# How do the units for angular velocity come out of $\omega = \sqrt{k/m}$?

I'm confused about an exercise of a book. I understand that the units for angular velocity is $\text{rad/s}$; but I don't understand, how can I get it from the relation $\omega=\sqrt{k/m}$.

Solving this equation: $\omega^2=(10^4\text{ N/m})/50\text{ kg}$. From this, I get these units:

• For $\mathrm{N}$: $\mathrm{kg\ s^2/m}$,

• $1/\mathrm{m}$, and

• $1/\mathrm{kg}$

So, I get, $\mathrm{s^2/m^2}$.

Can you help me to realize what can I do?

A Newton is 1 ${\rm kg\cdot \rm m/s^2}$, not 1 ${\rm kg\cdot s^2/m}$. Also, you need to take the square root at the end.