Talk:Radian per second

Untitled 1

The following equation is not correct

2π rad/s = 1 Hz

it says that an angular velocity is equal to an ordinary frequency, which is a wrong way to put it ($\omega =\nu$). Instead one should say that an angular frequency of 2π rad/s corresponds to an ordinary frequency of 1 Hz. The same goes for the equation

1 rad/s = 1/2π Hz

Say we have an angular frequency $\omega =2\pi \ rad/s$. Then we can calculate the ordinary frequency:

$\nu (Hz)={\frac {\omega (rad/s)}{2\pi }}={\frac {2\pi }{2\pi }}\ Hz=1\ Hz$

i.e. we insert the bare value of the angular velocity in the relation between the the ordinary frequency and the angular velocity, and the output is in Hz. Another way to write the same is:

$\nu ={\frac {\omega }{2\pi }}\cdot {\frac {Hz}{rad/s}}={\frac {2\pi \ rad/s}{2\pi }}\cdot {\frac {Hz}{rad/s}}=1\ Hz$

where the units rad/s and Hz are used explicitly in the formula. 2.110.114.86 (talk) 22:33, 15 May 2015 (UTC)