{\omega T}}{\omega}} = \color{red}{\frac{\color{black}{2\pi}}{\omega}}$$
Which, after cancelling, leaves $$T = \frac{2\pi}{\omega}$$

You could also check your answer for dimensional correctness.
Consider the equation $T = \frac{\omega}{2\pi}$.  Assuming everything's in SI units, on the left the units are seconds and on the right the units are inverse seconds.  That couldn't be right.
Consider the equation $T = \frac{2\pi}{\omega}$.  On the left the units are seconds.  On the right, the units are 1 over inverse seconds.  I.e. seconds.  So this formula is at least correct dimensionally.
